U.S. patent application number 13/841304 was filed with the patent office on 2014-03-06 for system and method for refining coordinate-based three-dimensional images obtained from a three-dimensional measurement system.
This patent application is currently assigned to Digital Signal Corporation. The applicant listed for this patent is Digital Signal Corporation. Invention is credited to Richard L. Sebastian, ANATOLEY T. ZHELEZNYAK.
Application Number | 20140063189 13/841304 |
Document ID | / |
Family ID | 50184589 |
Filed Date | 2014-03-06 |
United States Patent
Application |
20140063189 |
Kind Code |
A1 |
ZHELEZNYAK; ANATOLEY T. ; et
al. |
March 6, 2014 |
System and Method for Refining Coordinate-Based Three-Dimensional
Images Obtained from a Three-Dimensional Measurement System
Abstract
A system uses range and Doppler velocity measurements from a
lidar system and images from a video system to estimate a six
degree-of-freedom trajectory of a target and generate a
three-dimensional image of the target. The system may refine the
three-dimensional image by reducing the stochastic components in
the transformation parameters between video frame times.
Inventors: |
ZHELEZNYAK; ANATOLEY T.;
(Great Falls, VA) ; Sebastian; Richard L.;
(Frederick, MD) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Digital Signal Corporation; |
|
|
US |
|
|
Assignee: |
Digital Signal Corporation
Alexandria
VA
|
Family ID: |
50184589 |
Appl. No.: |
13/841304 |
Filed: |
March 15, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61693969 |
Aug 28, 2012 |
|
|
|
Current U.S.
Class: |
348/46 |
Current CPC
Class: |
G06T 7/521 20170101;
G06T 2207/10044 20130101; G06T 2207/10016 20130101; G01S 17/89
20130101; G01S 17/86 20200101; G06T 7/55 20170101; G01S 17/34
20200101; G01S 17/58 20130101 |
Class at
Publication: |
348/46 |
International
Class: |
G01S 17/89 20060101
G01S017/89 |
Claims
1. A system for refining 3D images, the system comprising: a lidar
subsystem configured to direct at least two beams toward the
target, generate a first set of line scan 3D measurements for a
plurality of points on the target for a first beam of the at least
two beams, and generate a second set of overscan 3D measurements
for the plurality of points on the target for a second beam of the
at least two beams; a video subsystem configured to provide a set
of the video frames of the target; and a processor configured to:
receive, from the lidar subsystem, the line scan 3D measurements
and the set of overscan 3D measurements, receive, from the video
subsystem, the a set of the video frames of the target, determine,
at each frame time, a plurality of .DELTA.z offsets between pre
over-scan measurements and the line scan 3D measurements and post
over-scan measurements and the line scan 3D measurements, and
adjust a plurality of transformation parameters based on a least
square optimization.
2. A system for refining 3D images, the system comprising: a lidar
subsystem configured to direct at least two beams toward the
target, and generae a plurality of 3D measurements for a plurality
of points on the target for each beam of the at least two beams; a
video subsystem configured to provide the set of the video frames
of the target; and a processor configured to: receive, from the
lidar subsystem, the plurality of 3D measurements, receive, from
the video subsystem, the set of the video frames of the target,
transform each of the set of video frames to a next frame time and
a previous frame time to generate a set of transformed video
frames, compare a pixel intensity of the transformed video frames,
determine one or more video offsets between the transformed video
frames, and using the determined one or more offsets, determine
corrections to the transformation parameters based on the
multi-frame least square optimization.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority to U.S. Provisional Patent
Application No. 61/693,969, which was filed on Aug. 28, 2012, and
is incorporated herein by reference as if reproduced below in its
entirety.
FIELD OF THE INVENTION
[0002] The invention is generally related to combining lidar (i.e.,
laser radar) measurements and video images to generate three
dimensional images of targets, and more particularly, to refining
the three dimensional images of the targets.
BACKGROUND OF THE INVENTION
[0003] Various conventional systems attempt to merge lidar
measurements and video images to obtain three dimensional images of
targets. Typically, these conventional systems require some
pre-specified initial model of the target in order to combine lidar
measurements with the video image to form a three dimensional
image.
[0004] Unfortunately, the pre-specified initial model places
significant restraints on the ability of the systems to combine
lidar measurements with the video image and as a result, the three
dimensional image is seldom sufficient for purposes of identifying
the target.
[0005] Furthermore, these conventional systems typically are unable
to adequately account for motion of the target and hence often
require that the target remain substantially motionless during an
image capture period.
[0006] What is needed is an improved system and method for
capturing three dimensional images using lidar and video
measurements and refining the three dimensional images to account
for stochastic errors.
SUMMARY OF THE INVENTION
[0007] Various implementations of the invention combine
measurements generated by a a lidar system with images generated by
a video system to resolve a six degrees of freedom trajectory that
describes motion of a target. Once this trajectory is resolved, an
accurate three-dimensional image of the target may be generated. In
some implementations of the invention, the system may refine the 3D
image by reducing the stochastic components in the transformation
parameters (i.e., v.sub.x, v.sub.y, v.sub.z, .omega..sub.x,
.omega..sub.y and .omega..sub.z) between video frame times.
[0008] These implementations, their features and other aspects of
the invention are described in further detail below.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] FIG. 1 illustrates a combined lidar and video camera system
according to various implementations of the invention.
[0010] FIG. 2 illustrates a lidar (i.e., laser radar) according to
various implementations of the invention.
[0011] FIG. 3 illustrates a scan pattern for a lidar subsystem that
employs two lidar beams according to various implementations of the
invention.
[0012] FIG. 4 illustrates a scan pattern for a lidar subsystem that
employs four lidar beams according to various implementations of
the invention.
[0013] FIG. 5 illustrates a relationship between points acquired
from the lidar subsystem from separate beams at substantially the
same instance of time that may be used to estimate an x-component
of angular velocity of a target according to various
implementations of the invention.
[0014] FIG. 6 illustrates a relationship between points acquired
from the lidar subsystem from separate beams at substantially the
same instance of time that may be used to estimate a y-component of
angular velocity of a target according to various implementations
of the invention.
[0015] FIG. 7 illustrates a relationship between points acquired
from the video subsystem that may be used to estimate a
two-dimensional (e.g. x and y components) translational velocity
and a z-component of angular velocity of a target according to
various implementations of the invention.
[0016] FIG. 8 illustrates a scan pattern of a lidar beam according
to various implementations of the invention.
[0017] FIG. 9 illustrates a timing diagram which may be useful for
describing various timing aspects associated with measurements from
the lidar subsystem according to various implementations of the
invention.
[0018] FIG. 10 illustrates a timing diagram which may be useful for
describing various timing aspects associated with measurements from
the lidar subsystem in relation to measurements from the video
subsystem according to various implementations of the
invention.
[0019] FIG. 11 illustrates a block diagram useful for processing
lidar measurements and video images according to various
implementations of the invention.
[0020] FIG. 12 illustrates a block diagram useful for processing
lidar measurements and video images according to various
implementations of the invention.
[0021] FIG. 13 illustrates a block diagram useful for processing
lidar measurements and video images according to various
implementations of the invention.
[0022] FIG. 14 illustrates a block diagram useful for processing
lidar measurements and video images according to various
implementations of the invention.
[0023] FIG. 15 illustrates a block diagram useful for processing
lidar measurements and video images according to various
implementations of the invention.
[0024] FIG. 16 illustrates a flowchart depicting example operations
performed by a system for refining a 3D image, according to various
aspects of the invention.
[0025] FIG. 17 illustrates a flowchart depicting example operations
performed by a system for refining a 3D image, according to various
aspects of the invention.
DETAILED DESCRIPTION
[0026] FIG. 1 illustrates a combined lidar and video camera system
100 according to various implementations of the invention. Various
implementations of the invention utilize synergies between lidar
measurements and video images to resolve six degrees of freedom for
motion of a target to a degree not otherwise possible with either a
lidar or video camera alone.
[0027] Combined system 100 includes a lidar subsystem 130, a video
subsystem 150, and a processing system 160. As illustrated, lidar
subsystem 130 includes two or more lidar beam outputs 112
(illustrated as a beam 112A, a beam 112B, a beam 112(n-1), and a
beam 112n); two or more reflected beam inputs 114 each
corresponding to one of beams 112 (illustrated as a reflected beam
114A, a reflected beam 1146, a reflected beam 114(n-1), and a
reflected beam 114n); two or more lidar outputs 116 each associated
with a pair of beam 112/reflected beam 114 (illustrated as a lidar
output 116A associated with beam 112A/reflected beam 114A, a lidar
output 116B associated with beam 112B/reflected beam 114B, a lidar
output 116(n-1) associated with beam 112(n-1)/reflected beam
114(n-1), and a lidar output 116n associated with beam
112n/reflected beam 114n).
[0028] In some implementations of the invention, beam steering
mechanism 140 may be employed to steer one or more beams 112 toward
target 190. In some implementations of the invention, beam steering
mechanism 140 may include individual steering mechanisms, such as a
steering mechanism 140A, a steering mechanism 140B, a steering
mechanism 140C, and a steering mechanism 140D, each of which
independently steers a beam 112 toward target 190. In some
implementations of the invention, one beam steering mechanism 140
may independently steer pairs or groups of beams 112 toward target
190.
