Computing the Extended Persistent Homology Transform of binary images

The Persistent Homology Transform, and the Euler Characteristic Transform are topological analogs of the Radon transform that can be used in statsistical shape analysis. In this talk I will consider an interesting variant called the Extended Persistent Homology Transform (XPHT) which replaces the normal persistent homology with extended persistent homology. We are particularly interested in the application of the XPHT to binary images. This paper outlines an algorithm for efficient calculation of the XPHT exploting relationships between the PHT of the boundary curves to the XPHT of the foreground.