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.

Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers

The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by $k$--means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well--founded, but also superior in a practical application.