[0029] In some implementations of the invention, beam steering
mechanism 140 may include one or more mirrors, each of which may or
may not be separately controlled, each mirror steering one or more
beams 112 toward target 190. In some implementations of the
invention, beam steering mechanism 140 may directly steer an
optical fiber of beam 112 without use of a mirror. In some
implementations of the invention, beam steering mechanism 140 may
be controlled to steer beams 112 in azimuth and/or elevation.
Various techniques may be used by beam steering mechanism 140 to
steer beam(s) 112 toward target 190 as would be appreciated.
[0030] In some implementations of the invention, beam steering
mechanism 140 may be used to control both an azimuth angle and an
elevation angle of two beams 112 toward the target. By controlling
both the azimuth angle and the elevation angle, the two beams 112
may be used to scan a volume for potential targets or track
particular targets such as target 190. Other scanning mechanisms
may be employed as would be apparent. In some implementations of
the invention, the two beams 112 may be offset from one another. In
some implementations of the invention, the two beams 112 may be
offset vertically (e.g., in elevation) or horizontally (e.g., in
azimuth) from one another by a predetermined offset and/or a
predetermined angle, either of which may be adjustable or
controlled.
[0031] In some implementations of the invention, beam steering
mechanism 140 may be used to control both an azimuth angle and an
elevation angle of four beams 112 toward the target. In some
implementations, the four beams 112 may be arranged with horizontal
and vertical separations. In some implementations, the four beams
may be arranged so as to form at least two orthogonal separations.
In some implementations, the four beams may be arranged in a
rectangular pattern, with pairs of beams 112 offset from one
another vertically and horizontally. In some implementations, the
four beams may be arranged in other patterns, with pairs of beams
112 offset from one another. The separations of the four beams 112
may be predetermined offsets and/or predetermined angles, which may
be fixed, adjustable and/or controlled.
[0032] A certain portion of each beam 112 may be reflected back
from target 190 to lidar subsystem 130 as reflected beam 114. In
some implementations of the invention and as illustrated in FIG. 1,
reflected beam 114 follows the same optical path (though in
reverse) as beam 112. In some implementations of the invention, a
separate optical path may be provided in lidar subsystem 130 or in
combined system 100 to accommodate reflected beam 114.
[0033] In some implementations of the invention, lidar subsystem
130 receives a reflected beam 114 corresponding to each beam 112,
processes reflected beam 114, and outputs lidar output 116 to
processing system 160.
[0034] Combined system 100 also includes video subsystem 150. Video
subsystem 150 may include a video camera for capturing two
dimensional images 155 of target 190. Various video cameras may be
used as would be apparent. In some implementations of the
invention, the video camera may output images 155 as pixels at a
particular resolution and at a particular image or frame rate.
Video images 155 captured by video subsystem 150 are forwarded to
processing system 160. In some implementations of the invention,
lidar subsystem 130 and video subsystem 150 are offset from one
another in terms of position and orientation. In particular, lidar
measurements typically correspond to three dimensions (e.g., x, y,
and z) whereas video images typically correspond to two dimensions
(e.g., x and y). Various implementations of invention calibrate
lidar subsystem 130 with video subsystem 150 to ensure that data
provided by each system refers to the same location in a given
coordinate system as would be apparent.
[0035] Combined system 110 may include one or more optional video
subsystems (not otherwise illustrated) for capturing additional
two-dimensional images 155 of target 190 from different positions,
perspectives or angles as would be apparent.
[0036] In some implementations of the invention, processing system
160 receives lidar outputs 116 from lidar subsystem 130 and images
155 from video subsystem 150 and stores them in a memory or other
storage device 165 for subsequent processing. Processing system 160
processes lidar outputs 116 and images 155 to generate a
three-dimensional image of target 190. In some implementations of
the invention, processing system 160 determines a trajectory of
target 190 from a combination of lidar outputs 116 and images 155
and uses the trajectory to generate a motion stabilized
three-dimensional image of target 190.
[0037] In some implementations of the invention, lidar subsystem
130 may include, for each of beams 112, a dual frequency, chirped
coherent laser radar system capable of unambiguously and
simultaneously measuring both range and Doppler velocity of a point
on target 190. Such a laser radar system is described in co-pending
U.S. application Ser. No. 11/353,123, entitled "Chirped Coherent
Laser Radar System and Method," (the "Chirped Lidar
Specification"), which is incorporated herein by reference in its
entirety. For purposes of clarity, a "beam" referenced in the
Chirped Lidar Specification is not the same as a "beam" referred to
in this description. More particularly, in the Chirped Lidar
Specification, two beams are described as output from the laser
radar system, namely a first beam having a first frequency (chirped
or otherwise) and a second beam having a second frequency (chirped
or otherwise) that are simultaneously coincident on a point on a
target to provide simultaneous measurements of both range and
Doppler velocity of the point on the target. For purposes of
simplicity and clarity, a singular "beam" as discussed herein may
refer to the combined first and second beams output from the laser
radar system described in the Chirped Lidar Specification. The
individual beams discussed in the Chirped Lidar Specification are
referred to herein henceforth as "signals." Nonetheless, various
implementations of the invention may employ beams other than those
described in the Chirped Lidar Specification provided these beams
provide simultaneous range and Doppler velocity measurements at
points on the target.
[0038] FIG. 2 illustrates a lidar 210 that may be used to generate
and process beam 112 and reflected beam 114 to provide lidar output
116 according to various implementations of the invention. Each
lidar 210 unambiguously determines a range and Doppler velocity of
a point on target 190 relative to lidar 210. Lidar 210 includes a
first frequency lidar subsection 274 and a second frequency lidar
subsection 276. First frequency lidar subsection 274 emits a first
frequency target signal 212 toward target 190 and second frequency
lidar subsection 276 emits a second frequency target signal 214
toward target 190. The frequencies of first target signal 212 and
second target signal 214 may be chirped to create a dual chirp
system.
[0039] First frequency lidar subsection 274 may include a laser
source controller 236, a first laser source 218, a first optical
coupler 222, a first signal delay 244, a first local oscillator
optical coupler 230, and/or other components. Second frequency
lidar subsection 276 may include a laser source controller 238, a
second laser source 220, a second optical coupler 224, a second
signal delay 250, a second local oscillator optical coupler 232
and/or other components.
[0040] First frequency lidar subsection 274 generates first target
signal 212 and a first reference signal 242. First target signal
212 and first reference signal 242 may be generated by first laser
source 218 at a first frequency that may be modulated at a first
chirp rate. First target signal 212 may be directed toward a
measurement point on target 190 either independently or combined
with second target signal 214. First frequency lidar subsection 274
may combine target signal 256 that was reflected from target 190
with first reference signal 242, which is directed over a path with
a known or otherwise fixed path length, to result in a combined
first target signal 262.
[0041] Second frequency lidar subsection 276 may be collocated and
fixed with respect to first frequency lidar subsection 274 (i.e.,
within lidar 210). More particularly, the relevant optical
components for transmitting and receiving the respective laser
signals may be collocated and fixed. Second frequency lidar
subsection 276 may generate second target signal 214 and a second
reference signal 248. Second target signal 214 and second reference
signal 248 may be generated by second laser source 220 at a second
frequency that may be modulated at a second chirp rate. In some
implementations of the invention, the second chirp rate is
different from the first chirp rate.
[0042] Second target signal 214 may be directed toward the same
measurement point on target 190 as first target beam 212. Second
frequency lidar subsection 276 may combine one portion of target
signal 256 that was reflected from target 190 with second reference
signal 248, which is directed over a path with a known or otherwise
fixed path length, to result in a combined second target signal
264.
[0043] Processor 234 receives combined first target signal 262 and
combined second target signal 264 and measures a beat frequency
caused by a difference in path length between each of the reflected
target signals and its corresponding reference signal, and by any
Doppler frequency created by target motion relative to lidar 210.
The beat frequencies may then be combined linearly to generate
unambiguous determinations of range and Doppler velocity of target
190 as set forth in the Chirped Lidar Specification. In some
implementations, processor 234 provides the range and Doppler
velocity measurements to processing system 160. In some
implementations, processor 234 is combined with processing system
160; in such implementations, processing system 160 receives
combined first target signal 262 and combined second target signal
264 and uses them to determine range and Doppler velocity.
[0044] As described, each beam 112 provides simultaneous
measurements of range and Doppler velocity of a point on target 190
relative to lidar 210. According to various implementations of the
invention, various numbers of beams 112 may be used to provide
these measurements of target 190. In some implementations of the
invention, two or more beams 112 may be used. In some
implementations of the invention, three or more beams 112 may be
used. In some implementations of the invention four or more beams
112 may be used. In some implementations of the invention, five or
more beams 112 may be used.
[0045] In various implementations of the invention, beams 112 may
be used to gather measurements for different purposes. For example,
in some implementations of the invention, a particular beam 112 may
be used for purposes of scanning a volume including target 190. In
some implementations of the invention, multiple beams 112 may be
used to accomplish such scanning. In some implementations of the
invention, a particular beam 112 may be used to monitor a
particular feature or position on target 190. In some
implementations of the invention, multiple beams 112 may be used to
independently monitor one or more features and/or positions on
target 190. In some implementations of the invention, one or more
beams 112 may be used to scan target 190 while one or more other
beams 112 may be used to monitor one or more features and/or
positions on target 190.
