This dissertation, "3D Metric Reconstruction From Uncalibrated Circular Motion Image Sequences" by Huang, Zhong, 鐘煌, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled 3D Metric Reconstruction from Uncalibrated Circular Motion Image Sequences submitted by Zhong Huang for the degree of Doctor of Philosophy at The University of Hong Kong May 2006 Circular motion is a practical motion for model acquisition. This thesis addresses the problem of metric reconstruction from uncalibrated circular motion image sequences from both the theoretical and practical viewpoints. The cameras are assumed to have constant intrinsic parameters, but the actual camera motion need not be known. A stratified geometric approach is taken to devise solutions. Algorithms for motion estimation, metric reconstruction and surface extraction are developed, by which an object model can be reconstructed systematically. First, a reconstruction method for circular motion is developed with the aim of estimating the unknown rotation angles of the camera robustly. This is achieved by enforcing the knowledge of the type of motion (i.e. the rotational motion constraint) in a factorization-based projective reconstruction, yielding what is called a circular projective reconstruction. Furthermore, a three-stage reconstruction approach with image points incrementally added in different stages of reconstructions is presented for computing a circular projective reconstruction from a long circular motion image sequence. This approach can cope with the missing data problem which inherently exists in a long image sequence. Second, the problem of computing a metric reconstruction from a circular projective reconstruction is considered. Two camera calibration methods are II proposed for resolving the metric reconstruction ambiguity in a circular projective reconstruction by exploring available calibration constraints. The methods are based on a new decomposition of a rectifying homography and developed for the cases involving one circular motion image sequence or one circular motion image sequence with one additional image. Finally, a fast model reconstruction method is proposed to extract the surface of an object from a calibrated circular motion image sequence. It is shown that 3D rim curves with known order enclosing the object can be reconstructed by means of the object silhouettes and feature points. These ordered rim curves allow a triangulated surface mesh of the object model to be constructed efficiently. Throughout the thesis, experimental results are given to demonstrate the performance of the proposed algorithms, and these results are shown to be both accurate and stable. III DOI: 10.5353/th_b3704379 Subjects: Three-dimensional imaging Image reconstruction Cameras - Calibration Algorithms

This dissertation, "3D Reconstruction and Camera Calibration From Circular-motion Image Sequences" by Yan, Li, 李燕, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled "3D Reconstruction and Camera Calibration from Circular-Motion Image Sequences" Submitted by Li Yan for the degree of Doctor of Philosophy at The University of Hong Kong in December 2005 This thesis investigates the problem of 3D reconstruction from circular motion image sequences. The problem is normally resolved in two steps: projective reconstruction and then metric reconstruction by self-calibration. A key question considered in this thesis is how to make use of the circular motion information to improve the reconstruction accuracy and reduce the reconstruction ambiguity. The information is previously utilized by identifying the fixed image entities (e.g. the image of the rotation axis, vanishing line of the motion plane, etc). These fixed entities, however, only exist in constant intrinsic parameter sequences. In this thesis, circular motion constraints, which are valid for varying intrinsic parameter (e.g. zooming/refocusing) cameras, are formulated from the movement of camera center and principal plane. Based on the constraints, several novel algorithms are developed for each step of the whole 3D reconstruction procedure. For image sequences with known rotation angles, a circular projective reconstruction algorithm is proposed. We first formulate the circular motion constraints in the Euclidean frame, and then deduce the most general form of reconstruction in a projective frame that satisfies the circular motion constraints. The constraints are gradually enforced during an iterative process, resulting in a circular projective reconstruction. This approach can be used to deal with both cases of constant and varying intrinsic parameters. It is proved that the circular projective reconstruction retrieves metric reconstruction up to a two-parameter ambiguity representing a projective distortion along the rotation axis of the circular motion. Based on the circular projective reconstruction, a hierarchical self-calibration algorithm is proposed to estimate the remaining two parameters. Closed-form expressions of the absolute conic and its image are deduced in terms of the two parameters, which are then determined with zero-skew and unit aspect ratio assumptions. Alternatively, starting from a general (rather than circular) projective reconstruction, a stratified self-calibration algorithm is proposed to upgrade the projective reconstruction directly to a metric one. In this case, the plane at infinity is first identified with (i) the circular motion constraint on camera center and (ii) zero-skew and unit aspect ratio assumptions. With the knowledge of the plane at infinity, the camera calibration matrices can be readily obtained. All the above algorithms assume that the rotation angles are known. In the case if the angles are unknown, we provide two novel rotation angle recovery methods. For constant intrinsic parameter sequences, rotation angles can be recovered by using the fixed image entities. For varying intrinsic parameter sequences, it is shown that the movements of the camera center and principal plane form two concentric circles on the motion plane. By identifying the corresponding conic loci in 3D projective frame, the geometry of circular motion on the motion plane can be recovered. Compared with existing methods, the new method is more flexible in that it allows the intrinsic parameters to vary, and is simpler by avoi

