Epipolar Geometry in Stereo, Motion and Object Recognition: by Gang Xu, Zhengyou Zhang

By Gang Xu, Zhengyou Zhang

Appendix 164 three. a three. A. 1 Approximate Estimation of basic Matrix from common Matrix 164 three. A. 2 Estimation of Affine Transformation a hundred sixty five four restoration OF EPIPOLAR GEOMETRY FROM LINE SEGMENTS OR strains 167 Line Segments or directly strains 168 four. 1 four. 2 fixing movement utilizing Line Segments among perspectives 173 four. 2. 1 Overlap of 2 Corresponding Line Segments 173 Estimating movement via Maximizing Overlap a hundred seventy five four. 2. 2 Implementation info four. 2. three 176 Reconstructing 3D Line Segments four. 2. four 179 four. 2. five Experimental effects a hundred and eighty four. 2. 6 Discussions 192 four. three choosing Epipolar Geometry of 3 perspectives 194 four. three. 1 Trifocal Constraints for element fits 194 four. three. 2 Trifocal Constraints for Line Correspondences 199 four. three. three Linear Estimation of ok, L, and M utilizing issues and features 2 hundred four. three. four choosing digital camera Projection Matrices 201 four. three. five photograph move 203 four. four precis 204 five REDEFINING STEREO, movement AND item acceptance through EPIPOLAR GEOMETRY 205 five. 1 traditional methods to Stereo, movement and item popularity 205 five. 1. 1 Stereo 205 five. 1. 2 movement 206 five. 1. three item acceptance 207 five. 2 Correspondence in Stereo, movement and item popularity as 1D seek 209 five. 2. 1 Stereo Matching 209 xi Contents five. 2. 2 movement Correspondence and Segmentation 209 five. 2. three 3D item popularity and Localization 210 Disparity and Spatial Disparity house 210 5.

Show description

Read Online or Download Epipolar Geometry in Stereo, Motion and Object Recognition: A Unified Approach PDF

Similar computer vision & pattern recognition books

Markov Models for Pattern Recognition: From Theory to Applications

Markov versions are used to unravel tough trend reputation difficulties at the foundation of sequential info as, e. g. , computerized speech or handwriting reputation. This finished creation to the Markov modeling framework describes either the underlying theoretical innovations of Markov types - protecting Hidden Markov versions and Markov chain types - as used for sequential facts and offers the options essential to construct winning structures for sensible purposes.

Cognitive Systems

Layout of cognitive platforms for advice to humans poses an incredible problem to the fields of robotics and synthetic intelligence. The Cognitive structures for Cognitive tips (CoSy) undertaking used to be prepared to handle the problems of i) theoretical development on layout of cognitive structures ii) tools for implementation of platforms and iii) empirical experiences to additional comprehend the use and interplay with such structures.

Motion History Images for Action Recognition and Understanding

Human motion research and popularity is a comparatively mature box, but one that is usually no longer good understood by way of scholars and researchers. the big variety of attainable diversifications in human movement and visual appeal, digital camera perspective, and setting, current significant demanding situations. a few vital and customary difficulties stay unsolved by means of the pc imaginative and prescient neighborhood.

Data Clustering: Theory, Algorithms, and Applications

Cluster research is an unmanaged strategy that divides a collection of gadgets into homogeneous teams. This publication starts off with easy details on cluster research, together with the category of knowledge and the corresponding similarity measures, by means of the presentation of over 50 clustering algorithms in teams in accordance with a few particular baseline methodologies corresponding to hierarchical, center-based, and search-based equipment.

Additional info for Epipolar Geometry in Stereo, Motion and Object Recognition: A Unified Approach

Example text

Sometimes, this projection is also called the scaled orthographic projection. When Zc is unity, the projection becomes the orthographic one. 5 (a) Orthographic projection. 6 The weak perspective model. 5). 21) where Twp = Here ri denotes the ith row vector of the rotation matrix R, and ti is the ith element of the translation vector t. It is clear that the relation between 3D coordinates and image coordinates is linear. Let us examine the approximation error introduced by the weak perspective projection.

P = [B b). Assume that the rank of B is 3. In Sect. 2, we explained that, under the pinhole model, the optical center projects to [0,0, O)T (Le. s = 0). e. PC [B b) [ C] 1 =0 . 17) Given matrix P and an image point m, we can obtain the equation of the 3-D semi-line defined by the optical center C and point m. This line is called the optical ray defined by m. Any point on it projects to the single point m. We already know that C is on the optical ray. To define it, we need another point. e. This gives D = B- 1 ( -b + iii).

55). 61). Therefore, we obtain geometrically the same equation. Now we reverse the role of the two images, and consider the epipolar line l~ in the second image for a given point m in the first image. Line l~ goes through the epipole e'. e. the scale factor is chosen to be 1. ' = A' [I 0] ~] = A'(AR)-l(iD - At) = A'R-l A-liD - A'R-lt . The epipolar line l~ is thus represented by l~ = -, x iii = -(A'R-lt) x (A'R-lA-liD) = -(A'R-l)-T(t x A-liD) = -A'-TRT[t]x A -liD = FTiD. s~s'me' In the above, we have used the following properties: = det(A)A -T (x x y), • (Ax) x (Ay) 'rIx, y if matrix A is invertible.

Download PDF sample

Rated 4.38 of 5 – based on 5 votes

admin