Computing 3-D Motion in Custom Analog and Digital VLSI

This thesis examines a complete design framework for a real-time, autonomous system with specialized VLSI hardware for computing 3-D camera motion. In the proposed architecture, the first step is to determine point correspondences between two images. Two processors, a CCD array edge detector and a mixed analog/digital binary block correlator, are proposed for this task. The report is divided into three parts. Part I covers the algorithmic analysis; part II describes the design and test of a 32$\time $32 CCD edge detector fabricated through MOSIS; and part III compares the design of the mixed analog/digital correlator to a fully digital implementation.

Parallel Networks for Machine Vision

The amount of computation required to solve many early vision problems is prodigious, and so it has long been thought that systems that operate in a reasonable amount of time will only become feasible when parallel systems become available. Such systems now exist in digital form, but most are large and expensive. These machines constitute an invaluable test-bed for the development of new algorithms, but they can probably not be scaled down rapidly in both physical size and cost, despite continued advances in semiconductor technology and machine architecture. Simple analog networks can perform interesting computations, as has been known for a long time. We have reached the point where it is feasible to experiment with implementation of these ideas in VLSI form, particularly if we focus on networks composed of locally interconnected passive elements, linear amplifiers, and simple nonlinear components. While there have been excursions into the development of ideas in this area since the very beginnings of work on machine vision, much work remains to be done. Progress will depend on careful attention to matching of the capabilities of simple networks to the needs of early vision. Note that this is not at all intended to be anything like a review of the field, but merely a collection of some ideas that seem to be interesting.

A Comparison of Hardware Implementations for Low-Level Vision Algorithms

Early and intermediate vision algorithms, such as smoothing and discontinuity detection, are often implemented on general-purpose serial, and more recently, parallel computers. Special-purpose hardware implementations of low-level vision algorithms may be needed to achieve real-time processing. This memo reviews and analyzes some hardware implementations of low-level vision algorithms. Two types of hardware implementations are considered: the digital signal processing chips of Ruetz (and Broderson) and the analog VLSI circuits of Carver Mead. The advantages and disadvantages of these two approaches for producing a general, real-time vision system are considered.

Detecting Digital Forgeries Using Bispectral Analysis

With the rapid increase in low-cost and sophisticated digital technology the need for techniques to authenticate digital material will become more urgent. In this paper we address the problem of authenticating digital signals assuming no explicit prior knowledge of the original. The basic approach that we take is to assume that in the frequency domain a "natural" signal has weak higher-order statistical correlations. We then show that "un-natural" correlations are introduced if this signal is passed through a non-linearity (which would almost surely occur in the creation of a forgery). Techniques from polyspectral analysis are then used to detect the presence of these correlations. We review the basics of polyspectral analysis, show how and why these tools can be used in detecting forgeries and show their effectiveness in analyzing human speech.

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.

The Coupled Depth/Slope Approach to Surface Reconstruction

Reconstructing a surface from sparse sensory data is a well known problem in computer vision. Early vision modules typically supply sparse depth, orientation and discontinuity information. The surface reconstruction module incorporates these sparse and possibly conflicting measurements of a surface into a consistent, dense depth map. The coupled depth/slope model developed here provides a novel computational solution to the surface reconstruction problem. This method explicitly computes dense slope representation as well as dense depth representations. This marked change from previous surface reconstruction algorithms allows a natural integration of orientation constraints into the surface description, a feature not easily incorporated into earlier algorithms. In addition, the coupled depth/ slope model generalizes to allow for varying amounts of smoothness at different locations on the surface. This computational model helps conceptualize the problem and leads to two possible implementations- analog and digital. The model can be implemented as an electrical or biological analog network since the only computations required at each locally connected node are averages, additions and subtractions. A parallel digital algorithm can be derived by using finite difference approximations. The resulting system of coupled equations can be solved iteratively on a mesh-pf-processors computer, such as the Connection Machine. Furthermore, concurrent multi-grid methods are designed to speed the convergence of this digital algorithm.

Probabilistic Solution of Inverse Problems

In this thesis we study the general problem of reconstructing a function, defined on a finite lattice from a set of incomplete, noisy and/or ambiguous observations. The goal of this work is to demonstrate the generality and practical value of a probabilistic (in particular, Bayesian) approach to this problem, particularly in the context of Computer Vision. In this approach, the prior knowledge about the solution is expressed in the form of a Gibbsian probability distribution on the space of all possible functions, so that the reconstruction task is formulated as an estimation problem. Our main contributions are the following: (1) We introduce the use of specific error criteria for the design of the optimal Bayesian estimators for several classes of problems, and propose a general (Monte Carlo) procedure for approximating them. This new approach leads to a substantial improvement over the existing schemes, both regarding the quality of the results (particularly for low signal to noise ratios) and the computational efficiency. (2) We apply the Bayesian appraoch to the solution of several problems, some of which are formulated and solved in these terms for the first time. Specifically, these applications are: teh reconstruction of piecewise constant surfaces from sparse and noisy observationsl; the reconstruction of depth from stereoscopic pairs of images and the formation of perceptual clusters. (3) For each one of these applications, we develop fast, deterministic algorithms that approximate the optimal estimators, and illustrate their performance on both synthetic and real data. (4) We propose a new method, based on the analysis of the residual process, for estimating the parameters of the probabilistic models directly from the noisy observations. This scheme leads to an algorithm, which has no free parameters, for the restoration of piecewise uniform images. (5) We analyze the implementation of the algorithms that we develop in non-conventional hardware, such as massively parallel digital machines, and analog and hybrid networks.