The issue discusses methods to extract 3-dimensional (3D) models from plain images. In particular, the 3D information is obtained from images for which the camera parameters are unknown. The principles underlying such uncalibrated structure-from-motion methods are outlined. First, a short review of 3D acquisition technologies puts such methods in a wider context, and highlights their important advantages. Then, the actual theory behind this line of research is given. The authors have tried to keep the text maximally self-contained, therefore also avoiding to rely on an extensive knowledge of the projective concepts that usually appear in texts about self-calibration 3D methods. Rather, mathematical explanations that are more amenable to intuition are given. The explanation of the theory includes the stratification of reconstructions obtained from image pairs as well as metric reconstruction on the basis of more than 2 images combined with some additional knowledge about the cameras used. Readers who want to obtain more practical information about how to implement such uncalibrated structure-from-motion pipelines may be interested in two more Foundations and Trends issues written by the same authors. Together with this issue they can be read as a single tutorial on the subject.

In his master thesis, Sven Painer develops, implements, and evaluates a method to reconstruct the liver surface from monocular mini-laparoscopic sequences. The principal focus of his research is to create a basis for helping clinicians to write reports with quantitative descriptions of the liver surface. A Structure from Motion approach is performed to do a sparse reconstruction of the liver surface and subsequently this information is used in a variation based dense 3D reconstruction. The algorithms are formulated in a causal way, enabling the implementation to be run in real-time on an adequate hardware platform. The results show a significant performance increase and pave the way to give clinicians a feedback during video capturing to improve the quality of the reconstruction in the near future.

The problem of structure and motion recovery from image sequences is an important theme in computer vision. Considerable progress has been made in this field during the past two decades, resulting in successful applications in robot navigation, augmented reality, industrial inspection, medical image analysis, and digital entertainment, among other areas. However, many of these methods work only for rigid objects and static scenes. The study of non-rigid structure from motion is not only of academic significance, but also has important practical applications in real-world, nonrigid or dynamic scenarios, such as human facial expressions and moving vehicles. This practical guide/reference provides a comprehensive overview of Euclidean structure and motion recovery, with a specific focus on factorization-based algorithms. The book discusses the latest research in this field, including the extension of the factorization algorithm to recover the structure of non-rigid objects, and presents some new algorithms developed by the authors. Readers require no significant knowledge of computer vision, although some background on projective geometry and matrix computation would be beneficial. Topics and features: presents the first systematic study of structure and motion recovery of both rigid and non-rigid objects from images sequences; discusses in depth the theory, techniques, and applications of rigid and non-rigid factorization methods in three dimensional computer vision; examines numerous factorization algorithms, covering affine, perspective and quasi-perspective projection models; provides appendices describing the mathematical principles behind projective geometry, matrix decomposition, least squares, and nonlinear estimation techniques; includes chapter-ending review questions, and a glossary of terms used in the book. This unique text offers practical guidance in real applications and implementations of 3D modeling systems for practitioners in computer vision and pattern recognition, as well as serving as an invaluable source of new algorithms and methodologies for structure and motion recovery for graduate students and researchers.