Comment: Expert Elicitation for Reliable System Design

Comment: Expert Elicitation for Reliable System Design [arXiv:0708.0279]Comment: Published at http://dx.doi.org/10.1214/088342306000000547 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Convex relaxation of mixture regression with efficient algorithms

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data

Wide-baseline Stereo from Multiple Views: a Probabilistic Account

This paper describes a method for dense depth reconstruction from a small set of wide-baseline images. In a widebaseline setting an inherent difficulty which complicates the stereo-correspondence problem is self-occlusion. Also, we have to consider the possibility that image pixels in different images, which are projections of the same point in the scene, will have different color values due to non-Lambertian effects or discretization errors. We propose a Bayesian approach to tackle these problems. In this framework, the images are regarded as noisy measurements of an underlying ’true’ image-function. Also, the image data is considered incomplete, in the sense that we do not know which pixels from a particular image are occluded in the other images. We describe an EM-algorithm, which iterates between estimating values for all hidden quantities, and optimizing the current depth estimates. The algorithm has few free parameters, displays a stable convergence behavior and generates accurate depth estimates. The approach is illustrated with several challenging real-world examples. We also show how the algorithm can generate realistic view interpolations and how it merges the information of all images into a new, synthetic view

Segmentation based variational model for accurate optical flow estimation.

Chen, Jianing.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 47-54).Abstract also in Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Background --- p.1Chapter 1.2 --- Related Work --- p.3Chapter 1.3 --- Thesis Organization --- p.5Chapter 2 --- Review on Optical Flow Estimation --- p.6Chapter 2.1 --- Variational Model --- p.6Chapter 2.1.1 --- Basic Assumptions and Constraints --- p.6Chapter 2.1.2 --- More General Energy Functional --- p.9Chapter 2.2 --- Discontinuity Preserving Techniques --- p.9Chapter 2.2.1 --- Data Term Robustification --- p.10Chapter 2.2.2 --- Diffusion Based Regularization --- p.11Chapter 2.2.3 --- Segmentation --- p.15Chapter 2.3 --- Chapter Summary --- p.15Chapter 3 --- Segmentation Based Optical Flow Estimation --- p.17Chapter 3.1 --- Initial Flow --- p.17Chapter 3.2 --- Color-Motion Segmentation --- p.19Chapter 3.3 --- Parametric Flow Estimating Incorporating Segmentation --- p.21Chapter 3.4 --- Confidence Map Construction --- p.24Chapter 3.4.1 --- Occlusion detection --- p.24Chapter 3.4.2 --- Pixel-wise motion coherence --- p.24Chapter 3.4.3 --- Segment-wise model confidence --- p.26Chapter 3.5 --- Final Combined Variational Model --- p.28Chapter 3.6 --- Chapter Summary --- p.28Chapter 4 --- Experiment Results --- p.30Chapter 4.1 --- Quantitative Evaluation --- p.30Chapter 4.2 --- Warping Results --- p.34Chapter 4.3 --- Chapter Summary --- p.35Chapter 5 --- Application - Single Image Animation --- p.37Chapter 5.1 --- Introduction --- p.37Chapter 5.2 --- Approach --- p.38Chapter 5.2.1 --- Pre-Process Stage --- p.39Chapter 5.2.2 --- Coordinate Transform --- p.39Chapter 5.2.3 --- Motion Field Transfer --- p.41Chapter 5.2.4 --- Motion Editing and Apply --- p.41Chapter 5.2.5 --- Gradient-domain composition --- p.42Chapter 5.3 --- Experiments --- p.43Chapter 5.3.1 --- Active Motion Transfer --- p.43Chapter 5.3.2 --- Animate Stationary Temporal Dynamics --- p.44Chapter 5.4 --- Chapter Summary --- p.45Chapter 6 --- Conclusion --- p.46Bibliography --- p.4

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

Empirical Bayesian EM-based Motion Segmentation

A recent trend in motion-based segmentation has been to rely on statistical procedures derived from ExpectationMaximization (EM) principles. EM-based approaches have various attractives for segmentation, such as proceeding by taking non-greedy soft decisions with regards to the assignment of pixels to regions, or allowing the use of sophisticated priors capable of imposing spatial coherence on the segmentation. A practical difficulty with such priors is, however, the determination of appropriate values for their parameters. In this work, we exploit the fact that the EM framework is itself suited for empirical Bayesian data analysis to develop an algorithm that finds the estimates of the prior parameters which best explain the observed data. Such an approach maintains the Bayesian appeal of incorporating prior beliefs, but requires only a qualitative description of the prior, avoiding the requirement of a quantitative specification of its parameters. This eliminates the need for trial-a..