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1996 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Epipolar Geometry in Stereo, Motion and Object Recognition

A Unified Approach

verfasst von: Gang Xu, Zhengyou Zhang

Verlag: Springer Netherlands

Buchreihe : Computational Imaging and Vision

Enthalten in: Professional Book Archive

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
Brain, including the perceptual systems, is probably the last hardest nut for scientists to crack. There are different approaches to this end. Neurophysiologists and psychophysicists have been investigating brain at different but complementary levels for many years. Since vision is the most “visible” part of the brain, it is also the most intensively studied part of the brain.
Gang Xu, Zhengyou Zhang
Chapter 2. Camera Models and Epipolar Geometry
Abstract
In this chapter we present a detailed description of the epipolar geometry between two images taken by two different cameras or by a single camera at two different time instants. Since it is intimately related to camera models, we will start from modeling cameras, followed by several approximations to the full perspective projection.
Gang Xu, Zhengyou Zhang
Chapter 3. Recovery of Epipolar Geometry from Points
Abstract
In this chapter, we present a number of methods to recover the epipolar geometry between two images from point matches. When the images are calibrated (i.e. their intrinsic parameters are known), the problem is equivalent to determining motion and structure. This has been widely studied in the last fifteen years. The minimum number of required point matches is five, which may give at most ten real solutions [39]. If more than 5 point matches are given, there usually exists a unique solution. When 8 or more point matches are available, a linear technique exists to solve the motion, which, however, usually yields an estimate sensitive to noise. Least-squares techniques are exploited to obtain a more robust estimate. Readers are referred to [41, Chap.7] for a complete exposition of the problem of motion and structure from motion.
Gang Xu, Zhengyou Zhang
Chapter 4. Recovery of Epipolar Geometry from Line Segments or Straight Lines
Abstract
Essentially, two types of geometric primitives have been used in solving motion and structure problem, namely points and straight lines. When points are used, two perspective views are sufficient to recover the motion and structure of the scene, as was described in the last chapter. When straight lines are used, three perspective views are necessary. Closed-form solutions are available either for point correspondences [90, 162] (and see the last chapter for uncalibrated images) or for line correspondences [147, 89, 58]. Algorithms using both points and lines are also available [146, 59]. However, another important type of geometric primitives, namely that of line segments, has been since long ignored in motion and structure from motionl, although the importance of line segments in computer vision has never been underestimated (as a matter of a fact, straight lines are merely the geometric abstraction of line segments by ignoring their endpoints). The overlook of line segments in the domain of motion and structure from motion is probably due to the lack of mathematical elegance in representing line segments.
Gang Xu, Zhengyou Zhang
Chapter 5. Redefining Stereo, Motion and Object Recognition Via Epipolar Geometry
Abstract
In this chapter, we review correspondence problems in stereo, motion, and object recognition from the epipolar geometry point of view, and the analysis shows that once the epipolar geometry is recovered, all can be redefined as a 1D correspondence search problem plus a segmentation problem which can be solved simultaneously.
Gang Xu, Zhengyou Zhang
Chapter 6. Image Matching and Uncalibrated Stereo
Abstract
Matching different images of a single scene remains one of the bottlenecks in computer vision. A large amount of work has been carried out during the last 15 years, but the results are, however, not satisfactory. The only geometric constraint we know between two images of a single scene is the epipolar constraint. However, when the motion between the two images is unknown, the epipolar geometry is also unknown. The methods reported in the literature all exploit some heuristics in one form or another, for example, intensity similarity, which are not applicable to most cases. The difficulty is partly bypassed by taking long sequences of images over short time interval [27, 183]. Indeed, as the time interval is small and object velocity is constrained by physical laws, the interframe displacements of objects are bounded, i.e., the correspondence of a token at the subsequent instant must be in the neighborhood of the first. However, in many cases, such as a pair of uncalibrated stereo images, this technique does not apply. Developing a robust image matching technique is thus very important.
Gang Xu, Zhengyou Zhang
Chapter 7. Multiple Rigid Motions: Correspondence and Segmentation
Abstract
Motion has been one of the main research topics in computer vision [96]. Traditionally, people have divided the motion problem into correspondence and structure-from-motion [164]. Actually, however, there is another problem, that is, segmentation of motion images into different rigid objects. Segmentation is very important itself, because in many real world tasks like target following segmentation is a precondition, perhaps more frequently required than accurate shape recovery. Also, from a computational point of view, it has to be solved in the case of multiple motions for both correct correspondence and structure-from-motion computation.
Gang Xu, Zhengyou Zhang
Chapter 8. 3D Object Recognition and Localization with Model Views
Abstract
The conventional approaches to 3D object recognition are mostly based on 3D object models. They include model-based feature grouping [91], model-based geometrical reasoning [16], constrained search [49], model fitting guided by local feature [18], feature based geometric hashing [83], automatic generation of search trees [75]. All these approaches rely on explicit 3D data as object model in this or that way. Unfortunately, however, 3D data are not always available for every object. In the case of manufactured objects, the data used in designing may be available. If one has to obtain the data by vision, then the difficulty is that there is still no algorithm available that works in every kind of environment.
Gang Xu, Zhengyou Zhang
Chapter 9. Concluding Remarks
Abstract
What we have tried to do in this book is to present a detailed description of the epipolar geometry which underlies every pair of images of the same scene, to formulate the problems of stereo, motion and view-based object recognition under a unified framework from the epipolar geometry viewpoint, and to solve these problems in a unified manner.
Gang Xu, Zhengyou Zhang
Backmatter
Metadaten
Titel
Epipolar Geometry in Stereo, Motion and Object Recognition
verfasst von
Gang Xu
Zhengyou Zhang
Copyright-Jahr
1996
Verlag
Springer Netherlands
Electronic ISBN
978-94-015-8668-9
Print ISBN
978-90-481-4743-4
DOI
https://doi.org/10.1007/978-94-015-8668-9