A Circuit Grammar For Operational Amplifier Design

Electrical circuit designers seldom create really new topologies or use old ones in a novel way. Most designs are known combinations of common configurations tailored for the particular problem at hand. In this thesis I show that much of the behavior of a designer engaged in such ordinary design can be modelled by a clearly defined computational mechanism executing a set of stylized rules. Each of my rules embodies a particular piece of the designer's knowledge. A circuit is represented as a hierarchy of abstract objects, each of which is composed of other objects. The leaves of this tree represent the physical devices from which physical circuits are fabricated. By analogy with context-free languages, a class of circuits is generated by a phrase-structure grammar of which each rule describes how one type of abstract object can be expanded into a combination of more concrete parts. Circuits are designed by first postulating an abstract object which meets the particular design requirements. This object is then expanded into a concrete circuit by successive refinement using rules of my grammar. There are in general many rules which can be used to expand a given abstract component. Analysis must be done at each level of the expansion to constrain the search to a reasonable set. Thus the rule of my circuit grammar provide constraints which allow the approximate qualitative analysis of partially instantiated circuits. Later, more careful analysis in terms of more concrete components may lead to the rejection of a line of expansion which at first looked promising. I provide special failure rules to direct the repair in this case.

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.

Direct Estimation of Motion and Extended Scene Structure from a Moving Stereo Rig

We describe a new method for motion estimation and 3D reconstruction from stereo image sequences obtained by a stereo rig moving through a rigid world. We show that given two stereo pairs one can compute the motion of the stereo rig directly from the image derivatives (spatial and temporal). Correspondences are not required. One can then use the images from both pairs combined to compute a dense depth map. The motion estimates between stereo pairs enable us to combine depth maps from all the pairs in the sequence to form an extended scene reconstruction and we show results from a real image sequence. The motion computation is a linear least squares computation using all the pixels in the image. Areas with little or no contrast are implicitly weighted less so one does not have to explicitly apply a confidence measure.

CARPS: A Program which Solves Calculus Word Problems

A program was written to solve calculus word problems. The program, CARPS (CALculus Rate Problem Solver), is restricted to rate problems. The overall plan of the program is similar to Bobrow's STUDENT, the primary difference being the introduction of "structures" as the internal model in CARPS. Structures are stored internally as trees. Each structure is designed to hold the information gathered about one object. A description of CARPS is given by working through two problems, one in great detail. Also included is a critical analysis of STUDENT.