Mirror Symmetry Histograms for Capturing Geometric Properties in Images

We propose a data structure that captures global geometric properties in images: Histogram of Mirror Symmetry Coefficients. We compute such a coefficient for every pair of pixels, and group them in a 6-dimensional histogram. By marginalizing the HMSC in various ways, we develop algorithms for a range of applications: detection of nearly-circular cells; location of the main axis of reflection symmetry; detection of cell-division in movies of developing embryos; detection of worm-tips and indirect cell-counting via supervised classification. Our approach generalizes a series of histogram-related methods, and the proposed algorithms perform with state-of-the-art accuracy.