Ebook: Epipolar Geometry in Stereo, Motion and Object Recognition: A Unified Approach

Appendix 164 3. A 3. A. 1 Approximate Estimation of Fundamental Matrix from General Matrix 164 3. A. 2 Estimation of Affine Transformation 165 4 RECOVERY OF EPIPOLAR GEOMETRY FROM LINE SEGMENTS OR LINES 167 Line Segments or Straight Lines 168 4. 1 4. 2 Solving Motion Using Line Segments Between Two Views 173 4. 2. 1 Overlap of Two Corresponding Line Segments 173 Estimating Motion by Maximizing Overlap 175 4. 2. 2 Implementation Details 4. 2. 3 176 Reconstructing 3D Line Segments 4. 2. 4 179 4. 2. 5 Experimental Results 180 4. 2. 6 Discussions 192 4. 3 Determining Epipolar Geometry of Three Views 194 4. 3. 1 Trifocal Constraints for Point Matches 194 4. 3. 2 Trifocal Constraints for Line Correspondences 199 4. 3. 3 Linear Estimation of K, L, and M Using Points and Lines 200 4. 3. 4 Determining Camera Projection Matrices 201 4. 3. 5 Image Transfer 203 4. 4 Summary 204 5 REDEFINING STEREO, MOTION AND OBJECT RECOGNITION VIA EPIPOLAR GEOMETRY 205 5. 1 Conventional Approaches to Stereo, Motion and Object Recognition 205 5. 1. 1 Stereo 205 5. 1. 2 Motion 206 5. 1. 3 Object Recognition 207 5. 2 Correspondence in Stereo, Motion and Object Recognition as 1D Search 209 5. 2. 1 Stereo Matching 209 xi Contents 5. 2. 2 Motion Correspondence and Segmentation 209 5. 2. 3 3D Object Recognition and Localization 210 Disparity and Spatial Disparity Space 210 5.

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This book deals with one of the oldest problems in Computer Vision, namely to recover the 3-D geometric and kinematic structures of the world from two images, and to recognise a 3-D object in a cluttered scene from one or several views of this object in a different setting.
Several different problems have been unified through the use of a unique geometric concept. On the one hand, the geometrical point of view naturally leads to the consideration of the projective geometric structure which relates two images of the same object, the epipolar structure. On the other hand, the practitioner's point of view allows the reduction of the difficult 2-D search tasks encountered in the fundamental problems to much simpler 1-D search tasks, and, for the theoretically inclined reader, it ties the projective, affine and Euclidean structures of the scene to those of the images.
Audience: The authors have managed to avoid projective geometry in their exposition, and to guide the reader through the various aspects of epipolar geometry, stereo vision, motion analysis and object recognition using only the standard tools of linear algebra, thus making this a valuable book for a wide audience of researchers and engineers in image-related fields like vision, image processing, computer graphics, robotics, multi-media, and virtual reality.

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This book deals with one of the oldest problems in Computer Vision, namely to recover the 3-D geometric and kinematic structures of the world from two images, and to recognise a 3-D object in a cluttered scene from one or several views of this object in a different setting.
Several different problems have been unified through the use of a unique geometric concept. On the one hand, the geometrical point of view naturally leads to the consideration of the projective geometric structure which relates two images of the same object, the epipolar structure. On the other hand, the practitioner's point of view allows the reduction of the difficult 2-D search tasks encountered in the fundamental problems to much simpler 1-D search tasks, and, for the theoretically inclined reader, it ties the projective, affine and Euclidean structures of the scene to those of the images.
Audience: The authors have managed to avoid projective geometry in their exposition, and to guide the reader through the various aspects of epipolar geometry, stereo vision, motion analysis and object recognition using only the standard tools of linear algebra, thus making this a valuable book for a wide audience of researchers and engineers in image-related fields like vision, image processing, computer graphics, robotics, multi-media, and virtual reality.
Content:
Front Matter....Pages i-xix
Introduction....Pages 1-6
Camera Models and Epipolar Geometry....Pages 7-78
Recovery of Epipolar Geometry from Points....Pages 79-166
Recovery of Epipolar Geometry from Line Segments or Straight Lines....Pages 167-204
Redefining Stereo, Motion and Object Recognition Via Epipolar Geometry....Pages 205-219
Image Matching and Uncalibrated Stereo....Pages 221-245
Multiple Rigid Motions: Correspondence and Segmentation....Pages 247-267
3D Object Recognition and Localization with Model Views....Pages 269-289
Concluding Remarks....Pages 291-292
Back Matter....Pages 293-315

---

This book deals with one of the oldest problems in Computer Vision, namely to recover the 3-D geometric and kinematic structures of the world from two images, and to recognise a 3-D object in a cluttered scene from one or several views of this object in a different setting.
Several different problems have been unified through the use of a unique geometric concept. On the one hand, the geometrical point of view naturally leads to the consideration of the projective geometric structure which relates two images of the same object, the epipolar structure. On the other hand, the practitioner's point of view allows the reduction of the difficult 2-D search tasks encountered in the fundamental problems to much simpler 1-D search tasks, and, for the theoretically inclined reader, it ties the projective, affine and Euclidean structures of the scene to those of the images.
Audience: The authors have managed to avoid projective geometry in their exposition, and to guide the reader through the various aspects of epipolar geometry, stereo vision, motion analysis and object recognition using only the standard tools of linear algebra, thus making this a valuable book for a wide audience of researchers and engineers in image-related fields like vision, image processing, computer graphics, robotics, multi-media, and virtual reality.
Content:
Front Matter....Pages i-xix
Introduction....Pages 1-6
Camera Models and Epipolar Geometry....Pages 7-78
Recovery of Epipolar Geometry from Points....Pages 79-166
Recovery of Epipolar Geometry from Line Segments or Straight Lines....Pages 167-204
Redefining Stereo, Motion and Object Recognition Via Epipolar Geometry....Pages 205-219
Image Matching and Uncalibrated Stereo....Pages 221-245
Multiple Rigid Motions: Correspondence and Segmentation....Pages 247-267
3D Object Recognition and Localization with Model Views....Pages 269-289
Concluding Remarks....Pages 291-292
Back Matter....Pages 293-315
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