[0046] In some implementations of the invention, one or more beams
112 may scan target 190 to obtain a three dimensional image of
target 190 while one or more other beams 112 may be monitoring one
or more features and/or positions on target 190. In some
implementations of the invention, after a three dimensional image
of target 190 is obtained, one or more beams 112 may continue
scanning target 190 to monitor and/or update the motion aspects of
target 190 while one or more other beams 112 may monitor one or
more features and/or positions on target 110.
[0047] In some implementations of the invention, measurements
obtained via one or more beams 112 used to monitor and/or update
the motion aspects of target 190 may be used to compensate
measurements obtained via the one or more other beams 112 used to
monitor one or more features and/or positions on target 190. In
these implementations of the invention, the gross motion of target
190 may be removed from the measurements associated with various
features and/or positions on target 190 to obtain fine motion of
particular points or regions on target 190. In various
implementations of the invention, fine motion of target 190 may
include various vibrations, oscillations, or motion of certain
positions on the surface of target 190 relative to, for example, a
center of mass, a center of rotation, another position on the
surface of target 190 or other position. In various implementations
of the invention, fine motion of target 190 may include, for
example, relative motion of various features such as eyes, eyelids,
lips, mouth corners, facial muscles or nerves, nostrils, neck
surfaces, etc. or other features of target 190.
[0048] In some implementations of the invention, based on the gross
motion and/or the fine motion of target 190, one or more
physiological functions and/or physical activities of target 190
may be monitored. For example, co-pending U.S. patent application
Ser. No. 11/230,546, entitled "System and Method for Remotely
Monitoring Physiological Functions" describes various systems and
methods for monitoring physiological functions and/or physical
activities of an individual and is incorporated herein by reference
in its entirety.
[0049] In some implementations of the invention, one or more beams
112 may be used to monitor one or more locations on an eyeball of
target 190 and measure various position and motion aspects of the
eyeball at the each of these locations. Co-pending U.S. patent
application Ser. No. 11/610,867, entitled "System and Method for
Tracking Eyeball Motion" describes various systems and methods for
tracking the movement of an eyeball and is incorporated herein by
reference in its entirety.
[0050] In some implementations of the invention, one or more beams
112 may be used to focus on various features or locations on a face
of target 190 and measure various aspects of the face with respect
to the features or locations on the face of target 190. For
example, certain facial features or facial expressions may be
monitored over a period of time to infer a mental state of target
190, to infer an intent of target 190, to infer a deception level
of target 190 or to predict an event associated with target 190
(e.g., certain facial muscles may twitch just prior to a change in
expression or prior to speech).
[0051] In some implementations of the invention, one or more beams
112 may be used to monitor one or more locations on a neck of
target 190. The measured motion aspects of the neck of target 190
may be used to determine throat movement patterns, vocal cord
vibrations, pulse rate, and/or respiration rate. In some
implementations of the invention, one or more beams 112 may be used
to monitor one or more locations on an upper lip of target 190 to
detect and measure vibrations associated with speech of target 190.
These vibrations may be used to substantially reproduce the speech
of target 190.
[0052] In some implementations of the invention, one or more beams
112 may serve one purpose during a first period or mode of
operation of combined system 100 and may switch to serve a
different purpose during a second period or mode of operation of
combined system 100. For example, in some implementations of the
invention, multiple beams 112 may be used to measure various motion
aspects of target 190 so that processing system 160 may determine
or acquire a trajectory of target 190. Once the trajectory of
target 190 is acquired, some of the multiple beams 112 may switch
to monitoring certain other aspects or features of target 190 while
other ones of the multiple beams 112 measure motion aspects of
target 190 so that its trajectory can be maintained.
[0053] In some implementations of the invention, five beams 112
scan target 190 to obtain a three dimensional image of target 190.
In these implementations, four of these beams 112 each scan a
portion of target 190 (using various scanning patterns as described
in further detail below) while a fifth beam 112 performs an
"overscan" of target 190. The overscan may be a circular, oval,
elliptical or similar round scan pattern or a rectangular, square,
diamond or similar scan pattern or other scan pattern useful for
capturing multiple measurements of various points on target 190 (or
at least points within close proximity to one another) within
relatively short time intervals. These multiple measurements may
correspond to other measurements made by the fifth beam 112 (i.e.,
multiple visits to the same point by the fifth beam 112) or to
measurements made by one or more of the other four beams 112 (i.e.,
visits to the same point by the fifth beam and one or more of the
other four beams 112). In some implementations, the pattern of the
overscan may be selected to provide additional vertical and/or
horizontal spread between measurements of target 190. Both the
multiple measurements and additional spread may be used to improve
estimates of the motion of target 190. Use of the fifth beam 112 to
overscan target 190 may occur during each of the different modes of
operation referred to above.
[0054] In some implementations of the invention, once the
trajectory of target 190 is satisfactorily acquired, one or more
beams 112 may provide measurements useful for maintaining the
trajectory of target 190 as well as monitor other aspects of
features of target 190. In such implementations, other beams 112
may be used to scan for other targets in the scanning volume.
[0055] As illustrated in FIG. 1, a target coordinate frame 180 may
be used to express various measurements associated with target 190.
Various coordinate frames may be used as would be appreciated. In
some implementations of the invention, various ones of the
subsystems 130, 150 may express aspects of target 190 in coordinate
frames other than target coordinate frame 180 as would be
appreciated. For example, in some implementations of the invention,
a spherical coordinate frame (e.g., azimuth, elevation, range) may
be used to express measurements obtained via lidar subsystem 130.
Also for example, in some implementations of the invention, a two
dimensional pixel-based coordinate frame may be used to express
images 155 obtained via video subsystem 150. Various
implementations of the invention may use one or more of these
coordinate frames, or other coordinate frames, at various stages of
processing as will be appreciated.
[0056] As would be appreciated, in some implementations of the
invention, various coordinate transformations may be required to
transform measurements from lidar subsystem 130, which may be
expressed in a spherical coordinates with reference to lidar
subsystem 130 (sometimes referred to as a lidar measurement space),
to the motion aspects of target 190, which may be expressed in
Cartesian coordinates with reference to target 190 (sometimes
referred to as target space). Likewise, various coordinate
transformations may be required to transform measurements from
video subsystem 150, which may be expressed in Cartesian or pixel
coordinates with reference to video subsystem 150 (sometimes
referred to as video measurement space), to the motion aspects of
target 190. In addition, measurements from combined system 100 may
be transformed into coordinate frames associated with external
measurement systems such as auxiliary video, infrared,
hyperspectral, multispectral or other auxiliary imaging systems.
Coordinate transformations are generally well known.
[0057] As would be appreciated, in some implementations of the
invention, various coordinate transformations may be required to
transform measurements from lidar subsystem 130 and/or video
subsystem 150 to account for differences in position and/or
orientation of each such subsystem 130, 150 as would be
apparent.
[0058] FIG. 3 illustrates a scan pattern 300 which may be used to
scan a volume for targets 190 according to various implementations
of the invention. Scan pattern 300 includes a first scan pattern
section 310 and a second scan pattern section 320. First scan
pattern section 310 may correspond to a scan pattern of a first
beam 112 (e.g., beam 112A) that may be used to scan the volume (or
portion thereof). Second scan pattern section 320 may correspond to
a scan pattern of a second beam 112 (e.g., beam 112B) that may be
used to scan the volume (or portion thereof).
[0059] As illustrated in FIG. 3, the first beam 112 scans an upper
region of scan pattern 300 whereas the second beam 112 scans a
lower region of scan pattern 300. In some implementations of the
invention, the scan pattern sections 310, 320 may include an
overlap region 330. Overlap region 330 may be used to align or
"stitch together" first scan pattern section 310 with second scan
pattern section 320. In some implementations of the invention, scan
patterns 310, 320 do not overlap to form overlap region 330 (not
otherwise illustrated).
[0060] In implementations of the invention where lidar subsystem
130 employs a vertically displaced scan pattern 300 (such as that
illustrated in FIG. 3), first beam 112 is displaced vertically
(i.e., by some vertical distance, angle of elevation, or other
vertical displacement) from a second beam 112. In this way, the
pair of beams 112 may be scanned with a known or otherwise
determinable vertical displacement.
[0061] While scan pattern 300 is illustrated as having vertically
displaced scan pattern sections 310, 320 in FIG. 3, in some
implementations of the invention, scan pattern may have
horizontally displaced scan sections. In implementations of the
invention where lidar subsystem 130 employs a horizontally
displaced scan pattern (not otherwise illustrated), first beam 112
is displaced horizontally (i.e., by some horizontal distance, angle
of azimuth, or other horizontal displacement) from second beam 112.
In this way, the pair of beams 112 may be scanned with a known or
otherwise determinable horizontal displacement.
[0062] While FIG. 3 illustrates a scan pattern 300 with two
vertically displaced scan pattern sections 310, 320, various
numbers of beams may be stacked to create a corresponding number of
scan pattern sections as would be appreciated. For example, three
beams may be configured with either vertical displacements or
horizontal displacements to provide three scan pattern sections.
Other numbers of beams may be used either horizontally or
vertically as would be appreciated.
