An Optimal Scale for Edge Detection

Many problems in early vision are ill posed. Edge detection is a typical example. This paper applies regularization techniques to the problem of edge detection. We derive an optimal filter for edge detection with a size controlled by the regularization parameter $\\ lambda $ and compare it to the Gaussian filter. A formula relating the signal-to-noise ratio to the parameter $\\lambda $ is derived from regularization analysis for the case of small values of $\\lambda$. We also discuss the method of Generalized Cross Validation for obtaining the optimal filter scale. Finally, we use our framework to explain two perceptual phenomena: coarsely quantized images becoming recognizable by either blurring or adding noise.

A View on Dyslexia

We describe here, briefly, a perceptual non-reading measure which reliably distinguishes between dyslexic persons and ordinary readers. More importantly, we describe a regimen of practice with which dyslexics learn a new perceptual strategy for reading. Two controlled experiment on dyslexics children demonstrate the regimen's efficiency.

Notes on PCA, Regularization, Sparsity and Support Vector Machines

We derive a new representation for a function as a linear combination of local correlation kernels at optimal sparse locations and discuss its relation to PCA, regularization, sparsity principles and Support Vector Machines. We first review previous results for the approximation of a function from discrete data (Girosi, 1998) in the context of Vapnik"s feature space and dual representation (Vapnik, 1995). We apply them to show 1) that a standard regularization functional with a stabilizer defined in terms of the correlation function induces a regression function in the span of the feature space of classical Principal Components and 2) that there exist a dual representations of the regression function in terms of a regularization network with a kernel equal to a generalized correlation function. We then describe the main observation of the paper: the dual representation in terms of the correlation function can be sparsified using the Support Vector Machines (Vapnik, 1982) technique and this operation is equivalent to sparsify a large dictionary of basis functions adapted to the task, using a variation of Basis Pursuit De-Noising (Chen, Donoho and Saunders, 1995; see also related work by Donahue and Geiger, 1994; Olshausen and Field, 1995; Lewicki and Sejnowski, 1998). In addition to extending the close relations between regularization, Support Vector Machines and sparsity, our work also illuminates and formalizes the LFA concept of Penev and Atick (1996). We discuss the relation between our results, which are about regression, and the different problem of pattern classification.

Perceptual Evaluation of Video-Realistic Speech

abstract With many visual speech animation techniques now available, there is a clear need for systematic perceptual evaluation schemes. We describe here our scheme and its application to a new video-realistic (potentially indistinguishable from real recorded video) visual-speech animation system, called Mary 101. Two types of experiments were performed: a) distinguishing visually between real and synthetic image- sequences of the same utterances, ("Turing tests") and b) gauging visual speech recognition by comparing lip-reading performance of the real and synthetic image-sequences of the same utterances ("Intelligibility tests"). Subjects that were presented randomly with either real or synthetic image-sequences could not tell the synthetic from the real sequences above chance level. The same subjects when asked to lip-read the utterances from the same image-sequences recognized speech from real image-sequences significantly better than from synthetic ones. However, performance for both, real and synthetic, were at levels suggested in the literature on lip-reading. We conclude from the two experiments that the animation of Mary 101 is adequate for providing a percept of a talking head. However, additional effort is required to improve the animation for lip-reading purposes like rehabilitation and language learning. In addition, these two tasks could be considered as explicit and implicit perceptual discrimination tasks. In the explicit task (a), each stimulus is classified directly as a synthetic or real image-sequence by detecting a possible difference between the synthetic and the real image-sequences. The implicit perceptual discrimination task (b) consists of a comparison between visual recognition of speech of real and synthetic image-sequences. Our results suggest that implicit perceptual discrimination is a more sensitive method for discrimination between synthetic and real image-sequences than explicit perceptual discrimination.