Chapter 8. Ground from Figure Discrimination 8.5 Conclusions Chapter 8. Ground from Figure Discrimination Chapter 8. Ground from Figure Discrimination Chapter 8. Ground from Figure Discrimination

Visual processes deal with analyzing images and extracting information from them. They play an important role in many of todays industries, e.g., in the medical instrument industry, the electronic and micro-electronic industry, the movie industry, the robotics industry, and in many other elds which require automatic extraction of visual information from images. One of the major di culties in image analysis is that only a few subsets of the data features contain the useful information, while all others are not relevant for the task. The irrelevant features interfere with the visual process and make it more di cult, slower, and less accurate. Grouping processes, which rearrange the given data by eliminating the irrelevant data features and sorting the rest into groups each corresponding to a certain object, are indispensable in computer vision. In this thesis we propose a new framework for perceptual grouping in computer vision. The grouping information available to the process is represented by the grouping likelihood graph. We use this model to develop and analyze algorithms for several machine vision tasks. We present a grouping algorithm, a hypothesis veri cation algorithm, and a gure ground discrimination algorithm, which are based on known statistical tools, such as the Wald's Sequential Probability Ratio Test (SPRT), and the Maximum Likelihood criterion. The most important contribution of this work is the theoretical analysis of the algorithms|mainly the grouping algorithm. The performance analysis of the grouping algorithm allows us to predict the resulting grouping quality relative to the information available for the task. Such an analysis has never been done for grouping and is rarely found in other computer vision areas. This framework is fairly general, and does not depend on the domain. Three grouping algorithms, in three di erent domains, are synthesized as instances of the generic grouping method. They demonstrate the applicability and generality of this grouping method. Moreover, we show that the same perceptual information can be used for other visual tasks, such as gure ground discrimination, and hypothesis veri cation in object recognition. We believe that this framework could be useful for other tasks and domains in di erent levels of the visual system. iii Tecn io n C om pu te r Sc ie nc e D ep ar tm en t P h. D . T he si s P H D -1 99 701 1 99 7 5 The Cue Enhancement Procedure 49 5.1 Overview : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 49 5.2 Wald's SPRT and its Application to Cue Enhancement : : : : : : : : 50 5.3 Calculating P0fcm(A)g; P1fcm(A)g : : : : : : : : : : : : : : : : : : : 53 5.4 Optimizing the Raw Cue. : : : : : : : : : : : : : : : : : : : : : : : : 55 5.5 Conclusions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 56 6 Grouping Experimentation 59 6.1 A Heuristic Algorithm for the MLGC Criterion : : : : : : : : : : : : 59 6.2 Example 1: Grouping of Points Into Co-Linear Sets : : : : : : : : : : 62 6.3 Example 2: Grouping of Edgels Lying on Smooth Curves : : : : : : : 67 6.3.1 Creating a Saliency Map : : : : : : : : : : : : : : : : : : : : : 67 6.4 Example 3: Motion-Based Segmentation : : : : : : : : : : : : : : : : 71 7 Grouping-Based Hypothesis Veri cation 73 7.