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This thesis contributes to the problem of 3D reconstruction for deformable surfaces using a single camera. In order to model surface deformation, we use the isometric prior because many real object deformations are near-isometric. Isometry implies that the surface cannot stretch or compress. We tackle two different problems. The first is called Shape-from-Template where the object's deformed shape is computed from a single image and a texture-mapped 3D template of the object surface. Previous methods propose a differential model of the problem and compute the local analytic solutions. In the methods the solution related to the depth-gradient is discarded and only the depth solution is used. We demonstrate that the depth solution lacks stability as the projection geometry tends to affine. We provide alternative methods based on the local analytic solutions of first-order quantities, such as the depth-gradient or surface normals. Our methods are stable in all projection geometries. The second type of problem, called Non-Rigid Shape-from-Motion is the more general templatefree reconstruction scenario. In this case one obtains the object's shapes from a set of images where it appears deformed. We contribute to this problem for both local and global solutions using the perspective camera. In the local or point-wise method, we solve for the surface normal at each point assuming infinitesimal planarity of the surface. We then compute the surface by integration. In the global method we find a convex relaxation of the problem. This is based on relaxing isometry to inextensibility and maximizing the surface's average depth. This solution combines all constraints into a single convex optimization program to compute depth and works for a sparse point representation of the surface. We detail the extensive experiments that were used to demonstrate the effectiveness of each of the proposed methods. The experiments show that our local template-free solution performs better than most of the previous methods. Our local template-based method and our global template-free method performs better than the state-of-the-art methods with robustness to correspondence noise. In particular, we are able to reconstruct difficult, non-smooth and articulating deformations with the latter; while with the former we can accurately reconstruct large deformations with images taken at very long focal lengths.
7. Future directions -- Bibliography -- Authors' biographies.
The sixteen-volume set comprising the LNCS volumes 11205-11220 constitutes the refereed proceedings of the 15th European Conference on Computer Vision, ECCV 2018, held in Munich, Germany, in September 2018.The 776 revised papers presented were carefully reviewed and selected from 2439 submissions. The papers are organized in topical sections on learning for vision; computational photography; human analysis; human sensing; stereo and reconstruction; optimization; matching and recognition; video attention; and poster sessions.
The seven-volume set comprising LNCS volumes 8689-8695 constitutes the refereed proceedings of the 13th European Conference on Computer Vision, ECCV 2014, held in Zurich, Switzerland, in September 2014. The 363 revised papers presented were carefully reviewed and selected from 1444 submissions. The papers are organized in topical sections on tracking and activity recognition; recognition; learning and inference; structure from motion and feature matching; computational photography and low-level vision; vision; segmentation and saliency; context and 3D scenes; motion and 3D scene analysis; and poster sessions.
Reviews the emerging field of geodesic methods and features the following: explanations of the mathematical foundations underlying these methods; discussion on the state of the art algorithms to compute shortest paths; review of several fields of application, including medical imaging segmentation, 3-D surface sampling and shape retrieval
This book formalizes and analyzes the relations between multiple views of a scene from the perspective of various types of geometries. A key feature is that it considers Euclidean and affine geometries as special cases of projective geometry. Over the last forty years, researchers have made great strides in elucidating the laws of image formation, processing, and understanding by animals, humans, and machines. This book describes the state of knowledge in one subarea of vision, the geometric laws that relate different views of a scene. Geometry, one of the oldest branches of mathematics, is the natural language for describing three-dimensional shapes and spatial relations. Projective geometry, the geometry that best models image formation, provides a unified framework for thinking about many geometric problems are relevant to vision. The book formalizes and analyzes the relations between multiple views of a scene from the perspective of various types of geometries. A key feature is that it considers Euclidean and affine geometries as special cases of projective geometry. Images play a prominent role in computer communications. Producers and users of images, in particular three-dimensional images, require a framework for stating and solving problems. The book offers a number of conceptual tools and theoretical results useful for the design of machine vision algorithms. It also illustrates these tools and results with many examples of real applications.
Provides guidance to researchers and developers when assessing the suitability of different methods for various applications. The authors focus on the practical aspects of the methods available, such as time complexity and robustness. They also provide multiple examples of parameterizations generated using different methods.
A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.
Here is, for the first time, a book that clearly explains and applies new level set methods to problems and applications in computer vision, graphics, and imaging. It is an essential compilation of survey chapters from the leading researchers in the field. The applications of the methods are emphasized.