LADAR – Camera Registration Using Object Pose and 

Camera Calibration Algorithms 

By William F. Oberle and Gary A. Haas 

ARL-TR-3147 April 2004 

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ARL-TR-3147 April 2004 

LADAR – Camera Registration Using Object Pose and 

Camera Calibration Algorithms 

William F. Oberle and Gary A. Haas 

Weapons and Materials Research Directorate, ARL 

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 LADAR – Camera Registration Using Object Pose and Camera Calibration 

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14. ABSTRACT 

To be effective, combining or fusing data from a variety of sensors requires all the data to be placed within the context of a 

common coordinate system. The process of determining the relation between the various sensor coordinate systems is termed 

“registration”. This work investigates the registration between a LADAR sensor and an imagery camera. Both object pose and 

camera calibration algorithms are explored. The two methods providing the best results are an object pose method, POSIT, by 

DeMenthon and Davis, University of Maryland, College Park, and a camera calibration method by Bouguet. 

15. SUBJECT TERMS

 camera calibration; LADAR; object pose; sensor registration 

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iii

Contents 

List of Figures v 

List of Tables vi 

Acknowledgments vii 

1. Introduction 1 

2. Criteria and Candidate Methods 3 

3. Test Data 5 

4. Evaluation Procedure 12 

4.1 Synthetic Data ...............................................................................................................12 

4.2 Experimental Data.........................................................................................................13 

4.3 Comparing Rigid Body Transformations......................................................................15 

5. Evaluation Results 16 

5.1 Synthetic Data Results...................................................................................................16

5.1.1 Calculation 1......................................................................................................16 

5.1.2 Calculation 2......................................................................................................16 

5.1.3 Calculation 3......................................................................................................21 

5.2 Experimental Data Results ............................................................................................22 

5.2.1 Comparison With RLR and TLR ...........................................................................22 

5.2.2 Comparison With Image Pixel Locations .........................................................23 

6. Discussion and Conclusions 25 

7. References 29 

Appendix A. C++ Code for Mapping Original Intensity Image Pixels to Rotated 

Intensity Image Pixels 31 

Appendix B. Matched Points Riegl LADAR and Stereo Camera Pair 33 
iv

Appendix C. C++ Code to Read Data for the Rotated Intensity Image (created with the 

program in Appendix A) and to Determine 3-D Locations 35 

Appendix D. MATLAB Function to Map 3-D Points to Pixel Coordinates RBA Format 37 

Appendix E. Synthetic Pixel Coordinates 39 

Appendix F. MATLAB Function to Compare Two RBTs 41 

Appendix G. MATLAB Script File to Select Random Subsets and Perform a 

Comparison 43 

Appendix H. MATLAB Script File to Compare Mapping of LADAR Data to Left and 

Right Images Via Computed RBTs 45 

Appendix I. Rigid Body Transformations 47 

Appendix J. Calculated Transformation Between Left and Right Cameras 49 

Appendix K. RBT With Rotated LADAR Data 51 

Distribution List 53 
v

List of Figures 

Figure 1. Schematic of camera coordinate system and LOS to world point P. ..............................3 

Figure 2. LADAR and cameras mounted on HMMWV used for data collection. .........................6 

Figure 3. Schematic of LADAR (red) and camera (blue) coordinate systems. (LADAR is 

behind, above, and to the right of the camera.).........................................................................7 

Figure 4. Intensity image recorded by Riegl LADAR....................................................................7 

Figure 5. Left and right images from stereo camera pair................................................................8 

Figure 6. Matched points (+) in LADAR intensity image..............................................................9 

Figure 7. Matched points (+) for left stereo image. ........................................................................9 

Figure 8. Matched points (+) for right stereo image.....................................................................10 

Figure 9. Schematic of original and rotated LADAR intensity image .........................................10 

Figure 10. Header information and first two lines of the Reigl LADAR 3-D data output ...........11 

Figure 11. Error(R1,R2) for POSIT calculations, synthetic data calculation 2. ...........................17 

Figure 12. Angle between translation vector and Ts for POSIT calculations, synthetic data 

calculation 2.............................................................................................................................17 

Figure 13. Percent difference in vector norm between translation vector and Ts for POSIT 

calculations, synthetic data calculation 2.................................................................................18 

Figure 14. Error(R1,R2) for Tsai calculations, synthetic data calculation 2. ...............................18 

Figure 15. Angle between translation vector and Ts for Tsai calculations, synthetic data 

calculation 2.............................................................................................................................19 

Figure 16. Percent difference in vector norm between translation vector and Ts for Tsai 

calculations, synthetic data calculation 2.................................................................................19 

Figure 17. Error(R1,R2) for Bouguet calculations, synthetic data calculation 2..........................20 

Figure 18. Angle between translation vector and Ts for Bouguet calculations, synthetic data 

calculation 2.............................................................................................................................20 

Figure 19. Percent difference in vector norm between translation vector and Ts for Bouguet 

calculations, synthetic data calculation 2.................................................................................21 

Figure 20. Schematic of experimental stereo camera configuration and two possible 

translation vectors. ...................................................................................................................23 

Figure 21. Projected LADAR points (red square) via POSIT-calculated transfor-mation 

between LADAR and left camera; pixel locations used in calculation also shown (green 

triangle)....................................................................................................................................24 

Figure 22. Projected LADAR points (red square) via POSIT-calculated transfor-mation 

between LADAR and right camera; pixel locations used in calculation also shown (green 

triangle)....................................................................................................................................24 
vi

Figure 23. Projected LADAR points (red square) with Tsai calculated transformation 

between LADAR and left camera; pixel locations used in calculation also shown (green 

triangle)....................................................................................................................................25 

Figure 24. Projected LADAR points (red square) with Bouguet calculated trans-formation 

with rotated LADAR data between LADAR and left camera; pixel locations used in 

calculation also shown (green triangle). ..................................................................................28 

Figure 25. Projected LADAR points (red square) with Bouguet calculated trans-formation 

with rotated LADAR data between LADAR and right camera; pixel locations used in 

calculation also shown (green triangle). ..................................................................................28 

List of Tables 

Table 1. Intrinsic parameters for the cameras used in the study...................................................12 

Table 2. Results of synthetic data calculation 1 for the candidate methods. ................................16 

Table 3. Results for calculation 3 with synthetic data. .................................................................21 

Table 4. Results of the comparison for the different camera registrations with RLR and TLR........22 

Table 5. Statistical results of projecting the 3-D LADAR points onto the left and right 

camera images with the RBTs computed by the candidate methods.......................................23 

Table 6. Results of the comparison for the different camera registrations with RLR and TLR for 

the calculations using the rotated LADAR data. .....................................................................26 

Table 7. Results of the projection of the LADAR data onto the left camera image with 

rotated LADAR data for the candidate methods and non-rotated LADAR data for the 

POSIT method. ........................................................................................................................27 
vii

Acknowledgments

The authors would like to thank Thomas Haug of the U.S. Army Research Laboratory (ARL) for 

his time and effort in reviewing the report. His comments and suggestions proved valuable in 

the preparation of the final version of the report. Furthermore, we would like to thank Dr. Daniel 

DeMenthon of the University of Maryland, College Park, Maryland, for providing the POSIT 

code and the many discussions concerning the use of the code. 

This work was the outgrowth of research performed under Cooperative Research and 

Development Agreement No. 0312-A-C799 between the University of Maryland and ARL. 
viii

INTENTIONALLY LEFT BLANK. 
1

1. Introduction 

To accomplish autonomous mobility, an unmanned ground vehicle (UGV) relies on data 

supplied by a variety of sensors as it navigates its way through unfamiliar terrain. These 

mobility sensors can basically be classified into two categories: those that provide data 

concerning the location and orientation of the UGV relative to the world (navigation) and those 

that detect and provide data concerning the location of objects within the immediate environment 

of the UGV (obstacle detection). Sensors in the former category include inertial navigation 

systems and global positioning systems, while laser radar (LADAR) and imagery cameras 

(monocular or stereo) are examples of sensors in the latter category. Although current UGV 

architectures integrate or fuse1 navigation data, it does not appear that the same can be said for 

obstacle detection data. Yet, only through the integration or fusion of all available information 

can the data provided by the obstacle detection sensors be fully exploited. 

Essential to the data fusion procedure is the capability of expressing all data to be fused within 

the same reference frame. For obstacle detection sensors, the common reference frame of 

interest is preferably the same coordinate system used by the navigation sensors but more likely, 

the coordinate system associated with one of the sensors. Each sensor records data relative to its 

own individual coordinate system. Assuming mutually orthogonal coordinate axes with the 

same relative orientation (i.e., right-handed or left-handed coordinate system), at any instance in 

time, there exists a rigid body transformation (RBT) between the coordinate system of any pair 

of sensors. This RBT is parameterized by translations along and rotations about the three 

coordinate axes expressed as a rotation matrix and translation vector. Determining the RBT 

between sensors is referred to as “sensor registration.” 

Of interest in this report is sensor registration between a LADAR sensor and a calibrated2

imagery camera. In this case, the sensor registration problem is equivalent to the object pose 

problem, i.e., computation of the rotation matrix and translation vector between a threedimensional (3-D) object(s) and a camera, given a number of correspondences (matches) 

between 3-D object(s), reference points, and their images (DeMenthon and Davis, 1995).3 

Likewise, the LADAR-camera registration problem is conceptually similar to camera calibration. 

However, camera calibration is more general in that the camera calibration procedure estimates 

the intrinsic camera parameters and the registration RBT at the same time. 

 1Hall and Llinas define data fusion by “data fusion techniques combine data from multiple sensors and related information 

from associated databases to achieve improved accuracy and more specific inferences that could be achieved by the use of single

sensor alone” (Wald, 1999). 

