Affine Analysis of Image Sequences

by Larry S. Shapiro

• ISBN13: 9780521019781
• ISBN10: 0521019788
• Format: Paperback
• Copyright: 2005-09-15
• Publisher: Cambridge University Press

Summary

Computer vision is a rapidly growing field which aims to make computers 'see' as effectively as humans. In this book Dr Shapiro presents a new computer vision framework for interpreting time-varying imagery. This is an important task, since movement reveals valuable information about the environment. The fully-automated system operates on long, monocular image sequences containing multiple, independently-moving objects, and demonstrates the practical feasibility of recovering scene structure and motion in a bottom-up fashion. Real and synthetic examples are given throughout, with particular emphasis on image coding applications. Novel theory is derived in the context of the affine camera, a generalisation of the familiar scaled orthographic model. Analysis proceeds by tracking 'corner features' through successive frames and grouping the resulting trajectories into rigid objects using new clustering and outlier rejection techniques. The three-dimensional motion parameters are then computed via 'affine epipolar geometry', and 'affine structure' is used to generate alternative views of the object and fill in partial views. The use of all available features (over multiple frames) and the incorporation of statistical noise properties substantially improves existing algorithms, giving greater reliability and reduced noise sensitivity.

Table of Contents

Introduction	1	(8)
Motivation	1	(1)
Approach	1	(3)
Application: Model--based image coding	4	(1)
Thesis outline	5	(4)
Corner extraction and tracking	9	(26)
Introduction	9	(1)
Feature-based correspondence	9	(4)
Corner detection	13	(3)
The matcher	16	(8)
The tracker	24	(9)
Conclusions	33	(2)
The affine camera and affine structure	35	(26)
Introduction	35	(1)
Camera models	36	(7)
Affine stereo/motion equations	43	(1)
Affine structure using local coordinate frames	44	(8)
Affine structure without local coordinate frames	52	(7)
Conclusions	59	(2)
Clustering using maximum affinity spanning trees	61	(39)
Introduction	61	(1)
Maximum affinity spanning trees	62	(9)
Clustering concepts	71	(10)
The affinity measures	81	(5)
Termination criteria	86	(1)
Implementation	87	(4)
Results	91	(8)
Conclusions	99	(1)
Affine epipolar geometry	100	(15)
Introduction	100	(1)
The affine epipolar line	101	(2)
The affine fundamental matrix	103	(1)
Solving the affine epipolar equation	103	(8)
Experimental results	111	(1)
Epipolar geometry and CI space	112	(2)
Conclusions	114	(1)
Outlier rejection in an orthogonal regression framework	115	(29)
Introduction	115	(1)
Linear regression	116	(4)
Previous work on outlier rejection	120	(2)
Outlier rejection techniques	122	(12)
Error analysis	134	(4)
Affine epipolar geometry revisited	138	(2)
Conclusions	140	(4)
Rigid motion from affine epipolar geometry	144	(18)
Introduction	144	(1)
Motion ambiguities	145	(1)
Rigid motion: two views	146	(12)
Rigid motion: three views	158	(3)
Conclusions	161	(1)
Affine transfer	162	(13)
Introduction	162	(1)
Transfer using local coordinate frames	162	(1)
Transfer without local coordinate frames	163	(3)
Affine transfer using CI space	166	(2)
Results	168	(1)
Conclusions	168	(7)
Conclusions	175	(2)
Summary	175	(1)
Future work	175	(2)
Clustering proofs	177	(5)
MAST generation	177	(1)
Cluster Formation	178	(4)
Proofs for epipolar geometry minimisation	182	(4)
Cost function E1	182	(1)
Cost function E2	183	(1)
Cost function E3	184	(1)
Line-to-point and point-to-point cost functions	184	(2)
Proofs for outlier rejection	186	(4)
Matrix perturbation theory	186	(2)
Variance proofs	188	(2)
Rotation matrices	190	(2)
Angle-axis form	190	(1)
Euler-angle form	191	(1)
KvD form	191	(1)
KvD motion equations	192	(3)
KvD image motion equations	192	(2)
Epipolar-based image coordinates	194	(1)
Bibliography	195	(12)
Index	207