Directional ratio based on parabolic molecules and its application to the analysis of tubular structures

As advances in imaging technologies make more and more data available for biomedical applications, there is an increasing need to develop efficient quantitative algorithms for the analysis and processing of imaging data. In this paper, we intro-duce an innovative multiscale approach called Directional Ratio which is especially effective to distingush isotropic from anisotropic structures. This task is especially useful in the analysis of images of neurons, the main units of the nervous systems which consist of a main cell body called the soma and many elongated processes called neurites. We analyze the theoretical properties of our method on idealized models of neurons and develop a numerical implementation of this approach for analysis of fluorescent images of cultured neurons. We show that this algorithm is very effective for the detection of somas and the extraction of neurites in images of small circuits of neurons. 1