2Calibrated camera refers to a camera for which the intrinsic parameters are known. The intrinsic camera parameters include 

the image center (pixels), focal length (millimeters), physical dimensions of the image pixels (millimeters), and the angle 

between x-axis and y-axis of the pixels. See Trucco and Verri (1998) for additional details. 

3Some authors require that the entire geometry of the 3-D object be known for the object pose problem. In this report, a less 

restrictive viewpoint is taken (i.e., only a small number of points on the 3-D object must be specified). 
2

LADAR sensors provide 3-D coordinates (relative to the LADAR coordinate system) of objects 

within their field of view (FOV), whereas a camera provides a projective two-dimensional (2-D) 

image (i.e., measured intensity of reflected light) of objects in its FOV. Although distance 

measurements are not given by the camera data, the geometry of the camera does provide 

information relative to lines of sight (LOS) of objects relative to the camera coordinate system 

(see figure 1). In the figure, let P represent a world (LADAR) point in the FOV of the camera 

and P1 the image of P. If the camera is calibrated, the 3-D coordinates of P1 in the camera 

coordinate system are known. Thus, the ray OP1 defines the LOS for the world (LADAR) point 

P in the camera coordinate system. In the setting of the object pose problem, the LADARcamera registration problem can be posed as determining the RBT that maps the 3-D LADAR 

points into the camera coordinate system so that the mapped points lie on the appropriate LOS 

determined by the camera image points. This is also equivalent to projecting the 3-D LADAR 

onto the camera image in such a manner that the projected points coincide with the matched 

image points. Generally, one of two methods to solve the object pose problem is used. In the 

first method, optimization techniques are used to determine the RBT that minimizes the 

difference between the pixel coordinates of the projected 3-D points and their corresponding 

image points. The second method employs a two-step approach. First, 3-D coordinates of the 

known object points are determined in the camera coordinate system via the law of cosines.4 

This is followed in the second step by the determination of the RBT between the two sets of 3-D 

points (i.e., 3-D object points expressed in the world and camera coordinate systems). A more 

detailed description of the object pose problem is presented in Quan and Lan (1999) and 

references therein. For n matching points, Fischler and Bolles (1981) refer to this as the 

perspective-n-point problem (PnP problem). The camera calibration problem is described in 

almost all books on computer vision (e.g., Faugeras, 1993, or Trucco and Verri, 1998) and has 

been the focus of intense research in the vision community. Generally, methods to solve the 

camera calibration problem use the matched points and a camera model (e.g., pin-hole 

perspective camera) to generate a system of linear equations with the unknowns being the 

components of the RBT rotation matrix and translation vector, and intrinsic parameters. 

The remainder of the report is organized as follows. In section 2, the criteria for selecting a 

method for solving the LADAR-camera registration (object pose/camera calibration) problem are 

discussed, and candidate methods are identified. Section 3 provides details of the synthetic and 

experimental data used in evaluating candidate methods. Procedures used in evaluating the 

 4Consider two 3-D points, p1 and p2, on the object. Since the 3-D coordinates of p1 and p2 are known in the LADAR 

coordinate system, the distance between p1 and p2 can be determined. This distance is the same in both the camera and LADAR 

coordinate systems. Consider the triangle formed by p1, p2, and the camera center, O. Since the LOS to p1 and p2 can be 

determined, the angle ∠p1Op2 is known. Thus, the law of cosines can be used to write an equation expressing the distances Op1 

and Op2 (in the camera coordinate system) as a function of the distance p1p2 and the angle ∠p1Op2. If three points are 

considered, then three quadratic equations in the unknowns Op1, Op2, and Op3 can be solved simultaneously to obtain values for 

Op1, Op2, and Op3. It is then a simple calculation to determine the 3-D coordinates of p1, p2, and p3 in the camera coordinate 

system. The solution of the three simultaneous quadratic equations reduces to finding the roots of a single fourth order 

polynomial. 
3

candidate methods are discussed in section 4. Evaluation results are provided in section 5. 

Finally, section 6 provides a discussion of the results and conclusions. 

Optical 

Axis

Image

Plane

Image

Center

P

P1

P1 image of P

O

Camera

Center

Origin of Camera 

Coordinate System

Optical 

Axis

Image

Plane

Image

Center

P

P1

P1 image of P

Optical 

Axis

Image

Plane

Image

Center

P

P1

P1 image of P

Optical 

Axis

Image

Plane

Image

Center

P

P1

P1 image of P

O

Camera

Center

Origin of Camera 

Coordinate System

Figure 1. Schematic of camera coordinate system and 

LOS to world point P. 

2. Criteria and Candidate Methods 

As stated in the introduction, the intended use of the selected method is to determine the 

registration between a LADAR sensor and camera. These sensors will be mounted on an UGV 

traveling primarily over outdoor terrain. Although it is envisioned that the LADAR sensor and 

camera (most likely a stereo camera pair) will be rigidly mounted relative to each other within 

the “stereo rig,” periodic registration of the devices is likely to be necessary because of the 

vibration of the UGV as it travels over potentially rough terrain. Considering this operational 
4

domain, it would be desirable to have the candidate methods meet the following criteria. The 

method should 

1. be capable of handling real-world outdoor data typical of the UGV environment. 

2. be capable of working with sets of matched or control points that have no specific 

geometric construct. 

3. be capable of handling a wide range in the number of matched points. 

4. be capable of determining the registration with run times of less than several minutes. 

5. not require input data beyond the matched points and camera calibration information. 

6. provide a result without user intervention. 

The object pose and camera calibration problems have been studied by a large number of 

researchers (e.g., DeMenthon and Davis, 1995; Haralick, Lee, Ottenberg, and Nolle, 1991; 

Fischler and Bolles, 1981; Quan and Lan, 1999; Tsai, 1986 and 1987; Trucco and Verri, 1998, 

Faugeras, 1993; Willson, 1995; Baeten, 2003; Bouguet, 2003). None of the methods 

investigated for solving the object pose or camera calibration problems provided results for UGV 

environment-like data. In addition, results reported in the literature with these methods generally 

involved structured scenes, e.g., calibration posters. Thus, the first two criteria cannot be 

addressed on the basis of the literature review, nor will these two criteria be addressed in this 

report since the experimental data would also be considered a structured scene. 

For the object pose problem, the majority of methods ultimately require that the roots to a 

number of fourth order polynomials be determined (footnote 4, Quan and Lan, 1999). Both 

iterative and analytic methods have been applied to solving the required polynomials. However, 

as Quan and Lan (1999) state, “Iterative methods suffer from the problems of initialization and 

convergence, while algebraic methods applied to subsets suffer from poor noise filtering and the 

difficulty of selecting the common root from the noisy data.” To overcome these shortcomings, 

different researchers have imposed additional constraints on the problem to assist in determining 

the solution consistent with the input data. Fischler and Bolles (1981) introduced the random 

sample consensus (RANSAC) paradigm to minimize the impact of data outliers but also 

introduced the requirement to specify values for three unspecified parameters. Even after the 

input of outliers is purged, a separate method has to be applied to calculate the results. Others 

have restricted the image features associated with the matched points, generally lines or 

rectangles instead of points (Horaud, Conio, and Leboulleux, 1989; Abidi and Chandra, 1995). 

Still others have combined alternate image features with probabilistic approaches (Hanek, 

Navab, and Appel, 1999). However, the necessity to determine the roots of the fourth order 

polynomial remains. In addition, restricting image features violates the second criterion. 

Criterion number 3 eliminates those methods addressing the PnP problem for small values of n. 

Methods using a Newton-Raphson or similar approach to approximate the roots of the fourth 
5

order polynomial generally require a user-supplied initial estimate and do not satisfy the fifth 

criterion. 

Solutions to the camera calibration problem generally involve solving a system of linear 

equations. In general, the methods for solving systems of linear equations are consistent with the 

criteria listed previously. Thus, it would appear that camera calibration approaches offer the 

better possibility to address the LADAR-camera registration. Unfortunately, as Faugeras (1993, 

page 66) states, “But the fundamental instability of the (camera calibration) problem, ..., has 

delayed the availability of a robust and flexible technique, ...” This leads to most camera 

calibration methods being ill posed mathematically and highly susceptible to error because of 

noisy input data. To mitigate input noise, special surveyed calibration posters are often 

employed which is contrary to the second criterion. 

Cobzas, Zhang, and Jagersand (2002) addressed the registering of 3-D LADAR data to 2-D 

image data. Their conclusion was that point-based calibration methods performed best to 

recover a global registration between the sensors. Based on their observation and the previous 

discussion, both object pose and camera calibration methods operating directly on the matched 

points are selected as candidate methods for the LADAR-camera registration. 

The object pose method is by DeMenthon and Davis (1995) and termed “POSIT” (pose from 

orthography and scaling with iterations). Although this method does not guarantee convergence 

to a solution, testing performed with POSIT produced solutions in more than 99% of the test 

cases. Two camera calibration methods are chosen. The first is by Tsai5 (1986, 1987) and the 

second by Bouguet (2003). All three methods appear to have reasonable run times, best meet the 

criteria, and are highly recommended in the literature. Code for the POSIT calculations was 

provided by DeMenthon (January 2004). The Tsai method calculations were performed with 

Baeten’s (2003) MATLAB6

 version of Willson’s (1995) C implementation of Tsai’s method, 

both of which are available on line. The Camera Calibration Toolbox for MATLAB (available on 

line) (Bouguet, 2003) is used in the calculations based on Bouguet’s method. 

3. Test Data 

The test data consist of a combination of experimentally obtained and synthetically generated 

data. Experimental data used in this report were collected at the campus of the National Institute 

of Standards (NIST) in May 2003. A Riegl Z210 Laser Measurement Systems (LMS) (see 

references) LADAR sensor provided by NIST and a stereo camera pair (Sony DXC7 9000 

 5Non-coplanar calibration with full optimization option used. 

