  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
characterizing the geometry of objects on images, for example by detecting
approximate symmetries.
