Line Kinematics for Whole-Arm Manipulation

A Whole-Arm Manipulator uses every surface to both sense and interact with the environment. To facilitate the analysis and control of a Whole-Arm Manipulator, line geometry is used to describe the location and trajectory of the links. Applications of line kinematics are described and implemented on the MIT Whole-Arm Manipulator (WAM-1).

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.

Relative Affine Structure: Canonical Model for 3D from 2D Geometry and Applications

We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call "relative affine structure". Via a number of corollaries of our main results we show that our framework unifies previous work --- including Euclidean, projective and affine --- in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.

Automatically Recovering Geometry and Texture from Large Sets of Calibrated Images

Three-dimensional models which contain both geometry and texture have numerous applications such as urban planning, physical simulation, and virtual environments. A major focus of computer vision (and recently graphics) research is the automatic recovery of three-dimensional models from two-dimensional images. After many years of research this goal is yet to be achieved. Most practical modeling systems require substantial human input and unlike automatic systems are not scalable. This thesis presents a novel method for automatically recovering dense surface patches using large sets (1000's) of calibrated images taken from arbitrary positions within the scene. Physical instruments, such as Global Positioning System (GPS), inertial sensors, and inclinometers, are used to estimate the position and orientation of each image. Essentially, the problem is to find corresponding points in each of the images. Once a correspondence has been established, calculating its three-dimensional position is simply a matter of geometry. Long baseline images improve the accuracy. Short baseline images and the large number of images greatly simplifies the correspondence problem. The initial stage of the algorithm is completely local and scales linearly with the number of images. Subsequent stages are global in nature, exploit geometric constraints, and scale quadratically with the complexity of the underlying scene. We describe techniques for: 1) detecting and localizing surface patches; 2) refining camera calibration estimates and rejecting false positive surfels; and 3) grouping surface patches into surfaces and growing the surface along a two-dimensional manifold. We also discuss a method for producing high quality, textured three-dimensional models from these surfaces. Some of the most important characteristics of this approach are that it: 1) uses and refines noisy calibration estimates; 2) compensates for large variations in illumination; 3) tolerates significant soft occlusion (e.g. tree branches); and 4) associates, at a fundamental level, an estimated normal (i.e. no frontal-planar assumption) and texture with each surface patch.

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.