[0063] FIG. 4 illustrates a scan pattern 400 for lidar subsystem
130 that employs four beams 112 according to various
implementations of the invention. As illustrated in FIG. 4, lidar
subsystem 130 includes four beams 112 arranged to scan a scan
pattern 400. Scan pattern 400 may be achieved by having a first
pair of beams 112 displaced horizontally from one another and a
second pair of beams 112 displaced horizontally from one another
and vertically from the first pair of beam 112, thereby forming a
rectangular scanning arrangement. Other scanning geometries may be
used as would be apparent. Scan pattern 400 may be achieved by
controlling the beams independently from one another, as pairs
(either horizontally or vertically), or collectively, via beam
scanning mechanism(s) 140.
[0064] Scan pattern 400 includes a first scan pattern section 410,
a second scan pattern section 420, a third scan pattern section
430, and a fourth scan pattern section 440. In some implementations
of the invention, each of the respective scan pattern sections 410,
420, 430, 440 may overlap an adjacent scan pattern portion by some
amount (illustrated collectively in FIG. 4 as overlap regions 450).
For example, in some implementations of the invention, scan pattern
400 includes an overlap region 450 between first scan pattern
section 410 and third scan pattern section 430. Likewise, an
overlap region 450 exists between a first scan pattern section 410
and a second scan section 420. In some implementations of the
invention, various ones of these overlap regions 450 may not occur
or otherwise be utilized. In some implementations of the invention,
for example, only vertical overlap regions 450 may occur or be
utilized. In some implementations of the invention, only horizontal
overlap regions 450 may occur or be utilized. In some
implementations of the invention, no overlap regions 450 may occur
or be utilized. In some implementations of the invention, other
combinations of overlap regions 450 may be used.
[0065] As illustrated in FIG. 3 and FIG. 4, the use by lidar
subsystem 130 of multiple beams 112 may increase a rate at which a
particular volume (or specific targets within the volume) may be
scanned. For example, a given volume may be scanned twice as fast
using two beams 112 as opposed to scanning the same volume with one
beam 112. Similarly, a given volume may be scanned twice as fast
using four beams 112 as opposed to scanning the same volume with
two beams 112, and four times as fast as scanning the same volume
with one beam 112. In addition, multiple beams 112 may be used to
measure or estimate various parameters associated with the motion
of target 190 as will be discussed in more detail below.
[0066] According to various implementations of the invention,
particular scan patterns (and their corresponding beam
configurations) may be used to provide measurements and/or
estimates of motion aspects of target 190. As described above, each
beam 112 may be used to simultaneously provide a range measurement
and a Doppler velocity measurement at each point scanned.
[0067] In some implementations of the invention, for each beam 112,
a point scanned by that beam 112 may be described by an azimuth
angle, an elevation angle, and a time. Each beam 112 provides a
range measurement and a Doppler velocity measurement at that point
and time. In some implementations of the invention, each point
scanned by beam 112 may be expressed as an azimuth angle, an
elevation angle, a range measurement, a Doppler velocity
measurement, and a time. In some implementations of the invention,
each point scanned by beam 112 may be expressed in Cartesian
coordinates as a position (x, y, z), a Doppler velocity and a
time.
[0068] According to various implementations of the invention,
measurements from lidar subsystem 130 (i.e., lidar outputs 116) and
measurements from video subsystem 150 (frames 155) may be used to
measure and/or estimate various orientation and/or motion aspects
of target 190. These orientation and/or motion aspects of target
190 may include position, velocity, acceleration, angular position,
angular velocity, angular acceleration, etc. As these orientation
and/or motion aspects are measured and/or estimated, a trajectory
of target 190 may be determined or otherwise approximated. In some
implementations of the invention, target 190 may be considered a
rigid body over a given time interval and its motion may be
expressed as translational velocity components expressed in three
dimensions as v.sub.x.sup.trans, v.sub.y.sup.trans, and
v.sub.z.sup.trans, and angular velocity components expressed in
three dimensions as .omega..sub.x, .omega..sub.y, and .omega..sub.z
over the given time interval. Collectively, these translational
velocities and angular velocities correspond to six degrees of
freedom of motion for target 190 over the particular time interval.
In some implementations of the invention, measurements and/or
estimates of these six components may be used to express a
trajectory for target 190. In some implementations of the
invention, measurements and/or estimates of these six components
may be used to merge the three-dimensional image of target 190
obtained from lidar subsystem 130 with the two-dimensional images
of target 190 obtained from video subsystem 150 to generate
three-dimensional video images of target 190.
[0069] In some implementations of the invention, the instantaneous
velocity component v.sub.z(t) of a point on target 190 may be
calculated based on the range measurement, the Doppler velocity
measurement, the azimuth angle and the elevation angle from lidar
subsystem 130 as would be apparent.
[0070] Lidar subsystem 130 may be used to measure and/or estimate
translational velocity v.sub.z.sup.trans and two angular velocities
of target 190, namely .omega..sub.x and .omega..sub.y. For example,
FIG. 5 illustrates an exemplary relationship between points with
corresponding measurements from two beams 112 that may be used to
estimate x and y components of angular velocity of target 190
according to various implementations of the invention. More
particularly, and generally speaking, as illustrated in FIG. 5, in
implementations where beams 112 are displaced from one another
along the y-axis, a local velocity along the z-axis of point
P.sub.A determined via a first beam 112, a velocity of point
P.sub.B determined via a second beam 112, and a distance between
P.sub.A and P.sub.B may be used to estimate an angular velocity of
these points about the x-axis (referred to herein as .omega..sub.x)
as would be appreciated. In some implementations of the invention,
these measurements may be used to provide an initial estimate of
.omega..sub.x.
[0071] FIG. 6 illustrates another exemplary relationship between
points with corresponding measurements from two beams 112 that may
be used to estimate an angular velocity according to various
implementations of the invention. More particularly, as illustrated
in FIG. 6, in implementations were beams 112 are displaced from one
another on target 190 along the x-axis, a velocity of point P.sub.A
determined via a first beam 112, a velocity of point P.sub.B
determined by a second beam 112, and a distance between P.sub.A and
P.sub.B on target 190 along the x-axis may be used to estimate an
angular velocity of these points about the y-axis (referred to
herein as .omega..sub.y). In some implementations of the invention,
these measurements may be used to provide an initial estimate of
.omega..sub.y.
[0072] FIG. 5 and FIG. 6 illustrate implementations of the
invention where two beams 112 are disposed from one another along a
vertical axis or a horizontal axis, respectively, and the
corresponding range (which may be expressed in three-dimensional
coordinates x, y, and z) and Doppler velocity at each point are
measured at substantially the same time. In implementations of the
invention that employ beams 112 along a single axis (not otherwise
illustrated), an angular velocity may be estimated based on Doppler
velocities measured at different points at different times along
the single axis. As would be appreciated, better estimates of
angular velocity may obtained using: 1) measurements at points at
the extents of target 190 (i.e., at larger distances from one
another), and 2) measurements taken within the smallest time
interval (so as to minimize any effects due to acceleration).
[0073] FIG. 5 and FIG. 6 illustrate conceptual estimation of the
angular velocities about different axes, namely the x-axis and the
y-axis. In general terms, where a first beam 112 is displaced on
target 190 along a first axis from a second beam 112, an angular
velocity about a second axis orthogonal to the first axis may be
determined from the velocities along a third axis orthogonal to
both the first and second axes at each of the respective
points.
[0074] In some implementations of the invention, where two beams
are displaced along the y-axis from one another (i.e., displaced
vertically) and scanned horizontally with vertical separation
between scans, estimates of both .omega..sub.x and .omega..sub.y
may be made. While simultaneous measurements along the x-axis are
not available, they should be sufficiently close in time in various
implementations to neglect acceleration effects. In some
implementations of the invention where two beams 112 are displaced
along the x-axis from one another and at least a third beam 112 is
displaced along the y-axis from the pair of beams 112, estimates of
.omega..sub.x, .omega..sub.y and v.sub.z.sup.trans may be made. In
some implementations of the invention, estimates of both
.omega..sub.x, .omega..sub.y and v.sub.z.sup.trans may be made
using four beams 112 arranged in a rectangular fashion. In such
implementations, the measurements obtained from the four beams 112
include more information than necessary to estimate .omega..sub.x,
.omega..sub.y and v.sub.z.sup.trans. This so-called "overdetermined
system" may be used to improve the estimates of .omega..sub.x,
.omega..sub.y and v.sub.z.sup.trans as would be appreciated.
[0075] As has been described, range and Doppler velocity
measurements taken at various azimuth and elevation angles and at
various points in time by lidar subsystem 130 may be used to
estimate translational velocity v.sub.z.sup.trans and estimate two
angular velocities, namely, .omega..sub.x and .omega..sub.y, for
the rigid body undergoing ballistic motion.
