MORPHOLOGICAL DESCRIPTIONS USING THREE-DIMENSIONAL WAVEFRONTS

Jean Serra

Abstract

The present study deals with the analysis of three-dimensional binary objects whose structure is not obvious nor generally clearly visible. Our approach is illustrated through three examples taken from biological microscopy. In one of our examples, we need to extract the osteocytes contained in sixty confocal sections. The cells are not numerous, but are characterized by long branches, hence they will be separated using a directional wavefront The two other objects are more complex and will be analysed by means of a spherical wavefront In the first case, a kidney of a rat embryo, the tissue grows like a tree, where we want to detect the branches, their extremities,and their spatial arrangement. The wavefront method enables us to define precisely branches and extremities, and gives flexible algorithms. The last example deals with the embryonic growth of the chicken shinbone. The central part of the bone (or shaft) is structured as a series of nested cylinders following the same axis, and connected by more or less long bridges. Using wavefronts, we show that it is possible to separate the cylinders,and to extract and count the bridges that connect them.

Keywords
3-D geodesy; branching; Euler-Poincar6 constant; wavefront

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DOI: 10.5566/ias.v21.pS13-S21

Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)