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.

Recovering Heading for Visually-Guided Navigation

We present a model for recovering the direction of heading of an observer who is moving relative to a scene that may contain self-moving objects. The model builds upon an algorithm proposed by Rieger and Lawton (1985), which is based on earlier work by Longuet-Higgens and Prazdny (1981). The algorithm uses velocity differences computed in regions of high depth variation to estimate the location of the focus of expansion, which indicates the observer's heading direction. We relate the behavior of the proposed model to psychophysical observations regarding the ability of human observers to judge their heading direction, and show how the model can cope with self-moving objects in the environment. We also discuss this model in the broader context of a navigational system that performs tasks requiring rapid sensing and response through the interaction of simple task-specific routines.

Internet Fish

I have invented "Internet Fish," a novel class of resource-discovery tools designed to help users extract useful information from the Internet. Internet Fish (IFish) are semi-autonomous, persistent information brokers; users deploy individual IFish to gather and refine information related to a particular topic. An IFish will initiate research, continue to discover new sources of information, and keep tabs on new developments in that topic. As part of the information-gathering process the user interacts with his IFish to find out what it has learned, answer questions it has posed, and make suggestions for guidance. Internet Fish differ from other Internet resource discovery systems in that they are persistent, personal and dynamic. As part of the information-gathering process IFish conduct extended, long-term conversations with users as they explore. They incorporate deep structural knowledge of the organization and services of the net, and are also capable of on-the-fly reconfiguration, modification and expansion. Human users may dynamically change the IFish in response to changes in the environment, or IFish may initiate such changes itself. IFish maintain internal state, including models of its own structure, behavior, information environment and its user; these models permit an IFish to perform meta-level reasoning about its own structure. To facilitate rapid assembly of particular IFish I have created the Internet Fish Construction Kit. This system provides enabling technology for the entire class of Internet Fish tools; it facilitates both creation of new IFish as well as additions of new capabilities to existing ones. The Construction Kit includes a collection of encapsulated heuristic knowledge modules that may be combined in mix-and-match fashion to create a particular IFish; interfaces to new services written with the Construction Kit may be immediately added to "live" IFish. Using the Construction Kit I have created a demonstration IFish specialized for finding World-Wide Web documents related to a given group of documents. This "Finder" IFish includes heuristics that describe how to interact with the Web in general, explain how to take advantage of various public indexes and classification schemes, and provide a method for discovering similarity relationships among documents.

An Analog VLSI Chip for Estimating the Focus of Expansion

For applications involving the control of moving vehicles, the recovery of relative motion between a camera and its environment is of high utility. This thesis describes the design and testing of a real-time analog VLSI chip which estimates the focus of expansion (FOE) from measured time-varying images. Our approach assumes a camera moving through a fixed world with translational velocity; the FOE is the projection of the translation vector onto the image plane. This location is the point towards which the camera is moving, and other points appear to be expanding outward from. By way of the camera imaging parameters, the location of the FOE gives the direction of 3-D translation. The algorithm we use for estimating the FOE minimizes the sum of squares of the differences at every pixel between the observed time variation of brightness and the predicted variation given the assumed position of the FOE. This minimization is not straightforward, because the relationship between the brightness derivatives depends on the unknown distance to the surface being imaged. However, image points where brightness is instantaneously constant play a critical role. Ideally, the FOE would be at the intersection of the tangents to the iso-brightness contours at these "stationary" points. In practice, brightness derivatives are hard to estimate accurately given that the image is quite noisy. Reliable results can nevertheless be obtained if the image contains many stationary points and the point is found that minimizes the sum of squares of the perpendicular distances from the tangents at the stationary points. The FOE chip calculates the gradient of this least-squares minimization sum, and the estimation is performed by closing a feedback loop around it. The chip has been implemented using an embedded CCD imager for image acquisition and a row-parallel processing scheme. A 64 x 64 version was fabricated in a 2um CCD/ BiCMOS process through MOSIS with a design goal of 200 mW of on-chip power, a top frame rate of 1000 frames/second, and a basic accuracy of 5%. A complete experimental system which estimates the FOE in real time using real motion and image scenes is demonstrated.