[0076] In some implementations of the invention, .omega..sub.x,
.omega..sub.y and v.sub.z.sup.trans may be determined at each
measurement time from the measurements obtained at various points
as would be appreciated. In some implementations of the invention,
.omega..sub.x, .omega..sub.y and v.sub.z.sup.trans may be assumed
to be constant over an particular interval of time. In some
implementations of the invention, .omega..sub.x, .omega..sub.y and
v.sub.z.sup.trans may be determined at various measurement times
and subsequently averaged over a particular interval of time to
provide estimates of .omega..sub.x, .omega..sub.y and
v.sub.z.sup.trans for that particular interval of time as would be
appreciated. In some implementations of the invention, the
particular time interval may be fixed or variable depending, for
example, on the motion aspects of target 190. In some
implementations of the invention, a least squares estimator may be
used to provide estimates of .omega..sub.x, .omega..sub.y and
V.sub.z.sup.trans over a particular interval of time as would be
appreciated. Estimates of .omega..sub.x, .omega..sub.y and
V.sub.z.sup.trans may be obtained in other manners as would be
appreciated.
[0077] In some implementations of the invention, images from video
subsystem 150 may be used to estimate three other motion aspects of
target 190, namely translational velocity components
v.sub.x.sup.trans and v.sub.y.sup.trans and angular velocity
component .omega..sub.z over a given interval of time. In some
implementations of the invention, frames 155 captured by video
subsystem 150 may be used to estimate x and y components of
velocity for points on target 190 as it moves between frames 155.
FIG. 7 illustrates a change in position of a particular point or
feature I.sub.A between a frame 155 at time T and a frame 155 at
subsequent time T+.DELTA.t.
[0078] In some implementations of the invention, this change of
position is determined for each of at least two particular points
or features in frame 155 (not otherwise illustrated). In some
implementations of the invention, the change of position is
determined for each of many points or features. In some
implementations of the invention, translational velocity components
v.sub.x.sup.trans and v.sub.y.sup.trans, and angular velocity
component .omega..sub.z of target 190 may be estimated based on a
difference in position of a feature I.sub.A(T) and
I.sub.A(T+.DELTA.t) and a difference in time, .DELTA.t, between the
frames 155. These differences in position and time may be used to
determine certain velocities of the feature, namely,
v.sub.x.sup.feat and v.sub.y.sup.feat that may in turn be used to
estimate the translational velocity components v.sub.x.sup.trans
and v.sub.y.sup.trans, and angular velocity component .omega..sub.z
of target 190. Such estimations of velocity and angular velocity of
features between image frames are generally understood as would be
appreciated.
[0079] In some implementations of the invention, many features of
target 190 are extracted from consecutive frames 155. The
velocities v.sub.x.sup.feat and v.sub.y.sup.feat of these features
over the time interval between consecutive frames 155 may be
determined based on changes in position of each respective feature
between the consecutive frames 155. A least squares estimator may
be used to estimate the translational velocities v.sub.x.sup.trans
and v.sub.y.sup.trans, and the angular velocity .omega..sub.z from
the position changes of each the extracted features.
[0080] In some implementations of the invention, a least squares
estimator may use measurements from lidar subsystem 130 and the
changes in position of the features in frames 155 from video
subsystem 150 to estimate the translational velocities
v.sub.x.sup.trans, v.sub.y.sup.trans and V.sub.z.sup.trans and the
angular velocities .omega..sub.x, .omega..sub.y, and .omega..sub.z
of target 190.
[0081] As has been described above, lidar subsystem 130 and video
subsystem 150 may be used to estimate six components that may be
used describe the motion of target 190. These components of motion
may be collected over time to calculate a trajectory of target 190.
This trajectory may then be used to compensate for motion of target
190 to obtain a motion stabilized three dimensional image of target
190. In various implementations of the invention, the trajectory of
target 190 may be assumed to represent ballistic motion over
various intervals of time. The more accurately trajectories of
target 190 may be determined, the more accurately combined system
100 may adjust the measurements of target 190 to, for example,
represent three dimensional images, or other aspects, of target
190.
[0082] In various implementations of the invention, a rate at which
measurements are taken by lidar subsystem 130 is different from a
rate at which frames 155 are captured by video subsystem 150. In
some implementations of the invention, a rate at which measurements
are taken by lidar subsystem 130 is substantially higher than a
rate at which frames 155 are captured by video subsystem 150. In
addition, because beams 112 are scanned through a scan volume by
lidar subsystem 130, measurements at different points in the scan
volume may be taken at different times from one another; whereas
pixels in a given frame 155 are captured substantially
simultaneously (within the context of video imaging). In some
implementations of the invention, these time differences are
resolved in order to provide a more accurate trajectory of target
190.
[0083] As illustrated in FIG. 8, in some implementations of the
invention, a scan pattern 840 may be used to scan a volume for
targets. For purposes of explanation, scan pattern 840 represents a
pattern of measurements taken by a single beam. In some
implementations multiple beams may be used, each with their
corresponding scan pattern as would be apparent. As illustrated,
scan pattern 840 includes individual points 810 measured left to
right in azimuth at a first elevation 831, right to left in azimuth
at a second elevation 832, left to right in azimuth at a third
elevation 833, etc., until a particular scan volume is scanned. In
some implementations, scan pattern 840 may be divided into
intervals corresponding to various timing aspects associated with
combined system 100. For example, in some implementations of the
invention, scan pattern 840 may be divided into time intervals
associated with a frame rate of video subsystem 150. In some
implementations of the invention, scan pattern 840 may be divided
into time intervals associated with scanning a particular elevation
(i.e., an entire left-to-right or right-to-left scan). In some
implementations of the invention, scan pattern 840 may be divided
into time intervals associated with a roundtrip scan 820
(illustrated in FIG. 8 as a roundtrip scan 820A, a roundtrip scan
820B, and a roundtrip scan 820C) at one or more elevations (i.e., a
left-to-right and a return right-to-left scan at either the same or
different elevations). Similar timing aspects may be used in
implementations that scan vertically in elevation (as opposed to
horizontally in azimuth). Other timing aspects may be used as
well.
[0084] As illustrated in FIG. 8 and again for purposes of
explanation, each interval may include N points 810 which may in
turn correspond to the number of points 810 in a single scan (e.g.,
831, 832, 833, etc.) or in a roundtrip scan 820. A collection of
points 810 for a particular interval is referred to herein as a
sub-point cloud and a collection of points 810 for a complete scan
pattern 840 is referred to herein as a point cloud. In some
implementations of the invention, each point 810 corresponds to the
lidar measurements of range and Doppler velocity at a particular
azimuth, elevation, and a time at which the measurement was taken.
In some implementations of the invention, each point 810
corresponds to the lidar measurements of range (expressed x, y, z
coordinates) and Doppler velocity and a time at which the
measurement was taken.
[0085] FIG. 9 illustrates a timing diagram 900 useful for
describing various timing aspects associated with measurements from
lidar subsystem 130 according to various implementations of the
invention. Timing diagram 900 includes points 810 scanned by beam
112, sub-point clouds 920 formed from a plurality of points 810
collected over an interval corresponding to a respective sub-point
cloud 920, and a point cloud 930 formed from a plurality of
sub-point clouds 920 collected over the scan pattern. Timing
diagram 900 may be extended to encompass points 810 scanned by
multiple beams 112 as would be appreciated.
[0086] Each point 810 is scanned by a beam 112 and measurements
associated with each point 810 are determined by lidar subsystem
130. In some implementations of the invention, points 810 are
scanned via a scan pattern (or scan pattern section). The interval
during which lidar subsystem 130 collects measurements for a
particular sub-point cloud 920 may have a time duration referred to
as T.sub.SPC. In some implementations of the invention, the
differences in timing of the measurements associated with
individual points 810 in sub-point cloud 920 may be accommodated by
using the motion aspects (e.g., translational velocities and
angular velocities) for each point to adjust that point to a
particular reference time for sub-point cloud 920 (e.g.,
t.sub.RSPC). This process may be referred to as stabilizing the
individual points 810 for the motion aspects of target 190.
[0087] In some implementations of the invention, the velocities may
be assumed to be constant over the time interval (i.e., during the
time duration T.sub.SPC). In some implementations of the invention,
the velocities may not be assumed to be constant during the period
of the scan pattern and acceleration effects may need to be
considered to adjust the measurements of points 810 to the
reference time as would be appreciated. In some implementations of
the invention, adjustments due to subdivision of the time interval
may also need to be accommodated. As illustrated in FIG. 9, the
reference time for each sub-point cloud 920 may be selected at the
midpoint of the interval, although other reference times may be
used.
[0088] In some implementations of the invention, similar
adjustments may be made when combining sub-point clouds 920 into
point clouds 930. More particularly, in some implementations of the
invention, the differences in timing of the measurements associated
with sub-point clouds 920 in point cloud 930 may be accommodated by
using the motion aspects associated with the measurements.
[0089] In some implementations of the invention, the measurements
associated with each sub-point cloud 920 that is merged into point
cloud 930 are individually adjusted to a reference time associated
with point cloud 930. In some implementations of the invention, the
reference time corresponds to a frame time (e.g., time associated
with a frame 155). In other implementations of the invention, the
reference time correspond to an earliest of the measurement times
of points 1110 in point cloud 930, a latest of the measurement
times of points 1110 in point cloud 930, an average or midpoint of
the measurement times of points 1110 in point cloud 930, or other
reference time associated with point cloud 930.
[0090] Although not otherwise illustrated, in some implementations
of the invention, similar adjustments may be made to combine point
clouds 930 from individual beams 112 into aggregate point clouds at
a particular reference time. In some implementations of the
invention, this may be accomplished at the individual point level,
the sub-point cloud level or the point cloud level as would be
appreciated. For purposes of the remainder of this description,
sub-point clouds 920 and point clouds 930 refer to the collection
of points 810 at their respective reference times from each of
beams 112 employed by lidar subsystem 130 to scan target 190.
