Shape descriptors based on compressed sensing with application to neuron matching

In this paper we propose a novel compressed sensing based Fourier shape descriptor method to compute the shape feature vector of an arbitrary object. First, the object contour obtained via segmentation is represented as a complex-valued signal. We then formulate an optimization problem that exploits the sparsity of the shape feature of the contour. This results in a reduced size feature vector, which can efficiently represent the shape of an object as illustrated by the reconstruction results. Appropriate for general shape retrieval problems, we demonstrate the efficacy of our algorithm by retrieving structurally similar neurons from a database. Currently, the representation and matching of neurons, given the heterogeneous nature of the neuronal morphology and the characteristically complex branching patterns, is an open problem. Retrieval of structurally similar neurons will potentially enable classification of neurons imaged. The retrieval results obtained using our method provide evidence of efficacy with a 27% improvement over Sholl analysis, which is a standard shape descriptor used in neuroscience.