6MATLAB® is a registered trademark of The MathWorks. 

7

Not an acronym 
6

cameras) provided by the U.S. Army Research Laboratory (ARL) were used. A picture of the 

LADAR sensor and cameras mounted on the HMMWV (high mobility multipurpose wheeled 

vehicle) used for the data collection is shown in figure 2. Note that the LADAR sensor is 

mounted above, behind, and to the right of the stereo camera pair (relative to the camera 

coordinate system). A schematic of the LADAR and camera coordinate systems is shown in 

figure 3. The sensor coordinate systems are nearly aligned toward the scene, but the orientation 

of the axes is quite different. As will be seen in sections 5 and 6, this orientation of the two 

coordinate systems presents difficulties for the two camera calibration methods. NIST and ARL 

personnel jointly collected the data.8 An example of the imagery data recording the intensity of 

the reflected laser pulses recorded by the Riegl LADAR sensor is shown in figure 4. Image 

resolution is 536 by 616 (column by row) pixels and the image is rotated counter-clockwise by 

90 degrees because of the manner in which the LADAR data are collected. For each pixel in the 

intensity image, the Riegl LADAR software calculates the distance estimates as part of its 

standard output. The left and right images from the stereo cameras are shown in figure 5. 

Images are 640 by 480 (columns by row) pixels. 

Riegl LADAR

Stereo

Cameras

Figure 2. LADAR and cameras mounted on HMMWV used for data collection. 

In order to perform the registration calculations, the authors had to match the 3-D coordinates for 

points from the LADAR to 2-D pixel locations in the left and right camera images. The matching 

process is performed manually. For the purposes of identifying the matched points, the LADAR 

 8POCs: G. Haas (ARL/WMRD); P. Gillespie (ARL/SEDD); M. Shneier (NIST); H. Scott (NIST).
7

intensity image is used in combination with the camera image to select corresponding pixels in 

the three images. 

Scene

z

y

z

y

x

x

Scene

z

y

z

y

x

x

Figure 3. Schematic of LADAR (red) and 

camera (blue) coordinate systems. 

(LADAR is behind, above, and to the 

right of the camera.) 

Figure 4. Intensity image recorded by Riegl LADAR. 
8

Figure 5. Left and right images from stereo camera pair. 

The basic steps in the manual matching are 

1. Identify a feature common to all three images (LADAR intensity, left and right cameras). 

2. Determine by inspection the pixel location of the feature in each image. 

3. Use the Riegl output to match the feature pixel location in the LADAR intensity image 

with its 3-D coordinates. 

With this approach, 36 corresponding points were identified (see figures 6 through 8). However, 

manually matching points with the rotated LADAR intensity image in figure 4 with points in an 

upright camera image in figure 5 proved to be erroneous and tedious. Thus, the decision was 

made to rotate the LADAR intensity image. Rotating the image is easily accomplished with any 

image processing software. In the rotated image, pixel coordinates are mapped to new values to 

be consistent with the new orientation of the image and standard image notation. Figure 9 shows 

a schematic of the situation. The mapping of the pixel locations would be transparent except for 

the fact that the 3-D locations are associated with the pixels in the coordinates of the original 

intensity image, not the rotated intensity image. Thus, it is necessary to format the 3-D LADAR 

data to account for the pixel location change because of the rotation of the image. 

Figure 10 shows the header information and the first two lines of the original 3-D LADAR data 

file (besides the header information, there are as many as 536 * 616 = 330176 lines of 3-D 

position data). Each line of data consists of 11 entries identified in the header line VARIABLES. 

The first three entries are the 3-D coordinates (meters) of the object in the pixel. Entry number 4 

is the distance to the object computed with the standard Euclidean distance formula. This is 

followed by six entries not used in this report, which will not be discussed. The final entry is the 

measure id (D) that relates the data to a pixel location as defined by lines 3 through 5 of the 

header information. 
9

Figure 6. Matched points (+) in LADAR intensity image. 

Figure 7. Matched points (+) for left stereo image. 
10

Figure 8. Matched points (+) for right stereo image. 

(0,535)

(0,615)

(615,0)

(0,0) (535,0)

(0,0)

(535,615)

(615,535)

536 Columns

616 Rows

616 Columns

536 Rows

Original Ladar 

Image

Rotated Ladar 

Image

(0,535)

(0,615)

(615,0)

(0,0) (535,0)

(0,0)

(535,615)

(615,535)

536 Columns

616 Rows

616 Columns

536 Rows

Original Ladar 

Image

Rotated Ladar 

Image

Figure 9. Schematic of original and rotated LADAR intensity image. 
11

# ASCII Export File 

# Automatically generated by - 3D-RiSCAN 

# 3D data size - meas / line: 536 

# lines / image: 616 

# meas id = meas# + line# * (meas/line) 

# VARIABLES: X[m] Y[m] Z[m] R[m]_COR I cl_8_R cl_8_G cl_8_B P[deg]_COR 

A[deg]_COR D 

# FORMAT: %8.3f %8.3f %8.3f %8.3f %4.0f %4.0f %4.0f %4.0f %9.3f %9.3f %9.0f 

# 

 -11.903 3.789 2.608 12.761 140 255 255 255 78.209 162.344 0 

 -11.921 3.794 2.595 12.777 143 255 255 255 78.281 162.344 1 

Figure 10. Header information and first two lines of the Riegl LADAR 3-D data output.

If (XO,YO) represents the pixel coordinates in the original intensity image, (XR,YR) the 

corresponding pixel coordinates in the rotated image, and index the measure id for a line of data, 

then the following defines the mapping from the data in the original 3-D LADAR file to 3-D 

locations relative to the rotated LADAR intensity image. Line 5 of the header information in 

figure 10 defines the mapping from the measure id to pixels in the original intensity image. 

First, 

XO = meas# and YO = line#, 

which implies using line 5, 

index = XO + 536 * YO. (1) 

Now the relation between index and the pixel location in the original intensity image is defined 

by the standard approach used to store a 2-D array in a one-dimensional (1-D) array. Thus, 

XO = index mod 536, (2) 

and substituting equation 2 into equation 1 and solving for Yo, yields 

YO = (index - XO) / 536. 

Once the relation between the index and pixel coordinates in the original intensity image is 

computed, the mapping to the pixel coordinates in the rotated intensity image is given by 

XR = 615 - YO and, YR = XO. 

Appendix A provides a listing of the C++ program used to format the original LADAR data to 

correspond to the rotated intensity image. A complete listing of the matched points and the 3-D 

locations is provided in appendix B. A listing of the C++ code used to read the data for the 

rotated intensity image (created with the program in appendix A) and determine the 36 3-D 

locations is provided in appendix C. 

The candidate methods either assume calibrated cameras (POSIT) or require certain intrinsic 

parameters for each camera. The required values are provided in table 1. Each candidate 

method requires different intrinsic parameter input. The superscript indicates that if the 

parameter is required for a given method, P – POSIT, T – Tsai, B - Bouguet. 
12

Table 1. Intrinsic parameters for the cameras used in the study. 

Intrinsic Parameter Explanation Left 

Camera 

Right 

Camera 

Focal Length (pixel)P,B Camera focal length/physical size of picture element 865 852 

Center – XP,T,B (pixel) Horizontal pixel of intersection of optical axis and image plane 336 348 

Center – YP,T,B (pixel) Vertical pixel of intersection of optical axis and image plane 248 266 

NcxT Number of elements in a single row charge-coupled device 

(CCD) array 640 640 

NfxT Number of pixels in a single row CCD array 640 640 

dxT (millimeter) Horizontal distance between adjacent cells CCD array 0.01 0.01 

dyT (millimeter) Vertical distance between adjacent cells CCD array 0.01 0.01 

sxT Scale factor 1 1 

KcB Distortion coefficients All 0 All 0 

alpha_cB (radians) Skew coefficient 0 0 

4. Evaluation Procedure 

As mentioned in the introduction, the goal of the LADAR-camera registration is to determine the 

RBT that maps 3-D coordinates expressed in the coordinate system of the LADAR to 3-D 

coordinates in the coordinate system associated with the camera. This relationship can be 

expressed in one of two formats. The two formats differ, depending on which coordinate system 

is used to express the translation. If R is the rigid body rotation, pC a point represented in the 

camera coordinate system, and pL the same point in the LADAR coordinate system, then both of 

the following expressions can be use define the RBT between the LADAR and camera: 

 pC = R pL + TC or pC = R( pL – TL) (3) 

In the expression on the left, the translation is relative to the camera coordinate system, while the 

translation is relative to the LADAR coordinate system for the expression on the right. TC and 

TL are related by the relations 

 TC = -RTL or TL = -R-1TC.

Both formats are used in the report; the format given to the left in 3 is referred to as the rigid 

body A (RBA) and the format to the right as rigid body B (RBB). 

4.1 Synthetic Data 

Since no ground truth (i.e., the RBT between the LADAR and either camera image) is available, 

a set of synthetic image data is created with the 36 LADAR 3-D points from the set of matched 

points together with an arbitrary RBT. The RBT selected in RBA format is 
13

RS =

F

H

G

G

I

K

J

J

 0.08749666119173 0.99566917244726 0.03142026923014 

-0.04587594117370 0.03553521160292 - 0.99831490360395 

-0.99510789982882 0.08590778646042 0.04878647275366

and 

TS = b-0.33448540934011 0.89782925664977 15.22788837258931g. 

