APPLICATION AND ASSESSMENT OF MULTISCALE BENDING ENERGY FOR MORPHOMETRIC CHARACTERIZATION OF NEURAL CELLS

The estimation of the curvature of experimentally obtained curves is a n important issue in many applications of image analysis including bio physics, biology, particle physics, and high energy physics. However, the accurate calculation of the curvature of digital contours has prov en to be a difficult endeavor, mainly because of the noise and distort ions that are always present in sampled signals. Errors ranging from 1 % to 1000% have been reported with respect to the application of stand ard techniques in the estimation of the curvature of circular contours [M. Worring and A. W. M. Smeulders, CVGIP: Im. Understanding, 58, 366 (1993)]. This article explains how diagrams of multiscale bending ene rgy can be easily obtained from curvegrams and used as a robust genera l feature for morphometric characterization of neural cells. The bendi ng energy is an interesting global feature for shape characterization that expresses the amount of energy needed to transform the specific s hape under analysis into its lowest energy state (i.e., a circle). The curvegram, which can be accurately obtained by using digital signal p rocessing techniques (more specifically through the Fourier transform and its inverse, as described in this work), provides multiscale repre sentation of the curvature of digital contours. The estimation of the bending energy from the curvegram is introduced and exemplified with r espect to a series of neural cells. The masked high curvature effect i s reported and its implications to shape analysis are discussed. It is also discussed and illustrated that, by normalizing the multiscale be nding energy with respect to a standard circle of unitary perimeter, t his feature becomes an effective means for expressing shape complexity in a way that is invariant to rotation, translation, and scaling, and that is robust to noise and other artifacts implied by image acquisit ion. (C) 1997 American Institute of Physics.