Specialization of Perceptual Processes

In this report, I discuss the use of vision to support concrete, everyday activity. I will argue that a variety of interesting tasks can be solved using simple and inexpensive vision systems. I will provide a number of working examples in the form of a state-of-the-art mobile robot, Polly, which uses vision to give primitive tours of the seventh floor of the MIT AI Laboratory. By current standards, the robot has a broad behavioral repertoire and is both simple and inexpensive (the complete robot was built for less than $20,000 using commercial board-level components). The approach I will use will be to treat the structure of the agent's activity---its task and environment---as positive resources for the vision system designer. By performing a careful analysis of task and environment, the designer can determine a broad space of mechanisms which can perform the desired activity. My principal thesis is that for a broad range of activities, the space of applicable mechanisms will be broad enough to include a number mechanisms which are simple and economical. The simplest mechanisms that solve a given problem will typically be quite specialized to that problem. One thus worries that building simple vision systems will be require a great deal of {it ad-hoc} engineering that cannot be transferred to other problems. My second thesis is that specialized systems can be analyzed and understood in a principled manner, one that allows general lessons to be extracted from specialized systems. I will present a general approach to analyzing specialization through the use of transformations that provably improve performance. By demonstrating a sequence of transformations that derive a specialized system from a more general one, we can summarize the specialization of the former in a compact form that makes explicit the additional assumptions that it makes about its environment. The summary can be used to predict the performance of the system in novel environments. Individual transformations can be recycled in the design of future systems.

Feature Matching for Object Localization in the Presence of Uncertainty

We consider the problem of matching model and sensory data features in the presence of geometric uncertainty, for the purpose of object localization and identification. The problem is to construct sets of model feature and sensory data feature pairs that are geometrically consistent given that there is uncertainty in the geometry of the sensory data features. If there is no geometric uncertainty, polynomial-time algorithms are possible for feature matching, yet these approaches can fail when there is uncertainty in the geometry of data features. Existing matching and recognition techniques which account for the geometric uncertainty in features either cannot guarantee finding a correct solution, or can construct geometrically consistent sets of feature pairs yet have worst case exponential complexity in terms of the number of features. The major new contribution of this work is to demonstrate a polynomial-time algorithm for constructing sets of geometrically consistent feature pairs given uncertainty in the geometry of the data features. We show that under a certain model of geometric uncertainty the feature matching problem in the presence of uncertainty is of polynomial complexity. This has important theoretical implications by demonstrating an upper bound on the complexity of the matching problem, an by offering insight into the nature of the matching problem itself. These insights prove useful in the solution to the matching problem in higher dimensional cases as well, such as matching three-dimensional models to either two or three-dimensional sensory data. The approach is based on an analysis of the space of feasible transformation parameters. This paper outlines the mathematical basis for the method, and describes the implementation of an algorithm for the procedure. Experiments demonstrating the method are reported.

Transition Space

Informal causal descriptions of physical systems abound in sources such as encyclopedias, reports and user's manuals. Yet these descriptions remain largely opaque to computer processing. This paper proposes a representational framework in which such descriptions are viewed as providing partial specifications of paths in a space of possible transitions, or transition space. In this framework, the task of comprehending informal causal descriptions emerges as one of completing the specifications of paths in transition space---filling causal gaps and relating accounts of activity varied by analogy and abstraction. The use of the representation and its operations is illustrated in the context of a simple description concerning rocket propulsion.

Probabilistic Solution of Inverse Problems

In this thesis we study the general problem of reconstructing a function, defined on a finite lattice from a set of incomplete, noisy and/or ambiguous observations. The goal of this work is to demonstrate the generality and practical value of a probabilistic (in particular, Bayesian) approach to this problem, particularly in the context of Computer Vision. In this approach, the prior knowledge about the solution is expressed in the form of a Gibbsian probability distribution on the space of all possible functions, so that the reconstruction task is formulated as an estimation problem. Our main contributions are the following: (1) We introduce the use of specific error criteria for the design of the optimal Bayesian estimators for several classes of problems, and propose a general (Monte Carlo) procedure for approximating them. This new approach leads to a substantial improvement over the existing schemes, both regarding the quality of the results (particularly for low signal to noise ratios) and the computational efficiency. (2) We apply the Bayesian appraoch to the solution of several problems, some of which are formulated and solved in these terms for the first time. Specifically, these applications are: teh reconstruction of piecewise constant surfaces from sparse and noisy observationsl; the reconstruction of depth from stereoscopic pairs of images and the formation of perceptual clusters. (3) For each one of these applications, we develop fast, deterministic algorithms that approximate the optimal estimators, and illustrate their performance on both synthetic and real data. (4) We propose a new method, based on the analysis of the residual process, for estimating the parameters of the probabilistic models directly from the noisy observations. This scheme leads to an algorithm, which has no free parameters, for the restoration of piecewise uniform images. (5) We analyze the implementation of the algorithms that we develop in non-conventional hardware, such as massively parallel digital machines, and analog and hybrid networks.

Properties of Support Vector Machines

Support Vector Machines (SVMs) perform pattern recognition between two point classes by finding a decision surface determined by certain points of the training set, termed Support Vectors (SV). This surface, which in some feature space of possibly infinite dimension can be regarded as a hyperplane, is obtained from the solution of a problem of quadratic programming that depends on a regularization parameter. In this paper we study some mathematical properties of support vectors and show that the decision surface can be written as the sum of two orthogonal terms, the first depending only on the margin vectors (which are SVs lying on the margin), the second proportional to the regularization parameter. For almost all values of the parameter, this enables us to predict how the decision surface varies for small parameter changes. In the special but important case of feature space of finite dimension m, we also show that there are at most m+1 margin vectors and observe that m+1 SVs are usually sufficient to fully determine the decision surface. For relatively small m this latter result leads to a consistent reduction of the SV number.

Pose Determination of a Grasped Object Using Limited Sensing

This report explores methods for determining the pose of a grasped object using only limited sensor information. The problem of pose determination is to find the position of an object relative to the hand. The information is useful when grasped objects are being manipulated. The problem is hard because of the large space of grasp configurations and the large amount of uncertainty inherent in dexterous hand control. By studying limited sensing approaches, the problem's inherent constraints can be better understood. This understanding helps to show how additional sensor data can be used to make recognition methods more effective and robust.