A MATLAB (2001) function to map the 3-D LADAR coordinates to camera pixel coordinates 

for a given RBA RBT and a camera with a given center and focal length (intrinsic parameters) is 

given in appendix D. The intrinsic parameters used in the calculation are those for the left-hand 

camera (see table 1). Details about transforming 3-D points in the camera coordinate system to 

pixel units are given in Trucco and Verri (1998). The synthetic pixel data are provided in 

appendix E. Note that the synthetic pixel data are given to subpixel accuracy. Thus, if the 3-D 

LADAR points and the matching synthetic pixel data are used as input, then the RBT defined by 

RS and TS becomes the ground truth for the calculation. 

With the 3-D LADAR-synthetic pixel data as input, three different calculations will be 

performed for each candidate method: 

1. Estimate the LADAR-camera registration, i.e., RBT, for each candidate method with all 

36 3-D LADAR-synthetic pixel data combinations as input. Compare the results to the 

RBT defined by RS and TS in order to assess the method’s capability to determine the 

LADAR-camera registration during ideal conditions (i.e., noise-free input data). See 

appendix F for MATLAB function to compare RBTs. Details about the comparison 

methodology are given in section 4.3. 

2. In order to access the each candidate method’s stability with different number of input 

points, use randomly selected subsets of the 36 3-D LADAR-synthetic pixel data 

combinations as input for each candidate method and estimate the LADAR-camera 

registration. Use 10 subsets each of 4 through 35 points. Compare the results to the RBT 

defined by RS and TS. See appendix G for a MATLAB script file to randomly select 

subsets from the matched points and perform the calculation and comparison. 

3. In order to access each candidate method’s capabilities to deal with noisy input data, 

round the synthetic pixel data to the nearest integer pixel and estimate the LADARcamera registration for each candidate method with all 36 3-D LADAR-rounded 

synthetic pixel data combinations. Compare the results to the RBT defined by RS and TS. 

4.2 Experimental Data 

The experimental data consist of the 36 matched 3-D LADAR points and pixel locations in the 

left and right camera images (see appendix B). Although there is no ground truth (i.e., 

registration) relating the LADAR and cameras, results from the candidate methods with the 
14

experimental data as input will be analyzed in two ways to assess the “goodness” of the 

calculated registrations (LADAR-left camera and LADAR-right camera). 

First, an approximate registration between the left and right cameras is available from earlier 

work (Oberle, 2004). The LADAR-left camera and LADAR-right camera registrations 

calculated by each candidate method with the experimental data can be combined to provide an 

estimate of the registration between the left and right cameras. This estimate can be compared to 

the approximate registration in Oberle (2004). The format of the registration in Oberle (2004) is 

RBB with 3-D points in the coordinate system of the left camera being mapped to 3-D points in 

the right camera. This registration is defined by 

RLR =

F

H

G

G

I

K

J

J

 0.9998008 0.0164890 - 0.0104682

-0.0163086 0.9998658 - 0.0038292

 0.0104173 0.0039948 0.9999360

and 

TLR = b334.761 -1.676 - 3.927g. 

The units for the translation TLR are in millimeters. Since the units for the LADAR data are 

meters (see appendix B), any translation vector determined by a candidate method will have to 

be converted to compatible units with TLR before comparison. 

The second approach to assess the goodness of the LADAR-left camera and LADAR-right 

camera registrations calculated by each candidate method is to use the registration to project the 

3-D LADAR points onto the left (right) camera image with a pinhole projective camera model 

and compare the projected points to the actual pixel coordinates in the experimental data. 

However, care should be exercised when one is interpreting the results for this calculation. 

Although there is a unique registration between the LADAR sensor and camera, there may be 

alternate RBTs that result in “acceptable” projections of the 3-D LADAR points onto the image 

plane. An application such as integrating color information from a camera image with point 

location information observed by a LADAR sensor (common in UGV terrain classification) 

might work adequately with such a registration, while another application such as fusing 3-D 

observations from LADAR with 3-D observations from stereoscopic vision would require a more 

correct RBT. 

Therefore, the procedure to evaluate the candidate methods with the experimental data involves 

five steps. 

1. Use the 36 matched experimental points for the LADAR and left camera to determine the 

RBT between the LADAR and left camera. 

2. Repeat step 1 for the right camera with the experimental points for the LADAR and right 

camera. 
15

3. Use the results of steps 1 and 2 to determine the RBT between the left and right cameras. 

4. Compare the result of step 3 to RLR and TLR. 

5. Project the LADAR points to pixel coordinates with the RBTs determined in steps 1 and 

2. Use the intrinsic parameters in table 1 and the code in appendix D to perform the 

projection. Determine the mean and standard deviation between the projected pixel 

values and the actual pixel values for the left and right camera images. The MATLAB 

script file to perform this operation is given in appendix H. 

4.3 Comparing Rigid Body Transformations 

An RBT is defined by a rotation and translation. Thus, to compare two RBTs, metrics to 

compare both the rotations and translations must be defined. In this report, the metric for 

comparing rotations is 

Error , frob frob frobR R R

R

R

R 1 2

1

1

2

2

b g bg bg = − F

H

G I

K

J, 

R1 and R2 are two rotation matrices, and frob is the Frobenius norm defined for the n-by-m 

matrix [Aij] as 

frob

2

1

m

1

n

A A ij ij

i j

e j = d i = =

∑∑ . 

Manning (2003) states that if Error(R1,R2) < 0.001, excellent 3-D reconstructions result. This 

value will be used as the figure of merit in comparing the rotations. 

Translation vectors are defined by their magnitude and direction. The percentage difference in 

the translation vector norms will be used to compare the magnitudes. Directions will be 

compared via the scalar vector product (dot product) to determine the angle between the two 

translation vector directions. No figure of merit for these values was found in the literature. 

Thus, three measures will be used in comparing the RBTs. 
16

5. Evaluation Results 

5.1 Synthetic Data Results 

5.1.1 Calculation 1 

Table 2 contains the results of the first calculation for the candidate methods described in 

section 4.1. The computed RBT for each method is given in appendix I. 

Table 2. Results of synthetic data calculation 1 for the candidate methods. 

Method Error(R1,R2) Percent Difference 

Norms (%) 

Angle Between Vectors 

(milliradians) 

POSIT 3.6603e-005 -0.00542 0.01779 

Tsai 7.3911e-007 -0.00014 0.0000596 

Bouguet 7.92894e-13 -8.1087e-11 1.49012e-05 

The results shown in table 2 indicate excellent agreement between the computed RBTs and RS

and TS. In all cases, the Error(R1,R2) is less than our figure of merit 0.001. The two camera 

calibration methods, Tsai and Bouguet, produce more accurate results than the object pose 

method POSIT. This is not unexpected since POSIT internally quantizes the pixels during part 

of its calculation. Based on these results, all three methods remain viable alternatives. 

5.1.2 Calculation 2 

For each candidate method, using 10 sets each of 4 through 35 points results in 320 different 

registration estimations. Results for Error(R1,R2), percent difference in translation vector norm, 

and the angle between the computed RBT translation vector and TS are presented in figures 11 

through 19 for the different candidate methods. For each graph, the abscissa is the number of 

matching data points provided to the candidate method as input. No attempt was made to ensure 

that the same sets of points were entered in the different candidate methods. An examination of 

the figures indicates that all three methods produce results similar to those in table 2 for almost 

all size-matching point sets. POSIT shows the largest variability in results among the three 

methods. Tsai’s method did not produce results for matching point sets of less than eight points 

because of the use of the non-coplanar calibration option. Bouguet’s method produced the 

largest differences of any method for matching point sets of size 4 and 5 but had the lowest 

overall differences for all matching point sets of size 6 and above. Based on these results, it 

would appear that the camera calibration methods are slightly better than the POSIT method for 

input matching data point sets containing a small number of points. However, it is noted that the 

POSIT results remain acceptable for matching point set sizes above 5 (see figure 11). The 
17

POSIT results simply exhibit greater variability than the results from the camera calibration 

methods. As with the first calculation, all methods would appear to remain viable candidates. 

Figure 11. Error(R1,R2) for POSIT calculations, synthetic data calculation 2. 

Figure 12. Angle between translation vector and Ts for POSIT calculations, synthetic data calculation 2.

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

0 510 15 20 25 30 35

Number Data Points

Angle Between Translati

o

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

0 5 10 15 20 25 30 35

Number Data Points

Error(R1,R2)Cut Off Line for Figure of Merit
18

Figure 13. Percent difference in vector norm between translation vector and Ts for POSIT calculations, synthetic 

data calculation 2. 

Figure 14. Error(R1,R2) for Tsai calculations, synthetic data calculation 2. 

-0.60

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0 5 10 15 20 25 30 35

Number Data Points

Percent Difference in Vector Magnitude

(%)

0.00E+00

1.00E-06

2.00E-06

3.00E-06

4.00E-06

5.00E-06

6.00E-06

7.00E-06

8.00E-06

9.00E-06

1.00E-05

0 5 10 15 20 25 30 35

Number Data Points

Error(R1,R2)
19

Figure 15. Angle between translation vector and Ts for Tsai calculations, synthetic data calculation 2.

Figure 16. Percent difference in vector norm between translation vector and Ts for Tsai calculations, synthetic data 

calculation 2. 

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

4.00E-03

4.50E-03

5.00E-03

0 5 10 15 20 25 30 35

Number Data Points

Angle between Translation Vectors 

(milliradians)

-4.00E-03

-2.00E-03

0.00E+00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

1.00E-02

0 5 10 15 20 25 30 35

Number Data Points

Percent Difference in Vector Magnitude (%)
20

Figure 17. Error(R1,R2) for Bouguet calculations, synthetic data calculation 2. 

Figure 18. Angle between translation vector and Ts for Bouguet calculations, synthetic data calculation 2. 

