Pixhomology: a new algorithm for computing persistent homology for pixel data

In this work, we present a highly efficient algorithm for zero-dimensional Persistent Homology (PH) computation on images. Our approach hinges on a novel method for filtering simplicial complexes derived from pixel connections. Through comparative analyses with established adjacency matrix-based methodologies, we show that our algorithm, PixHomology, drastically reduces memory usage while also improving computational speed. It is important to notice that the very small memory footprint readily allows to process high-resolution images across a wide range of application areas ranging from astronomy to histology.