[0091] In some implementations of the invention, motion aspects of
target 190 may be assumed to be constant over various time
intervals. For example, motion aspects of target 190 may be assumed
to be constant over T.sub.SPC or other time duration. In some
implementations of the invention, motion aspects of target 190 may
be assumed to be constant over a given T.sub.SPC, but not
necessarily constant over T.sub.PC. In some implementations of the
invention, motion aspects of target 190 may be assumed to be
constant over incremental portions of T.sub.SPC, but not
necessarily over the entire T.sub.SPC. As a result, in some
implementations of the invention, a trajectory of target 190 may be
expressed as a piece-wise function of time, with each "piece"
corresponding to the motion aspects of target 190 over each
individual time interval.
[0092] In some implementations, timing adjustments to compensate
for motion may be expressed as a transformation that accounts for
the motion of a point from a first time to a second time. This
transformation, when applied to measurements from, for example,
lidar subsystem 130, may perform the timing adjustment from the
measurement time associated with a particular point (or sub-point
cloud or point cloud, etc.) to the desired reference time.
Furthermore, when the measurements are expressed as vectors, this
transformation may be expressed as a transformation matrix. Such
transformation matrices and their properties are generally well
known.
[0093] As would be appreciated, the transformation matrices may be
readily used to place a position and orientation vector for a point
at any time to a corresponding position and orientation vector for
that point at any other time, either forwards or backwards in time,
based on the motion of target 190. The transformation matrices may
be applied to sub-point clouds, multiple sub-point clouds and point
clouds as well. In some implementations, a transformation matrix
may be determined for each interval (or subinterval) such that it
may be used to adjust a point cloud expressed in one interval to a
point cloud expressed in the next sequential interval. In these
implementations, each interval has a transformation matrix
associated therewith for adjusting the point clouds for the
trajectory of target 190 to the next interval. In some
implementations, a transformation matrix may be determined for each
interval (or subinterval) such that it may be used to adjust a
point cloud expressed in one interval to a point cloud expressed in
the prior sequential interval. Using the transformation matrices
for various intervals, a point cloud can be referenced to any time,
either forward or backward.
[0094] FIG. 10 illustrates a timing diagram 1000 useful for
describing various timing aspects associated with measurements from
lidar subsystem 130 in relation to measurements from video
subsystem 150 according to various implementations of the
invention. In some implementations of the invention, point cloud
930 may be referenced to the midpoint of a time interval between
frames 155 or other time between frames 155. In some
implementations of the invention, point cloud 930 may be referenced
to a frame time corresponding to a particular frame 155. Point
cloud 930 may be referenced in other manners relative to a
particular frame 155 as would be appreciated.
[0095] As illustrated in FIG. 10, PC.sub.m-1 is the expression of
point cloud 930 referenced at the frame time of frame I.sub.n-1;
PC.sub.m is the expression of point cloud 930 referenced at the
frame time of frame I.sub.n; and PC.sub.m+1 is the expression of
point cloud 930 referenced at the frame time of frame I.sub.n+1;
and PC.sub.m+2 is the expression of point cloud 930 referenced at
the frame time of frame I.sub.1+2. In some implementations, point
cloud 930 may be referenced at other times in relation to the
frames and frames times as would be apparent.
[0096] As described above, a transformation matrix T.sub.i,i+1 may
be determined to transform an expression of point cloud 930 at the
i.sup.th frame time to an expression of point cloud 930 at the
(i+1).sup.th frame time. In reference to FIG. 10, a transformation
matrix T.sub.m-1,m may be used to transform PC.sub.m-1 to PC.sub.m;
a transformation matrix T.sub.m,m+1 may be used to transform
PC.sub.m to PC.sub.m+1; and a transformation matrix T.sub.m+1,m+2
may be used to transform PC.sub.m+1 to PC.sub.m+2. In this way,
transformation matrices may be used to express point clouds 930 at
different times corresponding to frames 155.
[0097] According to various implementations of the invention, the
transformation matrices which are applied to point cloud 930 to
express point cloud 930 from a first time to a second time are
determined in different processing stages. Generally speaking,
transformation matrices are directly related with six degree of
motion parameters .omega..sub.x, .omega..sub.y, .omega..sub.z,
v.sub.x.sup.trans, v.sub.y.sup.trans and v.sub.z.sup.trans that may
be calculated in two steps: first .omega..sub.x, .omega..sub.y, and
v.sub.z.sup.trans from lidar subsystem and second
v.sub.x.sup.trans, v.sub.y.sup.trans and .omega..sub.z, from video
subsystem.
[0098] FIG. 11 illustrates a block diagram of a configuration of
processing system 160 that may be used during a first phase of the
first processing stage to estimate a trajectory of target 190
according to various implementations of the invention. In some
implementations of the invention, during the first phase of the
first stage, a series of initial transformation matrices (referred
to herein as T.sub.i,i+1.sup.(0)) are determined from various
estimates of the motion aspects of target 190. As illustrated,
lidar subsystem 130 provides range, Doppler velocity, azimuth,
elevation and time for at each point as input to a least squares
estimator 1110 that is configured to estimate angular velocities
.omega..sub.x and .omega..sub.y and translational velocity
v.sub.z.sup.trans over each of a series of time intervals. In some
implementations of the invention, angular velocities o and
.omega..sub.y and translational velocity v.sub.z.sup.trans are
iteratively estimated by varying the size of the time intervals (or
breaking the time intervals into subintervals) as discussed above
until any residual errors from least squares estimator 1110 for
each particular time interval reach acceptable levels as would be
apparent. This process may be repeated for each successive time
interval during the time measurements of target 190 are taken by
lidar subsystem 130.
[0099] Assuming that target 190 can be represented over a given
time interval as a rigid body (i.e., points on the surface of
target 190 remain fixed with respect to one another) undergoing
ballistic motion (i.e., constant velocity with no acceleration), an
instantaneous velocity of any given point 810 on target 190 can be
expressed as:
v=v.sup.trans[.omega..times.(R-R.sub.c-v.sup.trans*.DELTA.t)] Eq.
(1)
where [0100] v is the instantaneous velocity vector of the given
point; [0101] v.sup.trans is the translational velocity vector of
the rigid body; [0102] .omega. is the rotational velocity vector of
the rigid body; [0103] R is the position of the given point on the
target; [0104] R.sub.c is the center of rotation for the target;
and [0105] .DELTA.t is the time difference of each measurement time
from a given reference time.
[0106] Given the measurements available from lidar subsystem 130,
the z-component of the instantaneous velocity may be expressed
as:
v.sub.z=v.sub.z.sup.trans+[.omega..times.(R-R.sub.c-v.sup.trans*.DELTA.t-
)].sub.z Eq. (2)
where [0107] v.sub.z is the z-component of the instantaneous
velocity vector; [0108] v.sub.z.sup.trans is the z-component of the
translational velocity vector; and [0109]
[.omega..times.(R-R.sub.c-v.sup.trans*.DELTA.t)].sub.z is the
z-component of the cross product.
[0110] In some implementations of the invention, frame-to-frame
measurements corresponding to various features from images 155 may
be made. These measurements may correspond to a position (e.g.,
x.sup.feat, y.sup.feat) and a velocity (e.g., v.sub.x.sup.feat,
v.sub.y.sup.feat) for each of the features and for each
frame-to-frame time interval. In implementations where a
z-coordinate of position is not available from video subsystem 150,
an initial estimate of z may be made using, for example, an average
z component from the points from lidar subsystem 130. Least squares
estimator 1120 estimates angular velocities .omega..sub.x,
.omega..sub.y, and .omega..sub.z and translational velocities
v.sub.x.sup.trans, v.sub.y.sup.trans, and v.sub.z.sup.trans which
may be expressed as a transformation matrix T.sub.i,i+1.sup.(0) for
each of the relevant time intervals. In some implementations of the
invention, a cumulative transformation matrix corresponding to the
arbitrary frame to frame time interval may be determined.
[0111] FIG. 12 illustrates a block diagram of a configuration of
processing system 160 that may be used during a second phase of the
first processing stage to estimate a trajectory of target 190
according to various implementations of the invention. In some
implementations of the invention, during the second phase of the
first stage, new transformation matrices (referred to herein as
T.sub.i,i+1.sup.(1)) are determined from various estimates of the
motion aspects of target 190. As illustrated, measurements from
lidar subsystem 130 of range, Doppler velocity, azimuth, elevation
and time for at each of the N points are input to a least squares
estimator 1110 of processing system 160 along with the
transformation matrices T.sub.i,i+1.sup.(0) to estimate angular
velocities .omega..sub.x and .omega..sub.y and translational
velocity v.sub.z.sup.trans over each of a series of time intervals
in a manner similar to that described above during the first
phase.
[0112] The primary difference between the second phase and the
first phase is that least squares estimator 1120 uses the
calculated z position of the features based on T.sub.i,i+1.sup.(0)
as opposed to merely an average of z position. Least squares
estimator 1120 estimates new angular velocities .omega..sub.x,
.omega..sub.y, and .omega..sub.z and new translational velocities
v.sub.x.sup.trans, v.sub.y.sup.trans, and v.sub.z.sup.trans which
may be expressed as a transformation matrix T.sub.i,i+1.sup.(1) for
each of the relevant time intervals. Again, in some implementations
of the invention, a cumulative transformation matrix corresponding
to the frame to frame time interval may be determined.
