Robustness by consensus

This thesis presents a paradigm for performing robust model fitting. Model fitting is an essential part of many algorithms that try to interpret data. Such algorithms normally use least squares based estimation for fitting purposes. The least squares procedure is very sensitive to noise and variations in the data. Furthermore, it is frequently the case that a model discontinuity exists in the data and it cannot be reliably detected by conventional methods. Recently, new robust estimation methods have been introduced that deal with several types of variations and model discontinuities. Some of these methods are analyzed and shown not to be effective in the presence of noise that is usually found in image and signal data. The new paradigm integrates basic robust estimation methods, a decomposition of the problem and a relative majority analysis to perform robust estimation. The robust estimate is a consensus among independent, invariant estimates of sub-problems. The consensus paradigm is shown to provide effective algorithms for signal and image estimation, edge detection, segmentation, and contour matching. The performance of these algorithms is analyzed and compared to existing methods. The paradigm can also be used in connection with other computer vision problems such as stereo, flow and shape from X, as well as for more general sensor fusion and hypotheses integration algorithms.