New Algorithms in Rigid-Body Registration and Estimation of Registration Accuracy

224 Pages·2008·3.99 MB·English

New Algorithms in Rigid-Body Registration and
Estimation of Registration Accuracy
by
Hedjazi Moghari Mehdi
A thesis submitted to the
Department of Electrical and Computer Engineering
in conformity with the requirements for
the degree of Doctor of Philosophy
Queen’s University
Kingston, Ontario, Canada
September 2008
Copyright c Hedjazi Moghari Mehdi, 2008
°
Abstract
Rigid-body registration is an important research area with major applications in
computer-assisted and image-guided surgery. In these surgeries, often the relation-
ship between the preoperative and intraoperative images taken from a patient must
be established. This relationship is computed through a registration process, which
finds a set of transformation parameters that maps some point fiducials measured
on a patient anatomy to a preoperative model. Due to point measurement error
caused by medical measurement instruments, the estimated registration parameters
are imperfect and this reduces the accuracy of the performed registrations. Medical
measurementinstrumentsoftenperturbthecollectedpointsfromthepatientanatomy
by heterogeneous noise. If the noise characteristics are known, they can be incorpo-
rated in the registration algorithm in order to more reliably and accurately estimate
the registration parameters and their variances.
Current techniques employed in rigid-body registration are primarily based on the
well-known Iterative Closest Points (ICP) algorithm. Such techniques are susceptible
to the existence of noise in the data sets, and are also very sensitive to the initial
alignment errors. Also, the literature offers no analytical solution on how to estimate
the accuracy of the performed registrations in the presence of heterogenous noise.
i
In an effort to alleviate these problems, we propose and validate various novel reg-
istration techniques based on the Unscented Kalman Filter (UKF) algorithm. This
filter is generally employed for analyzing nonlinear systems corrupted by additive
heterogenous Gaussian noise. First, we propose a new registration algorithm to fit
two data sets in the presence of arbitrary Gaussian noise, when the corresponding
points between the two data sets are assumed to be known. Next, we extend this
algorithm to perform surface-based registration, where point correspondences are not
available, but the data sets are roughly aligned. A solution to multi-body point and
surface-based registration problem is then proposed based on the UKF algorithm.
The outputs of the proposed UKF registration algorithms are then utilized to esti-
mate the accuracy of the performed registration. For the first time, novel derivations
are presented that can estimate the distribution of registration error at a target in
the presence of an arbitrary Gaussian noise.
ii
Acknowledgments
First, I would like to deeply thank my parents (Hossein& Fati) and my sister (Mona)
who have been my major supporters and encouragers while I have been abroad. Also,
I would like to especially thank Professors Mehrdad Abedi and Seyed Mohammad
Ahadi, my B.Sc. advisors, and Professor Abolghasem Raie, my M.Sc. advisor, in
the Department of Electrical and Computer Engineering at Amirkabir University of
Technology for encouraging and helping me to study my Ph.D. at Queen’s University
in Canada. I would like to thank Professors Majid Ahmadi and Behnam Shahrrava in
the Department of Electrical and Computer Engineering at the University of Windsor
for accepting me as a research assistant and helping me come to Canada.
My especial thanks to Professor Purang Abolmaesumi, my Ph.D. supervisor, who
accepted me as one of his students. Without his valuable support and guidance at
every stage, this work would not have been possible. I also wish to thank Professor
Armand from Johns Hopkins University, and Dr. Kunz and Dr. Beek from Kingston
General Hospital for providing me with medical data sets. Finally, I wish to thank
Dr. Ma, Mr. Chen and Mr. Tahmasebi for their collaboration and joint publications,
and Miss Bailey who helped me with my writing style.
Mehdi Hedjazi Moghari
September 26, 2008.
