The Three-Dimensional Interpretation of a Class of Simple Line-Drawings

We provide a theory of the three-dimensional interpretation of a class of line-drawings called p-images, which are interpreted by the human vision system as parallelepipeds ("boxes"). Despite their simplicity, p-images raise a number of interesting vision questions: *Why are p-images seen as three-dimensional objects? Why not just as flatimages? *What are the dimensions and pose of the perceived objects? *Why are some p-images interpreted as rectangular boxes, while others are seen as skewed, even though there is no obvious distinction between the images? *When p-images are rotated in three dimensions, why are the image-sequences perceived as distorting objects---even though structure-from-motion would predict that rigid objects would be seen? *Why are some three-dimensional parallelepipeds seen as radically different when viewed from different viewpoints? We show that these and related questions can be answered with the help of a single mathematical result and an associated perceptual principle. An interesting special case arises when there are right angles in the p-image. This case represents a singularity in the equations and is mystifying from the vision point of view. It would seem that (at least in this case) the vision system does not follow the ordinary rules of geometry but operates in accordance with other (and as yet unknown) principles.

SketchIT: A Sketch Interpretation Tool for Conceptual Mechanical Design

We describe a program called SketchIT capable of producing multiple families of designs from a single sketch. The program is given a rough sketch (drawn using line segments for part faces and icons for springs and kinematic joints) and a description of the desired behavior. The sketch is "rough" in the sense that taken literally, it may not work. From this single, perhaps flawed sketch and the behavior description, the program produces an entire family of working designs. The program also produces design variants, each of which is itself a family of designs. SketchIT represents each family of designs with a "behavior ensuring parametric model" (BEP-Model), a parametric model augmented with a set of constraints that ensure the geometry provides the desired behavior. The construction of the BEP-Model from the sketch and behavior description is the primary task and source of difficulty in this undertaking. SketchIT begins by abstracting the sketch to produce a qualitative configuration space (qc-space) which it then uses as its primary representation of behavior. SketchIT modifies this initial qc-space until qualitative simulation verifies that it produces the desired behavior. SketchIT's task is then to find geometries that implement this qc-space. It does this using a library of qc-space fragments. Each fragment is a piece of parametric geometry with a set of constraints that ensure the geometry implements a specific kind of boundary (qcs-curve) in qc-space. SketchIT assembles the fragments to produce the BEP-Model. SketchIT produces design variants by mapping the qc-space to multiple implementations, and by transforming rotating parts to translating parts and vice versa.

Combining Associational and Causal Reasoning to Solve Interpretation and Planning Problems

This report describes a paradigm for combining associational and causal reasoning to achieve efficient and robust problem-solving behavior. The Generate, Test and Debug (GTD) paradigm generates initial hypotheses using associational (heuristic) rules. The tester verifies hypotheses, supplying the debugger with causal explanations for bugs found if the test fails. The debugger uses domain-independent causal reasoning techniques to repair hypotheses, analyzing domain models and the causal explanations produced by the tester to determine how to replace faulty assumptions made by the generator. We analyze the strengths and weaknesses of associational and causal reasoning techniques, and present a theory of debugging plans and interpretations. The GTD paradigm has been implemented and tested in the domains of geologic interpretation, the blocks world, and Tower of Hanoi problems.

Using Structural and Functional Information in Diagnostic Design

We wish to design a diagnostic for a device from knowledge of its structure and function. the diagnostic should achieve both coverage of the faults that can occur in the device, and should strive to achieve specificity in its diagnosis when it detects a fault. A system is described that uses a simple model of hardware structure and function, representing the device in terms of its internal primitive functions and connections. The system designs a diagnostic in three steps. First, an extension of path sensitization is used to design a test for each of the connections in teh device. Next, the resulting tests are improved by increasing their specificity. Finally the tests are ordered so that each relies on the fewest possible connections. We describe an implementation of this system and show examples of the results for some simple devices.

Representing and Reasoning About Change in Geologic Interpretation

Geologic interpretation is the task of inferring a sequence of events to explain how a given geologic region could have been formed. This report describes the design and implementation of one part of a geologic interpretation problem solver -- a system which uses a simulation technique called imagining to check the validity of a candidate sequence of events. Imagining uses a combination of qualitative and quantitative simulations to reason about the changes which occured to the geologic region. The spatial changes which occur are simulated by constructing a sequence of diagrams. The quantitative simulation needs numeric parameters which are determined by using the qualitative simulation to establish the cumulative changes to an object and by using a description of the current geologic region to make quantitative measurements. The diversity of reasoning skills used in imagining has necessitated the development of multiple representations, each specialized for a different task. Representations to facilitate doing temporal, spatial and numeric reasoning are described in detail. We have also found it useful to explicitly represent processes. Both the qualitative and quantitative simulations use a discrete 'layer cake' model of geologic processes, but each uses a separate representation, specialized to support the type of simulation. These multiple representations have enabled us to develop a powerful, yet modular, system for reasoning about change.

Structure and Interpretation of Computer Programs

"The Structure and Interpretation of Computer Programs" is the entry-level subject in Computer Science at the Massachusetts Institute of Technology. It is required of all students at MIT who major in Electrical Engineering or in Computer Science, as one fourth of the "common core curriculum," which also includes two subjects on circuits and linear systems and a subject on the design of digital systems. We have been involved in the development of this subject since 1978, and we have taught this material in its present form since the fall of 1980 to approximately 600 students each year. Most of these students have had little or no prior formal training in computation, although most have played with computers a bit and a few have had extensive programming or hardware design experience. Our design of this introductory Computer Science subject reflects two major concerns. First we want to establish the idea that a computer language is not just a way of getting a computer to perform operations, but rather that it is a novel formal medium for expressing ideas about methodology. Thus, programs must be written for people to read, and only incidentally for machines to execute. Secondly, we believe that the essential material to be addressed by a subject at this level, is not the syntax of particular programming language constructs, nor clever algorithms for computing particular functions of efficiently, not even the mathematical analysis of algorithms and the foundations of computing, but rather the techniques used to control the intellectual complexity of large software systems.