Topological Analysis of Human Gaze on Natural Image Space

In this study we develop a topological description for free-viewing gaze patterns on natural images, where the sequence of saccades and fixations can be understood as a matching between a subset of image patches in the periphery space to their corresponding subset in the fixation space. An image patch appears in the periphery before it gets fixated, so there is a bijective map between patches in these two signal spaces. Image patches in the fixation space could be taken as pixel signals from the screen and image patches in the peripheral space could be modeled as filtered signals. From each of the signal spaces, a distance matrix could be computed, describing the pairwise relationship between image patches in the space. We have shown that for each pair of real-valued symmetric matrices obtained from the two signal spaces, there exists an unique decomposition of the matrix into order preserving blocks of submatrices, such that in a matched pair of blocks, their corresponding order complexes are homeomorphic