[0113] FIG. 13 illustrates a block diagram of a configuration of
processing system 160 that may be used during a third phase of the
first processing stage to estimate a trajectory of target 190
according to various implementations of the invention. In some
implementations of the invention, during the third phase of the
first stage, new transformation matrices (referred to herein as
T.sub.i,i+1.sup.(2)) are determined from various estimates of the
motion aspects of target 190. As illustrated, lidar subsystem 130
provides range, Doppler velocity, azimuth, elevation and time for
at each of the points as input to a least squares estimator 1110 to
estimate angular velocities .omega..sub.x and .omega..sub.y and
translational velocity v.sub.z.sup.trans over each of a series of
time intervals in a manner similar to that described above during
the first phase. In this phase, calculated values of v.sub.x and
v.sub.y for each point based on T.sub.i,i+1.sup.(1) as determined
during the prior phase are input into least squares estimator 1120
as opposed to the feature measurements used above.
[0114] The primary difference between the third phase and the
second phase is that least squares estimator 1120 uses
T.sub.i,i+1.sup.(1) to describe motion between the relevant frames
155. Least squares estimators 1110, 1120 estimate new angular
velocities .omega..sub.x, .omega..sub.y, and .omega..sub.z and new
translational velocities v.sub.x.sup.trans, v.sub.y.sup.trans, and
v.sub.z.sup.trans which may be expressed as a transformation matrix
T.sub.i,i+1.sup.(2) for each of the relevant time intervals. Again,
in some implementations of the invention, a cumulative
transformation matrix corresponding to the frame to frame time
interval may be determined.
[0115] In various implementations of the invention, any of the
phases of the first processing stage may be iterated any number of
times as additional information is gained regarding motion of
target 190. For example, as the transformation matrices are
improved, each point 810 may be better expressed at a given
reference time in relation to its measurement time.
[0116] During the first processing stage, the translational
velocities of each point (not otherwise available from the lidar
measurements) may be estimated using features from the frames 155.
Once all velocity components are known or estimated for each point,
transformation matrices may be determined without using the feature
measurements as illustrated in FIG. 13.
[0117] FIG. 14 illustrates a block diagram of a configuration of
processing system 160 that may be used during a first phase of the
second processing stage to refine a trajectory of target 190
according to various implementations of the invention. The first
processing stage provides transformation matrices sufficient to
enable images 155 to be mapped onto images at any of the frame
times. Once so mapped, differences in pixels themselves (as opposed
to features in images 155) from different images transformed to the
same frame time may be used to further refine the trajectory of
target 190. In some implementations, various multi-frame
corrections may be determined, which in turn through the least
square estimator can be used for obtaining offsets between the
consecutive images .DELTA.x.sub.i,i+1, .DELTA.y.sub.i,i+1,
.DELTA..theta.z.sub.i,i+1. These corrections may be used to refine
the transformation matrices (for example, matrices
T.sub.i,i+1.sup.(2) to T.sub.i,i+1.sup.(3)). In some
implementations of the invention, during the first phase of the
second processing stage, a series of new transformation matrices
(referred to herein as T.sub.i,i+1.sup.(3)) are refinements of
T.sub.i,i+1.sup.(2) on the basis of the offsets between image
I.sub.i and an image I.sub.j, namely, .DELTA.x.sub.i,j,
.DELTA.y.sub.i,j, .DELTA..theta.z.sub.i,j. As illustrated, an
estimator 1410 determines a difference between an image I.sub.i and
an image I.sub.j using the appropriate transformation matrix
T.sub.i,j.sup.(2) to express the images at the same frame time.
[0118] FIG. 15 illustrates a block diagram of a configuration of
processing system 160 that may be used during a second phase of the
second processing stage to further refine a trajectory of target
190 according to various implementations of the invention. To the
extent that additional accuracy is necessary, the transformation
matrices from the first phase of the second processing stage (e.g.,
T.sub.i,i+1.sup.(3) may be used in connection with the measurements
from lidar subsystem 130 to further refine the transformation
matrices (referred to herein as T.sub.i,i+1.sup.(4)). In some
implementations of the invention, during this phase, measurements
from lidar subsystem 130 that occur within any overlap regions 360,
450 are used. These measurements correspond to multiple
measurements taken for the same point (or substantially the same
point) at different times. This phase is based on the premise that
coordinate measurements of the same point on target 190 taken
different times should transform precisely to one another with a
perfect transformation matrix, i.e. points measured at the
different times that have the same x and y coordinates should have
the same z coordinate. In other words, all coordinates of the
underlying points should directly map to one another at the
different points in time. The differences in z coordinates (i.e.,
corrections) between the measurements at different times can be
extracted and input to the least square estimator. Through the
least square estimator, the corrections to the transformation
parameters between the consecutive frames may obtained and may be
expressed as .DELTA.z.sub.i,i+1, .DELTA..theta.x.sub.i,i+1, and
.DELTA..theta.y.sub.i,i+1. These corrections may be used to refine
the transformation matrices T.sub.i,i+1.sup.(3) to
T.sub.i,i+1.sup.(4). In some implementations of the invention,
multiple measurements corresponding to use of an overscan beam may
be used in a similar manner.
[0119] As described herein, obtaining accurate transformation
parameters allows on one hand the six degrees-of-freedom ("6DOF")
tracking of targets, and on the other hand generation of the motion
compensated 3D image of the target that can be reproduced at any
frame time during the scanning.
[0120] Stochastic errors present in each set of transformation
parameters may be accumulated upon successive transformations. Such
stochastic errors in the transformation parameters is due to the
stochastic error of the respective video and lidar
measurements.
[0121] According to various implementations of the invention, the
3D images may be refined by reducing the stochastic components in
the transformation parameters (i.e., v.sub.x, v.sub.y, v.sub.z,
.omega..sub.x, .omega..sub.y and .omega..sub.z) between video frame
times. In some implementations, the 3D images may be refined on the
basis of matching the transformed coordinates and pixels positions.
In other words, the stochastic component for the set of
transformation parameters may be reduced, which ultimately leads to
the 3D image refinement. As described with respect to FIG. 11
above, during the first processing stage, the transformation
parameters may be calculated self-consistently from the Doppler
velocity measurements made by the lidar subsystem 130 (e.g.,
v.sub.z, .omega..sub.x, .omega..sub.y and referred to as the lidar
transformation parameters or lidar parameters) and the measurements
obtained from the series of 2D video images from video subsystem
150 (e.g., v.sub.x, v.sub.y, .omega..sub.z and referred to as the
video transformation parameters or video parameters). In some
implementations, the processing system 160 may refine the
transformation parameters by first, refining the lidar parameters
and then refining the video parameters, although the order here is
not important.
[0122] In some implementations, refinement of the lidar parameters
may be based on the assumption that--for the motion compensated 3D
image transformed to a particular frame time, the z offset of the
subsequent overscan measurements (from a fifth beam 112, for
example) from the line scan measurements (from one or more of the
four beams using various scanning patterns described herein) should
be the same. Refinement of the lidar parameters may be accomplished
by transforming the stationary image (e.g., point cloud) to a frame
time associated with the frames used during the first stage. Next,
the overscan lidar measurements taken during the inter-frame time
intervals immediately before a given frame time and immediately
after the given frame time may be gathered/selected/identified for
each of the frames, and may be referred to respectively as pre and
post over-scan measurements. By definition, these pre and post
over-scan measurements cross the multiple line scans of the other
beams (i.e., beams other than that/those used for the overscan) in
the scan pattern. For each scan line and at each frame time,
processing system 160 may determine .DELTA.z offsets between the
points (i.e., lidar measurements) in the line scan relative to each
of the pre over-scan measurements (i.e., also "points") and the
post over-scan measurements. If the stochastic measurement errors
were "0" and the transformation parameters ideal, the .DELTA.z
offsets (both for pre and post overscan measurements) would be
zero. However, these .DELTA.z offsets are typically not zero. In
some implementations of the invention, when the lidar
transformation parameters may be updated by imposing the condition
that pre and post over-scan measurements should be offset from the
same line scan measurements by the same amount. To correct the
lidar transformation parameters, processing system 160 may use a
least-squares optimization to minimize the difference between the
.DELTA.z offsets relative to pre and post over-scan measurements
over the respective set of frame times as would be appreciated.
This results in a set of equations where all inter-frame
transformation parameters are inter-related, such as the same
subset of parameters (except for the first and last ones) enter
explicitly in one equation from the pre over-scan measurements and
in another equation as the post over-scan measurements. This
process may be applied to all overscan measurements at their
respective times as would be appreciated. In addition, in some
implementations, this procedure can be iterated, since in general
the least square optimization favors the iterations.
[0123] In some implementations, processing system 160 may refine
the video transformation parameters utilizing similar principles.
Using the transformation parameters, not only can any 3D point be
transformed to any frame time, but any video image (more
appropriately, any pixel in any image) may be transformed to any
frame time (and any other time as well). For video images, if the
measurement errors were "0" and the transformation parameters
ideal, a video image transformed to a different frame time should
coincide with the video image originally captured at that frame
time (i.e., the only untransformed video image at that frame time).