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 5 10 15 20 25 30 35

Number Data Points

Error(R1,R2)

0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

5.00E-04

6.00E-04

7.00E-04

8.00E-04

9.00E-04

1.00E-03

0 5 10 15 20 25 30 35

Number Data Points

Angle Between Translation Vectors 

(milliradians)
21

Figure 19. Percent difference in vector norm between translation vector and Ts for Bouguet calculations, synthetic 

data calculation 2.

5.1.3 Calculation 3 

Table 3 contains the results for the third calculation for the candidate methods with the synthetic 

data as described in section 4.1. The computed RBT for each method is given in appendix I. 

Table 3. Results for calculation 3 with synthetic data. 

Method Error(R1,R2) Percent Difference 

Norms (%) 

Angle Between Vectors 

(milliradians) 

POSIT 0.00196351029138 0.56183452476 0.804915808 

Tsai 0.00220136645337 -2.052962869152 2.120393461 

Bouguet 0.00849822281720 -1.01400487131609 0.49919040174060 

The only change in the input data for this calculation was the rounding of the image pixel points. 

This introduces an average error of approximately 0.25 pixel in the horizontal and vertical pixel 

values of each of the 36 2-D image points. Although the results in table 3 show that all three 

candidate methods produced poorer results compared to the error-free input data (table 2), the 

POSIT results did not degrade as much as the two camera calibration methods. This greater 

sensitivity of the camera calibration methods to noisy input data is consistent with the earlier 

comment by Faugeras (1993) and the observations of other researchers (e.g., Tapper, McKerrow, 

and Abrantes, 2002). The results of calculation 3 do not provide any reason to eliminate any of 

the candidate methods. However, the relatively large increase in errors for the camera 

calibration methods is worrisome. 

-1.00E-06

0.00E+00

1.00E-06

2.00E-06

3.00E-06

4.00E-06

5.00E-06

6.00E-06

0 5 10 15 20 25 30 35

Number Data Points

Percent Difference in Vector Magnitude (%)
22

5.2 Experimental Data Results 

5.2.1 Comparison With RLR and TLR

Table 4 contains the results of the comparison between the calculated transformation between the 

left and right cameras, and the transformation defined by RLR and TLR as described in section 4.2. 

The computed RBT for each method is given in appendix J. 

Table 4. Results of the comparison for the different camera registrations with RLR and TLR. 

Method Error(R1,R2) Percent Difference 

Norms (%) 

Angle Between Vectors 

(milliradians) 

POSIT 0.01204432894 -8.454 839.944 

Tsai 1.018288745457 -94.747 1456.860 

Bouguet 0.13158480563191 -76.143 1404.218 

Upon initial inspection of the results in table 4, it would appear that none of the results for the 

candidate methods compare well with the transformation defined by RLR and TLR. POSIT 

performs best among the candidates. Given the fact that RLR and TLR only approximately defines 

the registration between the cameras, the POSIT results would be considered good except for the 

difference of almost 840 milliradians (48 degrees) between the translation vectors. However, 

DeMenthon (April 2004) notes that the magnitude of the angle between the translation vectors 

may be misleading in situations when the distance between the camera centers (i.e., camera 

baseline) is small compared to the distance to scene elements. Assuming that TLR is a reasonable 

approximation to the true translation vector, the distance between the camera centers is roughly 

0.334788 meter. Referring to appendix B, the majority of scene elements (32 of the 36 LADAR 

points) are between approximately 7.5 and 17.5 meters from the sensors. Consider figure 20 

which schematically portrays the experimental configuration of the stereo cameras and two 

possible translation vectors. In this situation, the effective error in the estimated depth for the 

cameras is given by 0.334788 * tan(.839944) = 0.373458 meter. This represents only 2% to 5% 

of the depth of scene elements. Based on this result, the POSIT calculation compares favorably 

with RLR and TLR. The unknown in the calculation is the error in the input data since the 

matching of points was manually performed. However, at most there should be no more than a 

1- to 2-pixel error in the image pixel coordinates. The Riegl LMS Z210 documentation indicates 

3-D location errors of less than 20 parts per million. 
23

Figure 20. Schematic of experimental stereo camera configuration and 

two possible translation vectors. 

5.2.2 Comparison With Image Pixel Locations 

The results for the projection of the 3-D LADAR onto the left and right camera images are 

shown in table 5 for the mean and standard deviation and in figures 21 through 23. Figures 21 

and 22 are for the projections with RBTs computed by POSIT. Except for the four points in the 

foreground and lower right corner of the pink square of the calibration stand, the POSIT 

projections onto the left and right images agree well with the input pixel locations. These five 

points contribute significantly to the standard deviations in table 5 for the horizontal and vertical 

pixel differences observed in the left and right camera images. On the other hand, the Tsai and 

Bouguet methods produce extremely poor results. The means and standard deviations in table 5 

for these methods are very large. Figure 23 shows the projection of the 3-D LADAR points onto 

the left camera image for the Tsai RBT. As can be observed, only 29 of the 36 points even 

project onto the image, and these are not close to the actual pixel locations. No points were 

projected onto the right camera image with the Tsai RBT or onto either camera image with the 

Bouguet RBTs. Based on these results, the POSIT method would appear to be the best method 

to use in attempting to register LADAR sensors and cameras. 

Table 5. Statistical results of projecting the 3-D LADAR points onto the left and right camera images with the 

RBTs computed by the candidate methods. 

Method Left Camera Right Camera 

 Horizontal Vertical Horizontal Vertical 

Mean 

(pixels) 

Standard 

Deviation 

(pixels) 

Mean 

(pixels) 

Standard 

Deviation 

(pixels) 

Mean 

(pixels) 

Standard 

Deviation 

(pixels) 

Mean 

(pixels) 

Standard 

Deviation 

(pixels) 

POSIT -5.39 12.54 0.045 20.44 3.63 13.12 -4.74 16.99 

Tsai -214.29 168.31 37.86 34.63 -1940.1 10470 539.73 2661 

Bouguet -70694 487190 -89962 610429 5635 8178 7501 11752 

Left 

Camera

Center

Right 

Camera

Center

0.334788 m

Error In

Camera Depth

Calculated

Translation

Vector

True

Translation

Vector

Left 

Camera

Center

Right 

Camera

Center

0.334788 m

Error In

Camera Depth

Calculated

Translation

Vector

True

Translation

Vector
24

Figure 21. Projected LADAR points (red square) via POSIT-calculated transformation between LADAR and left camera; pixel locations used in 

calculation also shown (green triangle).

Figure 22. Projected LADAR points (red square) via POSIT-calculated transformation between LADAR and right camera; pixel locations used in 

calculation also shown (green triangle).
25

Figure 23. Projected LADAR points (red square) with Tsai-calculated transformation 

between LADAR and left camera; pixel locations used in calculation also 

shown (green triangle).

6. Discussion and Conclusions 

The focus of this report is to identify potential methods to register LADAR sensor and camera 

information in order to facilitate the fusion of the LADAR and camera data. Since LADAR data 

are 3-D and camera data are 2-D, the registration problem in this case is conceptually equivalent 

to both the object prose and camera calibration problems. Fortunately, both the object pose and 

camera calibration problems have been heavily studied and discussed in the computer vision 

literature. Drawing on this body of work, we selected three methods representing work in these 

areas to determine their applicability to the LADAR-camera registration problem. The methods 

are an object pose method, POSIT (DeMenthon, 1995), and two camera calibration methods, one 

by Tsai (1986, 1987) and the other by Bouguet (2003). 

Both synthetically generated (error free with ground truth) and experimental data without ground 

truth are used to evaluate the three methods. Results for all three methods involving the 

synthetically generated data compared favorably with the ground truth. However, it does appear, 

based on the limited calculations performed in the report, that the camera calibration methods are 

more sensitive to noisy input data. 
26

Except for the POSIT calculation, results for the experimental data are far less favorable. None 

of the camera calibration methods appeared to predict well the translation vector for the 

registration. The poor results of the projections of the 3-D LADAR points onto the left and right 

camera images for the Tsai and Bouguet methods are especially surprising, given their 

performances as documented in the vision literature. To address this concern, the orientation of 

the LADAR and camera coordinate systems is investigated. As shown in figure 3, the negative 

x-axis of the LADAR coordinate system is the axis along which depth is measured. Generally, 

depth is measured along the z-axis, and division by the z-component of the 3-D point is used to 

convert to homogeneous image coordinates. To investigate if the orientation of the LADAR 

coordinate system axes is the source of the poor performance of the Tsai and Bouguet methods, 

additional calculations are performed. Specifically, the experimental data calculations are 

repeated with the 3-D LADAR data rotated (basis vectors re-ordered) so that the axis orientation 

is roughly that of the camera data. Each 3-D LADAR data point is multiplied by the rotation 

matrix: 

0 1 0

0 0 -1 .

-1 0 0

    =      

R

In the Bouguet calculations, this is equivalent to using R and the vector (0 0 0) T = as the 

initial RBT estimate. The results of these calculations, together with the POSIT results with no 

rotation of the LADAR data, are provided in tables 6 and 7. The Tsai calculations for the 

LADAR to right camera produced unstable results (different results for repeated calculations 

with the same input, error message: possible handedness problem with data reported for several 

of the calculations). Appendix K lists the RBT from the POSIT and Bouguet calculations. 

Projections of the LADAR points onto the left and right camera images for the Bouguet 

calculations are given in figures 24 and 25. The projections for the POSIT calculations are the 

same as with the non-rotated LADAR data and are shown in figures 21 and 22. 

Table 6. Results of the comparison for the different camera registrations with RLR and TLR for the calculations 

using the rotated LADAR data. 

