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Title: A morphological approach to curvature-based evolution of curves and surfaces
Authors: Marquez-Neila, Pablo
Baumela, Luis
Alvarez, Luis 
UNESCO Clasification: 120601 Construcción de algoritmos
120602 Ecuaciones diferenciales
120326 Simulación
120304 Inteligencia artificial
Keywords: Computer vision
Curve evolution
Mathematical morphology
Morphological snakes
Issue Date: 2014
Journal: IEEE Transactions on Pattern Analysis and Machine Intelligence 
Abstract: We introduce new results connecting differential and morphological operators that provide a formal and theoretically grounded approach for stable and fast contour evolution. Contour evolution algorithms have been extensively used for boundary detection and tracking in computer vision. The standard solution based on partial differential equations and level-sets requires the use of numerical methods of integration that are costly computationally and may have stability issues. We present a morphological approach to contour evolution based on a new curvature morphological operator valid for surfaces of any dimension. We approximate the numerical solution of the curve evolution PDE by the successive application of a set of morphological operators defined on a binary level-set and with equivalent infinitesimal behavior. These operators are very fast, do not suffer numerical stability issues, and do not degrade the level set function, so there is no need to reinitialize it. Moreover, their implementation is much easier since they do not require the use of sophisticated numerical algorithms. We validate the approach providing a morphological implementation of the geodesic active contours, the active contours without borders, and turbopixels. In the experiments conducted, the morphological implementations converge to solutions equivalent to those achieved by traditional numerical solutions, but with significant gains in simplicity, speed, and stability.
ISSN: 0162-8828
DOI: 10.1109/TPAMI.2013.106
Source: IEEE Transactions on Pattern Analysis and Machine Intelligence [ISSN 0162-8828],v. 36, nº 1, (6529072), p. 2-17
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