1209.4850 (Mireille Boutin et al.)

The Pascal Triangle of a Discrete Image: Definition, Properties and
Application to Shape Analysis    [PDF]

Mireille Boutin, Shanshan Huang

We define the Pascal Triangle of a discrete (gray scale) image as a pyramidal arrangement of complex-valued moments and we explore its geometric significance. In particular, we show that the entries of row k of this triangle correspond to the Fourier series coefficients of the moment of order k of the Radon transform of the image. Group actions on the plane can be naturally prolonged onto the entries of the Pascal Triangle. We study the prolongation of some common group actions, such as rotations and reflections, and we propose simple tests for detecting equivalences and self-equivalences under these group actions. The motivating application of this work is the problem of recognizing "shapes" on images, for example characters, digits or simple graphics.

View original: http://arxiv.org/abs/1209.4850