Method Error(R1,R2) Percent Difference 

Norms (%) 

Angle Between Vectors 

(milliradians) 

POSIT 

Non-Rotated LADAR Data 0.01204432894 -8.454 839.944 

POSIT 

Rotated LADAR Data 0.01204432894 -8.454 839.944 

Tsai 

Rotated LADAR Data Unstable Results Unstable Results Unstable Results 

Bouguet 

Rotated LADAR Data 0.00432979323664 1.3606 23.008 
27

Table 7. Results of the projection of the LADAR data onto the left camera image with rotated LADAR data for 

the candidate methods and non-rotated LADAR data for the POSIT method. 

Method Left Camera Right Camera 

 Horizontal Vertical Horizontal Vertical 

Mean 

(pixels) 

Standard 

Deviation 

(pixels) 

Mean 

(pixels) 

Standard 

Deviation 

(pixels) 

Mean 

(pixels) 

Standard 

Deviation 

(pixels) 

Mean 

(pixels) 

Standard 

Deviation 

(pixels) 

POSIT 

Non-Rotated 

LADAR Data 

-5.39 12.54 0.045 20.44 3.63 13.12 -4.74 16.99 

POSIT 

Rotated 

LADAR Data 

-5.39 12.54 0.045 20.44 3.63 13.12 -4.74 16.99 

Tsai 

Rotated 

LADAR Data 

1.06 18.52 -1.41 24.27 Unstable Results Unstable Results 

Bouguet 

Rotated 

LADAR Data 

-0.043 11.449 0.0272 15.8213 -0.0161 10.26 0.0429 15.73 

The results in tables 6 and 7 clearly show the improvement in the results produced by Bouguet’s 

method using the rotated LADAR data. In general, for UGV applications, the approximate 

orientation of the LADAR and camera coordinate systems is known. Thus, it should always be 

possible to re-order the 3-D LADAR data to align the depth along the LADAR coordinate 

system z-axis. Based on the results for the data set used in the paper, such an alignment of the 

LADAR data results in an excellent LADAR-camera registration (table 6) for Bouguet’s method. 

Thus, Bouguet’s method would appear to be the method of choice for estimating the LADARcamera registration. If, on the other hand, the objective is to determine a projection of the 

LADAR data onto the left and right camera images, the results in table 7 and figures 21, 22, 24, 

and 25 would indicate little to choose between POSIT and Bouguet’s method. Since the POSIT

calculation did not require pre-processing of the LADAR data, it would appear to be the better 

choice between the two methods. However, even in this situation, it is recommended that 

Bouguet’s method (with suitably aligned LADAR data) be employed with results compared to 

the POSIT results. 
28

Figure 24. Projected LADAR points (red square) with Bouguet calculated transformation with rotated LADAR data between LADAR and left camera; 

pixel locations used in calculation also shown (green triangle).

Figure 25. Projected LADAR points (red square) with Bouguet calculated transformation with rotated LADAR data between LADAR and right camera; 

pixel locations used in calculation also shown (green triangle).
29

7. References 

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Quadrangular Targets: Algorithm and Evaluation. IEEE Transactions on Patter Analysis 

and Machine Intelligence May 1995, 17 (5), 534–538. 

Baeten, J. Camera Calibration Under Matlab, Tsai camera calibration code software. 

Katholieke Universiteit Leuven, Belgium, 2003. Matlab code available online at web site: 

www.khlim.be/~jbaeten/star/camcalE.html. 

Bouguet, J.-Y. Camera Calibration Toolbox for Matlab, web site: http://www.vision.caltech. 

edu/bouguetj/, 2003. 

Cobzas, D.; Zhang, H.; Jagersand, M. A Comparative Analysis of Geometric and Image-Based 

Volumetric and Intensity Data Registration Algorithms. Proc. of IEEE International 

Conference on Robotics and Automation (ICRA 2002), Washington DC, May 2002. 

DeMenthon, D. F., Private Communications, University of Maryland, College Park, Maryland, 

January 2004. 

DeMenthon, D. F., Private Communications, University of Maryland, College Park, Maryland, 

April 2004. 

DeMenthon, D. F.; Davis, L. S. Model-Based Object Pose in 25 Lines of Code. International 

Journal of Computer Vision 1995, 15, 123–141. 

Faugeras, O. Three-Dimensional Computer Vision: A Geometric Viewpoint; The MIT Press: 

Cambridge, Massachusetts, 1993. 

Fischler, M.; Bolles, R. C. Random Sample Consensus: A Paradigm for Model Fitting with 

Applications to Image Analysis and Automated Cartography. Communications of the 

Association for Computing Machinery (ACM) June 1981, 24 (6), 381–395. 

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Approach using Points, Lines and Cylinders. IEEE Conference on Computer Vision and 

Pattern Recognition 1999, II, 544–550. 

Haralick, R. M.; Lee, C.; Ottenberg, K.; Nolle, M. Analysis and Solutions of the Three Point 

Perspective Pose Estimation Problem. Proceedings IEEE Conference of Computer Vision 

and Pattern Recognition, Maui, Hawaii, 1991; 592–598. 

Horaud, R.; Conio, B.; Leboulleux, O. An Analytic Solution for the Perspective 4-Point 

Problem. IEEE Computer Vision, Graphics, and Image Processing 1989, 47, 33–44. 
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Manning, R. A. Screw-Transform Manifolds for Camera Self Calibration. Ph.D. Thesis, 

University of Wisconsin-Madison, 2003. 

Oberle, W. F. The Effect of Variability in Stereo Camera Calibration and Registration 

Parameters on Three-Dimensional Reconstruction Distance Estimates; ARL-TR-3140; U. S. 

Army Research Laboratory: Aberdeen Proving Ground, Maryland, February 2004. 

Quan, L.; Lan, Z. Linear N-Point Camera Pose Determination. IEEE Transactions on Pattern 

Analysis and machine Intelligence July 1999, 21 (7), 774–780. 

Riegl Laser Measurement Systems GmbH, Horn, Austria, web site: www.riegl.com. 

Tapper, M.; McKerrow, P. J.; Abrantes, J. Problems Encountered in the Implementation of 

Tsai’s Algorithm for Camera Calibration. Proceedings 2002 Australasian Conference on 

Robotics and Automation, Auckland, 27–November 2002, 66 – 70. 

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http://www.mathworks.com, 2001. 

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Upper Saddle River, New Jersey, 1998. 

Tsai, R. An Efficient and Accurate Camera Calibration Technique for 3D Machine Vision. 

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Beach, FL, June 1986, 364 – 374,. 

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Automation August 1987, RA-3 (4), 323–344. 

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www/TsaiCode.html. 

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Remote Sensing May 1999, 37 (3), 1190. 
31

Appendix A. C++ Code for Mapping Original Intensity Image Pixels to 

Rotated Intensity Image Pixels 

#include <iostream> 

#include <fstream> 

#include <math.h> 

#include <stdlib.h> 

#include <iomanip> 

using namespace std; 

void main() 

{ 

 double x,y,z,r,a1,a2; 

 long int i,red,b,g,index; 

 char cLine[160]; 

 int iXO,iYO,iXR,iYR; 

 ifstream input(<Original LADAR data file>,ios::in | ios::binary); 

 ofstream output(<Output file>, ios::out | ios::binary); 

 

 for (int jj=0; jj<8;jj++) // Read and discard header information 

 { 

 input.getline(cLine,159,'\n'); 

 } 

output << "All information is relative to the upright image. X axis 

away from image:\n"; 

 output << "Y axis to right: Z axis upward\n"; 

output << setw(10) << "x" << setw(10) << "y" << setw(10) << "z" << 

setw(10) << "range" << setw(10) << "x(image)" << setw(10) << "y(image) 

\n"; 

WHILE (INPUT >> X >> Y >> Z >> R >> I >> RED >> B >> G >> A1 >> A2 >> INDEX) 

 { 

 cout << index; 

 iXO = index % 536; // Compute x coordinate in original image 

iYO = floor((index - iXS)/536); // Compute y coordinate in 

original image 

 iXR=615-iYO; // Compute x coordinate in rotated/upright image 

 iYR=iXO; // Same for y coordinate in rotate/upright image 

output << setw(10) << x << setw(10) << y << setw(10) << z << 

setw(10) << r << setw(10) << iXR << setw(10) << iYR << endl; 

 } 

 input.close(); 

 output.close(); 

} 
32

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33

Appendix B. Matched Points Riegl LADAR and Stereo Camera Pair 

LADAR 

Pixel 

LADAR 

3-D Location (m) 