iii
Table of Contents
Abstract i
Acknowledgments iii
Table of Contents iv
List of Tables vii
List of Figures x
Glossary xiv
Chapter 1:
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Registration Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Contributions and Organization . . . . . . . . . . . . . . . . . . . . . 7
Chapter 2:
Rigid-body Registration . . . . . . . . . . . . . . . . . . . 10
2.1 Pairwise Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Multi-body Registration . . . . . . . . . . . . . . . . . . . . . . . . . 20
iv
2.3 Accuracy of the Performed Registration . . . . . . . . . . . . . . . . . 26
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Chapter 3:
Kalman Filtering and its Extensions . . . . . . . . . . . 31
3.1 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Extended Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3 Unscented Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Unscented Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Chapter 4:
UKF Pairwise Registration . . . . . . . . . . . . . . . . . 39
4.1 UKF Pairwise Point-based Registration . . . . . . . . . . . . . . . . . 40
4.2 UKF Pairwise Surface-based Registration . . . . . . . . . . . . . . . . 69
4.3 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 93
Chapter 5:
UKF Multi-body Registration . . . . . . . . . . . . . . . 98
5.1 UKF Multi-body Point-based Registration . . . . . . . . . . . . . . . 99
5.2 UKF Multi-body Surface-based Registration . . . . . . . . . . . . . . 102
5.3 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 111
Chapter 6:
Measurement of the Registration Accuracy . . . . . . . 114
6.1 Isotropic FLE Distribution . . . . . . . . . . . . . . . . . . . . . . . . 116
v
6.2 Arbitrary FLE Distribution . . . . . . . . . . . . . . . . . . . . . . . 141
6.3 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 171
Chapter 7:
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 175
7.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
Appendix A:
Statistical Anatomical Atlas Generation . . . . . . . . 200
Appendix B:
Local Point Descriptor . . . . . . . . . . . . . . . . . . . 202
Appendix C:
Proof of Cramer-Rao inequality . . . . . . . . . . . . . 205
vi
List of Tables
4.1 PerformancecomparisonamongUKF,Umeyama, andHornalgorithms
when FLE is isotropic and identical. . . . . . . . . . . . . . . . . . . . 55
4.2 PerformancecomparisonbetweenUKFandUmeyamaalgorithmswhen
FLE is inhomogeneous and anisotropic. . . . . . . . . . . . . . . . . . 56
4.3 Performance comparison between UKF and Umeyama algorithm when
FLE is anisotropic and identical. . . . . . . . . . . . . . . . . . . . . . 59
4.4 Performance comparison between UKF and Umeyama algorithm when
FLE is anisotropic and inhomogeneous. . . . . . . . . . . . . . . . . . 60
4.5 Sensitivity of UKF registration algorithm to variance of anisotropic
and identical FLE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.6 SensitivityofUKFregistrationalgorithmtovarianceofinhomogeneous
and anisotropic FLE. . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.7 Performance of UKF registration algorithm with 20% error in vari-
±
ance of FLE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.8 Performance of UKF registration algorithm with 50% error in vari-
±
ance of FLE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.9 Sensitivity of UKF registration algorithm to number of observations. 67
4.10 Performance comparison between UKF and EKF registration algo-
rithm when number of registering points is 30. . . . . . . . . . . . . . 68
vii
4.11 Performance comparison between UKF and EKF registration algo-
rithm when number of registering points is 150. . . . . . . . . . . . . 69
4.12 Comparison of convergence rate between UKF and ICP registration
algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.13 Sensitivity comparison of UKF and ICP registration algorithms to out-
liers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.1 Performance comparison between UKF and Pennec multi-body regis-
tration algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2 Convergence rate of UKF multi-body registration algorithm. . . . . . 107
6.1 Performance comparison between proposed and Fitzpatrick and West
TRE algorithms in estimation of TRE distribution. . . . . . . . . . . 130
6.2 Performance comparison between proposed and Fitzpatrick and West
algorithms in estimation of mean-squared value of TRE. . . . . . . . 130
6.3 Performance comparison between proposed and Fitzpatrick and West
algorithms when data sets are symmetric. . . . . . . . . . . . . . . . . 133
6.4 Performance comparison between proposed and Fitzpatrick and West
algorithms when data sets are asymmetric. . . . . . . . . . . . . . . . 134
6.5 Performanceofproposedalgorithminestimationofmean-squaredvalue
of TRE for different data sets. . . . . . . . . . . . . . . . . . . . . . . 142
6.6 Performance of ML TRE estimator when FLE is isotropic and inho-
mogeneous. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
6.7 Performance of ML TRE estimator when FLE is isotropic and identical.164
6.8 Performance of ML TRE estimator when FLE is anisotropic and iden-
tical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
viii
6.9 Performance of ML TRE estimator when FLE is anisotropic and inho-
mogeneous. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.10 Mean (mm) and variance (mm2) of error difference between the com-
puted root mean squared values of TRE at different target locations. 168
ix