Mireille Boutin (School of ECE and Dept. of Math, Purdue University)
Light-weight Methods for Automatic Recognition in Mobile Applications
Abstract: Portable computing devices such as tablets and smart phones are now ubiquitous. For better or for worse, society now expects these devices to replace and even outperform human experts in many domain of applications. In this talk, I will describe some automatic recognition problems which I came across as part of my research on portable device applications, namely the problems of automatically recognizing HAZMAT placards, automatically reading Arabic characters, and interpreting gang graffiti. These problems, I will argue, justify the need for a mathematical theory of shape that is amenable to discrete, noisy data. As a tentative first step towards such a theory, I will define the Pascal Triangle of a discrete gray-scale image as a pyramidal arrangement of complex-valued moments and explore its geometric significance. In particular, we will observe that the entries of row k of this pyramid correspond to the Fourier series coefficients of the order k moment of the Radon transform of the image. Group actions on the plane can be naturally prolonged onto the entries of the Pascal triangle; we will propose simple tests for equivalence and self-equivalence under some common group actions. This is joint work with my graduate students Shanshan Huang and Andrew Haddad. |
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