c ○ 2003 Kluwer Academic Publishers. Manufactured in The Netherlands. Understanding the Behavior of SFM Algorithms: A Geometric Approach

Abstract. We put forth in this paper a geometrically motivated motion error analysis which is capable of supporting investigation of global effect such as inherent ambiguities. This is in contrast with the usual statistical kinds of motion error analyses which can only deal with local effect such as noise perturbations, and where much of the results regarding global ambiguities are empirical in nature. The error expression that we derive allows us to predict the exact conditions likely to cause ambiguities and how these ambiguities vary with motion types such as lateral or forward motion. Given the erroneous 3-D motion estimates caused by the inherent ambiguities, it is also important to study the behavior of the resultant distortion in depth recovered under different motion-scene configurations. Such an investigation may alert us to the occurrence of ambiguities under different conditions and be more careful in picking the solution. Our formulation, though geometrically motivated, was also put to use in modeling the effect of noise and in revealing the strong influence of feature distribution. Experiments on both synthetic and real image sequences were conducted to verify the various theoretical predictions. Keywords: structure from motion, error analysis, epipolar constraint, inherent ambiguity, depth distortio

Object Tracking in Distributed Video Networks Using Multi-Dimentional Signatures

From being an expensive toy in the hands of governmental agencies, computers have evolved a long way from the huge vacuum tube-based machines to today\u27s small but more than thousand times powerful personal computers. Computers have long been investigated as the foundation for an artificial vision system. The computer vision discipline has seen a rapid development over the past few decades from rudimentary motion detection systems to complex modekbased object motion analyzing algorithms. Our work is one such improvement over previous algorithms developed for the purpose of object motion analysis in video feeds. Our work is based on the principle of multi-dimensional object signatures. Object signatures are constructed from individual attributes extracted through video processing. While past work has proceeded on similar lines, the lack of a comprehensive object definition model severely restricts the application of such algorithms to controlled situations. In conditions with varying external factors, such algorithms perform less efficiently due to inherent assumptions of constancy of attribute values. Our approach assumes a variable environment where the attribute values recorded of an object are deemed prone to variability. The variations in the accuracy in object attribute values has been addressed by incorporating weights for each attribute that vary according to local conditions at a sensor location. This ensures that attribute values with higher accuracy can be accorded more credibility in the object matching process. Variations in attribute values (such as surface color of the object) were also addressed by means of applying error corrections such as shadow elimination from the detected object profile. Experiments were conducted to verify our hypothesis. The results established the validity of our approach as higher matching accuracy was obtained with our multi-dimensional approach than with a single-attribute based comparison

Robust techniques for the estimation of structure from motion in the uncalibrated case

Robust techniques are developed for determining structure from motion in the uncalibrated case. The structure recovery is based on previous work [7] in which it was shown that a camera undergoing unknown motion and having an unknown, and possibly varying, focal length can be self-calibrated via closed-form expressions in the entries of two matrices derivable from an instantaneous optical flow field. Critical to the recovery process is the obtaining of accurate numerical estimates, up to a scalar factor, of these matrices in the presence of noisy optical flow data. We present techniques for the determination of these matrices via least-squares methods, and also a way of enforcing a dependency constraint that is imposed on these matrices. A method for eliminating outlying flow vectors is also given. Results of experiments with real-image sequences are presented that suggest that the approach holds promise.Michael J. Brooks, Wojciech Chojnacki, Anton van den Hengel, Luis Baumel