Left Camera 

Image 

Right Camera 

Image 

X Y x y z X Y X Y 

156 120 -17.557 -4.845 1.009 103 155 87 174 

238 141 -16.413 -2.754 0.480 206 178 187 195 

234 167 -16.525 -2.851 -0.061 201 212 183 229 

235 189 -16.527 -2.838 -0.526 201 236 183 253 

218 188 -16.723 -3.235 -0.510 184 235 167 252 

218 167 -16.731 -3.237 -0.061 183 213 166 229 

297 125 -15.398 -1.408 0.759 280 156 259 173 

278 125 -15.661 -1.813 0.775 260 158 240 174 

219 96 -16.619 -3.191 1.449 183 125 164 143 

237 97 -16.327 -2.758 1.397 206 124 186 142 

219 140 -16.696 -3.206 0.514 182 177 165 195 

313 95 -7.681 -0.541 0.667 329 37 277 55 

347 95 -7.586 -0.209 0.659 374 37 321 55 

347 127 -14.699 -0.428 0.686 373 81 322 97 

313 126 -7.709 -0.543 0.368 328 81 277 98 

439 129 -7.643 0.680 0.337 462 84 409 99 

439 158 -7.651 0.680 0.058 504 85 452 98 

409 159 -7.711 0.391 0.048 503 129 451 143 

409 129 -7.640 0.388 0.336 461 128 409 142 

99 170 -18.547 -6.582 -0.146 32 221 20 241 

125 172 -18.271 -5.822 -0.189 65 223 50 242 

177 181 -11.851 -2.924 -0.259 132 207 106 225 

261 185 -11.632 -1.595 -0.308 242 209 213 225 

245 170 -11.728 -1.851 -0.087 223 191 196 208 

276 170 -16.239 -1.920 -0.121 260 191 230 206 

276 199 -11.812 -1.390 -0.521 259 226 232 242 

245 199 -11.496 -1.814 -0.509 224 226 196 243 

263 200 -11.715 -1.578 -0.532 244 227 217 243 

259 200 -11.755 -1.644 -0.536 239 227 211 242 

316 208 -9.429 -0.634 -0.522 320 220 282 236 

314 266 -9.523 -0.664 -1.225 317 299 280 313 

284 266 -9.555 -1.024 -1.233 277 301 242 315 

214 343 -4.380 -0.853 -1.015 205 312 102 327 

248 379 -4.378 -0.658 -1.218 266 377 164 392 

217 378 -4.350 -0.830 -1.214 209 376 110 392 

250 310 -4.421 -0.652 -0.825 273 249 166 266 
34

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35

Appendix C. C++ Code to Read Data for the Rotated Intensity Image 

(created with the program in Appendix A) and to Determine 3-D Locations 

#include <iostream> 

#include <fstream> 

#include <math.h> 

#include <stdlib.h> 

#include <iomanip> 

using namespace std; 

void main() 

{ 

 char cBuffer[100]; 

 int iCount = 0, iFlag, i, j, iCount1 = 0; 

 double data[100][9] = {0}, dJunk[6]; 

 bool bFlag = true; 

 ofstream OutPutData(<Output File Name>,ios::out|ios::binary); 

 while(bFlag) 

 { 

 cout << "Enter Riegl Image X Y:\n|------->>"; 

 cin >> data[iCount][0] >> data[iCount][1]; 

 cout << "Enter Left Image X Y:\n|------->>"; 

 cin >> data[iCount][5] >> data[iCount][6]; 

 cout << "Enter Right Image X Y:\n|------->>"; 

 cin >> data[iCount][7] >> data[iCount][8]; 

 iCount++; 

 cout << "Continue? |------->>\n"; 

 cin >> iFlag; 

 if(iFlag == 0) bFlag = false; 

 } 

 

 ifstream ReadData(<Input Data File>,ios::in | ios::binary); 

 for(i = 0; i < 3; i++) 

 ReadData.getline(cBuffer,sizeof(cBuffer)); 

 for(i = 0; i < 284682; i++)// There are 284682 lines of data 

 { 

 cout << "WORKING READING LINE: " << i << endl; 

ReadData >> dJunk[0] >> dJunk[1] >> dJunk[2] >> dJunk[3] >> dJunk[4] >> 

dJunk[5]; 

 for(j = 0; j < iCount; j++) 

 { 

 bFlag = false; 

 if( data[j][0] == dJunk[4] && data[j][1] == dJunk[5]) 

 { 

 data[j][2] = dJunk[0]; 

 data[j][3] = dJunk[1]; 

 data[j][4] = dJunk[2]; 

 iCount1++; 

 bFlag = true; 

 } 
36

 if (bFlag) break; 

 } 

 if(iCount == iCount1) break; 

 } 

 ReadData.close(); 

 for(i = 0; i < iCount; i++) 

 { 

 for(int j = 0 ; j < 9; j++) 

 { 

 OutPutData << data[i][j] << "\t"; 

 } 

 OutPutData << endl; 

 } 

 OutPutData.close(); 

} 
37

Appendix D. MATLAB Function to Map 3-D Points to Pixel Coordinates 

RBA Format 

function [CamPixel]= MapPts(rotNew1,transNew1,LadarPts,focalLength,centerLocation) 

% This function will compute the pixel locations of LadarPts under the 

% rigid-body transformation defined by (rotNew1,transNew1) for a camera 

% with the focalLength and camera centerLocation. The assumption is that 

% the rigid-body transformation is defined by pt(camera) = 

% rotNew1*pt(Ladar)+transNew1 

r0 = rotNew1 * LadarPts'; 

NumPts = length(LadarPts); 

for i=1:NumPts % Translataion is added 

 r1(1,i) = r0(1,i) + transNew1(1); 

 r1(2,i) = r0(2,i) + transNew1(2); 

 r1(3,i) = r0(3,i) + transNew1(3); 

end 

for i=1:3 

 for j=1:NumPts 

 r2(i,j) = r1(i,j)/r1(3,j); % Divide by Z coordinate 

 end 

end 

r3 = r2 .*focalLength; 

r4 = r3(1:2,:); % Select pixel coordinates 

for j = 1:NumPts 

 r5(1,j) = r4(1,j)+centerLocation(1); 

 r5(2,j) = r4(2,j)+centerLocation(2); 

end 

CamPixel = r5; % Return pixel coordinates 
38

INTENTIONALLY LEFT BLANK. 
39

Appendix E. Synthetic Pixel Coordinates 

1.0e+002 * 

 1.57740805375936 2.62013720111079 

 2.11894457809250 2.77628643947216 

 2.08801300881948 2.92469652490331 

 2.08671272940100 3.05298895046885 

 1.98035686146655 3.04427458696963 

 1.98477891560029 2.92111014475443 

 2.49126644629362 2.70613220452927 

 2.37772860358684 2.69929769711073 

 2.01154553183972 2.50748582644764 

 2.12625149304475 2.52260415161046 

 1.99883626877053 2.76385718297269 

 2.78317368772487 2.69385351425107 

 2.91001273192363 2.70033132558568 

 2.77316862153503 2.73270680529859 

 2.77827121881786 2.80708619332384 

 3.24084016564146 2.83349769827049 

 3.23723551750734 2.93891997313893 

 3.12680610410456 2.93916186592248 

 3.13086695611266 2.83033471412728 

 1.13546354326037 2.91379893079620 

 1.32611132377672 2.93164498856752 

 1.97284811919576 2.99600602200180 

 2.40252357198268 3.02600538329852 

 2.32260406641536 2.95138250814487 

 2.34282698539017 2.94978251045506 

 2.46772628326252 3.09576078765975 

 2.32721010394602 3.09033720635560 

 2.40599354018993 3.09832110535040 

 2.38478828376005 3.09866277366173 

 2.72276828227229 3.12493200210836 

 2.70306414433192 3.37148976237305 

 2.57590623396992 3.37029633409025 

 2.64941218052097 3.40516424123719 

 2.73309795950656 3.49801370764481 

 2.65661900992197 3.49516632130007 

 2.74155170873795 3.32196448051251 
40

INTENTIONALLY LEFT BLANK. 
41

Appendix F. MATLAB Function to Compare Two RBTs 

function[frob,angle,diffmag]=CompRBT(Rot1,Trans1,RotBase,TransBase) 

% This program will compute the statistics associated with the two 

% rigid-body transformations defined by (Rot1,Trans1) and 

% (RotBase,TransBase). The translations are assumed to be 3-by-1 column 

% vectors. See text for details. Calculations call the function 

% frobenious.m which takes as an argument the matrix for which the 

% frobenious norm will be determine. The return values are non-dimensional 

% for frob, milliradians for angle, and % for diffmag. 

% Start with the rotation matrix error. 

t1 = Rot1/frobenious(Rot1); 

t2 = RotBase/frobenious(RotBase); 

t3 = t1-t2; 

frob = frobenious(t3); 

% Next the percent difference in the translation vector norms. 

t1 = norm(Trans1); 

t2 = norm(TransBase); 

diffmag = (t1-t2)/t2*100; 

% Finally the angle between the vectors is computed. 

t3 = dot(Trans1,TransBase)/t1/t2; % Cosine of angle between vectors 

angle = acos(t3)*1000; 

function[norm]=frobenious(a) 

norm = sqrt(sum(sum(a.*a))); 
42

INTENTIONALLY LEFT BLANK. 
43

Appendix G. MATLAB Script File to Select Random Subsets and Perform a 

Comparison 

% This MATLAB script is ComparisonPosit.m and is used to perform 

% calculation 2 for the synthetic data as described in the body of the 

% text. Will select 10 each subsets of size 4 through 35. 

focalLength = focalLeft; % Left camera intrinsic data used in generating 

synthetic data 

centerLocation = centerLeft; 

fid=fopen('ComResultsPositRT.txt','w'); % Need to save certain information to 

files 

fid1=fopen('ComResultsPosit.txt','w'); % Error statistic only 

NumPts = 36; % 36 data points in synthetic data 

for i=4:35% Range of point subset size 

 for i1 = 1:10 % Going to do each subset 10 times. 

 index =randperm(NumPts); % First need to get the indices for the 

desired points 

 % Get the data from the image and Ladar data 

 array1 = PixelSD(index(1:i),:); 

 array2 = LadarData(index(1:i),:); 

 % Run the appropriate method for the data set (in this case 

 % classicPosit 

 

[rotNew,transNew,cbillNew]=classicPosit(array1,array2,focalLength,centerLocat

ion); 

 if (sum(sum(isnan(rotNew))) > 0) % Check to see if invalid calculation 

 continue

 end 

 [u,s,v]=svd(rotNew); % Use SVD to ensure result is orthogonal 

 rotNew = u*v'; 

 % Compute error statistics and save results 

 fprintf(fid,'**************\n'); % Writing out the transformation 

 fprintf(fid,'Number of Points = %d\n',i); 

 fprintf(fid,'%d\t%d\t%d\n',rotNew(1,1),rotNew(1,2),rotNew(1,3)); 

 fprintf(fid,'%d\t%d\t%d\n',rotNew(2,1),rotNew(2,2),rotNew(2,3)); 

 fprintf(fid,'%d\t%d\t%d\n',rotNew(3,1),rotNew(3,2),rotNew(3,3)); 

 fprintf(fid,'%d\t%d\t%d\n',transNew(1),transNew(2),transNew(3)); 

