Direct Computation of 3D Shape Invariants and the Focus of Expansion

Structure from motion often refers to the computation of 3D structure from a matched sequence of images. However, a depth map of a surface is difficult to compute and may not be a good representation for storage and recognition. Given matched images, I will first show that the sign of the normal curvature in a given direction at a given point in the image can be computed from a simple difference of slopes of line-segments in one image. Using this result, local surface patches can be classified as convex, concave, parabolic (cylindrical), hyperbolic (saddle point) or planar. At the same time the translational component of the optical flow is obtained, from which the focus of expansion can be computed.

Parallel Computation of Vernier Offsets, Curvature and Chevrons in Humans

A vernier offset is detected at once among straight lines, and reaction times are almost independent of the number of simultaneously presented stimuli (distractors), indicating parallel processing of vernier offsets. Reaction times for identifying a vernier offset to one side among verniers offset to the opposite side increase with the number of distractors, indicating serial processing. Even deviations below a photoreceptor diameter can be detected at once. The visual system thus attains positional accuracy below the photoreceptor diameter simultaneously at different positions. I conclude that deviation from straightness, or change of orientation, is detected in parallel over the visual field. Discontinuities or gradients in orientation may represent an elementary feature of vision.

Analytical Representation of Contours

The interpretation and recognition of noisy contours, such as silhouettes, have proven to be difficult. One obstacle to the solution of these problems has been the lack of a robust representation for contours. The contour is represented by a set of pairwise tangent circular arcs. The advantage of such an approach is that mathematical properties such as orientation and curvature are explicityly represented. We introduce a smoothing criterion for the contour tht optimizes the tradeoff between the complexity of the contour and proximity of the data points. The complexity measure is the number of extrema of curvature present in the contour. The smoothing criterion leads us to a true scale-space for contours. We describe the computation of the contour representation as well as the computation of relevant properties of the contour. We consider the potential application of the representation, the smoothing paradigm, and the scale-space to contour interpretation and recognition.

Implementing Universal Computation in an Evolutionary System

Evolutionary algorithms are a common tool in engineering and in the study of natural evolution. Here we take their use in a new direction by showing how they can be made to implement a universal computer. We consider populations of individuals with genes whose values are the variables of interest. By allowing them to interact with one another in a specified environment with limited resources, we demonstrate the ability to construct any arbitrary logic circuit. We explore models based on the limits of small and large populations, and show examples of such a system in action, implementing a simple logic circuit.

The Role of Chemical Mechanisms in Neural Computation and Learning

Most computational models of neurons assume that their electrical characteristics are of paramount importance. However, all long-term changes in synaptic efficacy, as well as many short-term effects, are mediated by chemical mechanisms. This technical report explores the interaction between electrical and chemical mechanisms in neural learning and development. Two neural systems that exemplify this interaction are described and modelled. The first is the mechanisms underlying habituation, sensitization, and associative learning in the gill withdrawal reflex circuit in Aplysia, a marine snail. The second is the formation of retinotopic projections in the early visual pathway during embryonic development.

Computation and Pre-Parametric Design

My work is broadly concerned with the question "How can designs bessynthesized computationally?" The project deals primarily with mechanical devices and focuses on pre-parametric design: design at the level of detail of a blackboard sketch rather than at the level of detail of an engineering drawing. I explore the project ideas in the domain of single-input single-output dynamic systems, like pressure gauges, accelerometers, and pneumatic cylinders. The problem solution consists of two steps: 1) generate a schematic description of the device in terms of idealized functional elements, and then 2) from the schematic description generate a physical description.

The Definition and Implementation of a Computer Programming Language Based on Constraints

The constraint paradigm is a model of computation in which values are deduced whenever possible, under the limitation that deductions be local in a certain sense. One may visualize a constraint 'program' as a network of devices connected by wires. Data values may flow along the wires, and computation is performed by the devices. A device computes using only locally available information (with a few exceptions), and places newly derived values on other, locally attached wires. In this way computed values are propagated. An advantage of the constraint paradigm (not unique to it) is that a single relationship can be used in more than one direction. The connections to a device are not labelled as inputs and outputs; a device will compute with whatever values are available, and produce as many new values as it can. General theorem provers are capable of such behavior, but tend to suffer from combinatorial explosion; it is not usually useful to derive all the possible consequences of a set of hypotheses. The constraint paradigm places a certain kind of limitation on the deduction process. The limitations imposed by the constraint paradigm are not the only one possible. It is argued, however, that they are restrictive enough to forestall combinatorial explosion in many interesting computational situations, yet permissive enough to allow useful computations in practical situations. Moreover, the paradigm is intuitive: It is easy to visualize the computational effects of these particular limitations, and the paradigm is a natural way of expressing programs for certain applications, in particular relationships arising in computer-aided design. A number of implementations of constraint-based programming languages are presented. A progression of ever more powerful languages is described, complete implementations are presented and design difficulties and alternatives are discussed. The goal approached, though not quite reached, is a complete programming system which will implicitly support the constraint paradigm to the same extent that LISP, say, supports automatic storage management.