Jorge Jara Wilde, Proyecto de Titulo: INGENIERO CIVIL EN INFORMÁTICAINFORMÁTICA, Universidad Austral de Chile, Valdivia, Chile.

In the field of image processing, the segmentation techniques allow to identify and to define regions of interest (ROIs) within an image. Applied to Biology and Biophysics, the segmentation of structures in microscopic images is indispensable for its later morphologic analysis.
This work applies to methods for the segmentation and morphologic characterization of biological structures, by means of parametric active contours that interact with gradient vector flow fields (GVF, generalized gradient vector flow fields, GGVF). The active contours are mathematical models that control the deformation of curves (two dimensions) or surfaces (three dimensions), by means of the action of intrinsic parameters (internal forces), and vector fields calculated as a function of the variations of intensities in the images (external forces). A functional of internal and external energy is defined that is aimed to be minimized by means of the equation of Euler-Lagrange; adding a time parameter to the model a solution with iterative methods can be approximated. Active contours in two dimensions were implemented first, and then extended in their formulation and application as active surfaces in three-dimensional ROIs. A criterion was settled down to optimize the resolution of contours in two dimensions, on the basis of the evaluation of curvature, inflection points and perimeter. For three dimensions surface meshes were evaluated, based on the precision in the calculation of area and regularity of curvature.
The developed methods were integrated to a computational application for image processing, being combined with other techniques of segmentation, reconstruction, visualization and parametrization of biological structures.

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