 

 [f,a,diff]=CompRBT(rotNew,transNew,RotSD,TransSD'); 

 fprintf(fid1,'%d\t%d\t%d\t%d\n',i,f,a,diff); % File #pts error(R1,R2) 

angle 

 diffmag 

 end % This is the end of the i1 loop. 

end % This is the end of i loop. 

fclose(fid); 

fclose(fid1); 
44

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45

Appendix H. MATLAB Script File to Compare Mapping of LADAR Data to 

Left and Right Images Via Computed RBTs 

% This script will use the rigid-body transformations to map a set 

% of 3-D points identified below (in the present case the LADAR data) to 

% the left and right images of a pair of cameras in order to compare the 

% accuracy of the mapping to the known image points. The computed values 

% are the mean and standard deviations of the mapped points to the known 

% image points. File: ComparePts.m 

% Mapping to Left image is performed 

[CamPixelLeft] = MapPts(RotPL,TransPL,LadarData,focalLeft,centerLeft); 

CamPixelLeft = CamPixelLeft'; 

% Plot the results on Image 

figure 

g1=imread('calWTargets2Left.ppm'); 

imshow(g1); 

hold on 

plot(CamPixelLeft(1:36,1),CamPixelLeft(1:36,2),'rs'); 

plot(LeftImage(1:36,1),LeftImage(1:36,2),'g^'); 

hold off 

A=CamPixelLeft - LeftImage; 

meanLeft=mean(A); 

stdevLeft=std(A); 

% Mapping to Right image is performed 

[CamPixelRight] = MapPts(RotPR,TransPR,LadarData,focalRight,centerRight); 

CamPixelRight=CamPixelRight'; 

% Plot the results on Image 

figure 

g1=imread('calWTargets2Right.ppm'); 

imshow(g1); 

hold on 

plot(CamPixelRight(1:36,1),CamPixelRight(1:36,2),'rs'); 

plot(RightImage(1:36,1),RightImage(1:36,2),'g^'); 

hold off 

A=CamPixelRight - RightImage; 

meanRight=mean(A); 

stdevRight=std(A); 
46

INTENTIONALLY LEFT BLANK. 
47

Appendix I. Rigid Body Transformations 

Calculation 1 Synthetic Data

POSIT Results: 

POSIT

 0.08748666618773 0.99566845370243 0.03147083635947

-0.04585758575663 0.03551371098605 -0.99831651201439

-0.99510990400993 0.08589620685912 0.04876592767895

    =

 

R

TPOSIT = ( ) -0.33455633740165 0.89803647081185 15.22704598173041

Tsai Results: 

Tsai

 0.087497 0.995669 0.031421

 -0.045876 0.035536 -0.998315

 -0.995108 0.085908 0.048787

    =

 

R

TTsai = ( ) -0.334484 0.897828 15.227867

Bouguet Results: 

RBouguet

0.08749666119233 0.99566917244720 0.03142026923023

-0.04587594117294 0.03553521160298 - 0.99831490360398

-0.99510789982880 0.08590778646105 0.04878647275293

=

F

H

G

G

I

K

J

J

TBouguet = b-0.33448540933926 0.89782925664899 15.22788837257698g
48

Calculation 3 Synthetic Data

POSIT Result:

RPOSIT

 0.08838084128758 0.99550902391960 0.03392064545307

 - 0.04476928444609 0.03442613693955 - 0.99840400252884

 - 0.99508795082035 0.08672118266350 0.04761083760550

=

F

H

G

G

I

K

J

J

TPOSIT = b-0.32896356714428 0.91275161928253 15.31301908881755g

Tsai Result:

Tsai

 0.090031 0.995464 0.030761

-0.046528 0.035057 -0.998302

-0.994852 0.088447 0.049473

    =

 

R

TTsai = ( ) -0.347514 0.903987 14.913345

Bouguet Result: 

RBouguet

 0.08236590309799 0.99613663662717 0.03045749786114

-0.05492915423154 0.03505247937352 - 0.99787479760999

-0.99508725548178 0.08051785428635 0.05760407206840

=

F

H

G

G

I

K

J

J

TBouguet = b g -0.32497859971989 0.89313339023542 15.07334937410542
49

Appendix J. Calculated Transformation Between Left and Right Cameras 

POSIT Result: 

RPOSIT

 0.99960296963107 0.01350158696889 - 0.02473075522642

-0.01366202010454 0.99988663530897 - 0.00632975016614

 0.02464248995963 0.00666510913820 0.99967410890188

=

F

H

G

G

I

K

J

J

TPOSIT = b0.20209774970646 0.03470469200352 - 0.22778169861526g 

(units in meters) 

Tsai Result: 

Tsai

 0.34038590296134 -0.36263792677361 0.86754318113310

-0.16174787504922 0.88630234522256 0.43394213643072

-0.92626943271505 -0.28803105200366 0.24302891000745

    =

 

R

TTsai = ( ) 1.80640315877847 2.12913142069132 -17.36208036043379 

(units in meters) 

Bouguet Result: 

RBouguet

0.99080254911237 - 0.08294852591746 - 0.10691047993790

0.09092714048446 0.99324808385759 0.07204511806185

0.10021259299983 - 0.08110355085536 0.99165500565615

=

F

H

G

G

I

K

J

J

TBouguet = b0.09036524651875 - 0.19845839189344 - 0.54790590935389g

(units in meters) 
50

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51

Appendix K. RBT With Rotated LADAR Data 

POSIT Result: 

RBT Left to Right Camera

 0.99960296963107 0.01350158696889 -0.02473075522642

-0.01366202010454 0.99988663530897 -0.00632975016614

 0.02464248995963 0.00666510913820 0.99967410890188

    =

 

R

T = ( ) 0.20209774970646 0.03470469200352 -0.22778169861526 

(units in meters) 

RBT LADAR to Left & Right Cameras

POSIT Left

 -0.01804441204342 0.99979479894226 -0.00920647609134

 0.01955163523604 -0.06370295006891 -0.99777736380022

 -0.99815909851653 -0.01818430754236 -0.01839814094038

→

    =

 

R

TPOSIT Left → = ( ) 0.28412019867384 -0.65591294859011 -1.80752603592876

(units in meters) 

POSIT Right

 0.00651548396152 0.99989344943916 -0.01306285716863

 0.02535246882550 -0.08636957903306 -0.99594053444074

-0.99696264989285 0.00615785889964 -0.02591250711268

→

    =

 

R

TPOSIT Right → ( ) 0.11173371995390 -0.68166055430343 -1.58181131726884

(units in meters) 

Tasi Result: Unstable results for LADAR to Right Camera – Error message: possible 

handedness problem in data 

Bouguet Result: 

RBT Left to Right Camera
52

 0.99971179944811 0.01873729760959 -0.01500772209572

-0.01881724903192 0.99980939677545 -0.00520396563945

 0.01490735332256 0.00548486989776 0.99987383555083

    =

 

R

T = ( ) 0.33915017084333 0.00062363907929 -0.01143244829854

(units in meters) 

RBT LADAR to Left & Right Cameras

Bouguet Left

-0.01356316099573 0.99975098568338 -0.01772025081386

 0.00026099474360 -0.01771834065446 -0.99984298381606

-0.99990798203912 -0.01356565625227 -0.00002061304530

→

    =

 

R

TBouguet Left → = ( ) 0.36290818771769 -0.81604891467805 -1.62854686949177

(units in meters) 

Bouguet Right

 0.00145197936667 0.99933445267465 -0.03644919002356

 0.00571965315642 -0.03645693154009 -0.99931885687725

-0.99998258851026 0.00124251363615 -0.00576878116893

R →

   

 

TBouguet Right → = ( ) 0.03271813694169 -0.80854854597228 -1.62103557239767

(units in meters) 
53

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 US ARMY RSCH LABORATORY 

 ATTN AMSRD ARL SE SE P GILLESPIE 

 N NASRABADI 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

 1 NATL INST OF STDS & TECHNOLOGY 

 ATTN DR M SHNEIER 

 BLDG 200 

 GAITHERSBURG MD 20899 

 2 UNIV OF MARYLAND 

 INST FOR ADV COMPUTER STUDIES 

 ATTN DR L DAVIS D DEMENTHON 

 COLLEGE PARK MD 20742-3251 

 ABERDEEN PROVING GROUND

 1 DIRECTOR 

 US ARMY RSCH LABORATORY 

 ATTN AMSRD ARL CI OK (TECH LIB) 

 BLDG 4600 

 2 DIRECTOR 

 US ARMY RSCH LABORATORY 

 ATTN AMSRD ARL WM J SMITH 

 T ROSENBERGER 

 BLDG 4600 

 2 DIRECTOR 

 US ARMY RSCH LABORATORY 

 ATTN AMSRD ARL WM B A HORST 

 W CIEPIELLA 

 BLDG 4600 

NO. OF 

COPIES ORGANIZATION

 16 DIRECTOR 

 US ARMY RSCH LABORATORY 

 ATTN AMSRD ARL WM BF H EDGE 

 M BARANOSKI P FAZIO 

 M FIELDS G HAAS (4 CYS) 

 T HAUG W OBERLE (4 CYS) 

 R PEARSON R VON WAHLDE 

 S WILKERSON 

 BLDG 390 

 2 DIRECTOR 

 US ARMY RSCH LABORATORY 

 ATTN AMSRD ARL WM RP C SHOEMAKER 

 J BORNSTEIN 

 BLDG 1121