By comparing pixel intensity of the transformed video image(s) and
the original image at a given frame time, corrections to the
transformation parameters may be derived. In some implementations
of the invention, the video image at frame time n, the video image
at frame time n-1 transformed to frame time n (the "transformed
pre-video image") and the video image at frame time n+1 transformed
to frame time n (the "transformed post-video image") may be
compared to one another. In other words, three video images
captured at consecutive frame times n-1, n, and n+1, respectively,
are each transformed to frame time n (clearly, no transformation of
the original video image at frame time n is necessary) using the
transformation parameters. Then, the pixel intensities of the
transformed pre-video image may be compared with those of the video
image, the pixel intensities of the video image may be compared
with those of the transformed post-video image, and the pixel
intensities of the transformed pre-video image may be compared with
those of the transformed post-video image. The first combination
determines the correction to the video transformation parameters
for the frame interval between n-1 and n (i.e., dv.sub.x.sup.(n-1),
dc.sub.y.sup.(n-1), d.omega..sub.z.sup.(n-1)), the second
combination determines the correction to the video transformation
parameters for the frame interval between n and n+1
(dv.sub.x.sup.(n), dv.sub.y.sup.(n), d.omega..sub.z.sup.(n)) and
the third combination determines a correction to the video
transformation parameters of both intervals. Thus, for each image
frame time the pre and post frame time corrections may be
determined, making it an inter-related system, which again may be
solved using the least square optimization. While described above
as a single frame time n approach, this process may be generalized
to any number of the video images and corresponding frame times as
would be appreciated. However, in some
applications/implementations, a tradeoff may exist between
increasing number of frames used and changing light conditions
(e.g., rapid changes in lighting may favor fewer number of frames
for the optimization whereas stable lighting conditions may favor
more number of frames for the optimization).
[0124] The following equations set forth the refinement process
described above in accordance with various implementations of the
invention.
T.sub.ijI.sub.j=I.sub.i.sup.(j)
T.sub.ikI.sub.j=I.sub.i.sup.(k)
Where
[0125] T.sub.ij is the initial transformation that transforms from
frame i to frame j, I.sub.i and I.sub.j are the original images i
and j, I.sub.i.sup.(j) is the original image j transformed to the
time frame of image i. In the absence of errors,
I.sub.i.sup.(j)=I.sub.i.sup.(k). The transformation correction
DT.sub.jk.sup.(i) that matches two transformed images may be
defined as:
DT.sub.ik.sup.(i)I.sub.i.sup.(k)=I.sub.i.sup.(j) Eq. (3)
[0126] Then, the corrected transformation may be:
T.sub.ik.sup.(c)=T.sub.ij.sup.-1DT.sub.jk.sup.(i)T.sub.ik. Eq.
(4)
[0127] An equation relating two consecutive transformation
corrections may have the form:
DT.sub.jm.sup.(p)=T.sub.pi DT.sub.jk.sup.(i)T.sub.is
DT.sub.km.sup.(s)T.sub.sp. Eq. (5)
[0128] If all transformation corrections are taken at the same
frame time, p=i=s, equation (5) may be simplified as:
DT.sub.jm.sup.(p)=DT.sub.jk.sup.(p)DT.sub.km.sup.(p). Eq. (6)
[0129] Equation (6) is the fundamental equation for multi-frame
image refinement. Equation (6) shows that operating in the same
frame time and in the linear approximation the corrections become
additive. Particularly, it shows that dx, dy, and d.theta..sub.z
are related through the multi-frame equation as:
dx.sup.(i).sub.i-1,i+1=dx.sup.(i).sub.i-1,i+dx.sup.(i).sub.i,i+1,
Eq. (7)
dy.sup.(i).sub.i-1,i+1=dy.sup.(i).sub.i-1,i+dy.sup.(i).sub.i,i+1,
Eq. (8)
d.theta..sub.z.sup.(i).sub.i-1,i+1=d.theta..sub.z.sup.(i).sub.i-1,id.the-
ta..sub.z.sup.(i).sub.i,i+1. Eq. (9)
[0130] In the single frame approach, the corrected transformation
T.sub.i,i+1.sup.(c) can be calculated either through the i.sup.th
or (i.sup.th+1) reference frame:
T.sub.i,i+1.sup.(c)=T.sub.i,i+1DT.sub.i,i+1.sup.(i+1)=DT.sub.i,i+1.sup.(-
i)T.sub.i,i+1. Eq. (10)
[0131] For practical purposes, the geometric mean may be used as
follows:
T.sub.i,i+1.sup.(c)=(T.sub.i,i+1DT.sub.i,i+1.sup.(i+1)DT.sub.i,i+1.sup.(-
i)T.sub.i,i+1).sup.1/2, Eq. (11)
[0132] which accounts for both forward and backward correction to
the image transformation.
[0133] The forward and backward corrections may be determined from
the least-square minimization. The forward and backward corrections
may be defined as the ones that have their own multi-frame
correction term:
dx.sub.i.sup.(F)=dx.sup.(i).sub.i-1,i+.alpha..sub.i.sup.(F), Eq.
(12)
dx.sub.i.sup.(B)=dx.sup.(i).sub.i,i+1+.alpha..sub.i.sup.(B), Eq.
(13)
dx.sub.i.sup.(2)=dx.sup.(i).sub.i-1,i+1+.alpha..sub.i.sup.(2), Eq.
(14)
which obey to the multi-frame equation:
dx.sub.i.sup.(2)=dx.sub.i.sup.(F)+dx.sub.i.sup.(B). Eq. (15)
[0134] Minimizing the functional of the multi-frame
corrections:
X=.SIGMA.[(.alpha..sup.(F)).sup.2.alpha.(.alpha..sup.(B)).sup.2+(.alpha.-
.sup.(2)).sup.2], Eq. (16)
[0135] the least-square multi-frame corrections may be obtained as
follows:
.alpha..sub.i.sup.(F)=.alpha..sub.i.sup.(B)=(dx.sup.(i).sub.i-1,i+1-dx.s-
up.(i).sub.i-1,i-dx.sup.(i).sub.i,i+)/3. Eq. (17)
[0136] In the similar way, in such formulation the multi-frame
corrections for dy and d.theta..sub.z may be obtained. The
multi-frame corrections (17) define the multi-frame lateral and
angular offsets (10-12), which in turn defines the transformation
correction:
DT = 1 - d .theta. z 0 dx d .theta. z 1 0 dy 0 0 1 0 0 0 0 1 Eq . (
18 ) ##EQU00001##
[0137] This via Eq. (11) produces the corrected transformation
matrix.
[0138] FIG. 16 illustrates a flowchart depicting example operations
performed by a system for refining a three dimensional image,
according to various aspects of the invention. In some
implementations, the described operations may be accomplished using
one or more of the components described herein. In some
implementations, various operations may be performed in different
sequences. In other implementations, additional operations may be
performed along with some or all of the operations shown in FIG.
16. In yet other implementations, one or more operations may be
performed simultaneously. In yet other implementations, one or more
operations may not be performed. Accordingly, the operations
described in FIG. 16 and other drawing figures are exemplary in
nature and, as such, should not be viewed as limiting.
[0139] In some implementations, in an operation 1602, process 1600
may receive a first set of line scan 3D measurements and a second
set of overscan 3D measurements (from lidar subsystem 130, for
example) for a plurality of points on a target, and at least one
video frame of the target (from video subsystem 150, for
example).
[0140] In some implementations, in an operation 1604, process 1600
may determine, at each frame time, the multiple .DELTA.z offsets
between the pre over-scan measurements and the line scans (referred
to as pre .DELTA.z offsets) and the post over-scan measurements and
the line scans (referred to as post .DELTA.z offsets).
[0141] In some implementations, in an operation 1606, process 1600
may adjust or update the lidar transformation parameters based on
determined pre and post .DELTA.z offsets by using the least square
optimization.
[0142] FIG. 17 illustrates a flowchart depicting example operations
performed by a system for refining a three dimensional image,
according to various aspects of the invention. In some
implementations, in an operation 1702, process 1700 may receive a
plurality of 3D measurements (from lidar subsystem 130, for
example) for a plurality of points on a target, and the video
frames of the target (from video subsystem 150, for example).
[0143] In some implementations, in an operation 1704, process 1700
may transform a video frame to a particular frame time to generate
transformed video frame (for example, a video frame at frame time
n-1 or n+1 transformed to frame time n). In some implementations,
process 1700 may transform each video frame to a next and previous
video frame. In some implementations, in an operation 1706, process
1700 may compare the pixel intensities of the transformed video
frames and determine the offsets between the transformed video
frames. In some implementations, in an operation 1708, process 1700
may determine corrections to the video transformation parameters on
the basis of the multi-frame least square optimization and may
update the transformation parameters.
[0144] While the invention has been described herein in terms of
various implementations, it is not so limited and is limited only
by the scope of the following claims, as would be apparent to one
skilled in the art. These and other implementations of the
invention will become apparent upon consideration of the disclosure
provided above and the accompanying figures. In addition, various
components and features described with respect to one
implementation of the invention may be used in other
implementations as well.
* * * * *