Title :
A Morphological Approach to Curvature-Based Evolution of Curves and Surfaces
Author :
Marquez-Neila, Pablo ; Baumela, Luis ; Alvarez, Luis
Author_Institution :
Dept. de Intel. Artificial, Univ. Politec. de Madrid, Madrid, Spain
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.
Keywords :
computer vision; numerical analysis; partial differential equations; stability; boundary detection; computer vision; curvature based evolution; curvature morphological operator; fast contour evolution algorithms; geodesic active contours; level set function; numerical solutions; numerical stability; partial differential equations; sophisticated numerical algorithms; tracking; turbopixels; Active contours; Approximation methods; Level set; Mathematical model; Numerical stability; Surface morphology; Three-dimensional displays; Computer vision; curve evolution; level-sets; mathematical morphology; morphological snakes;
Journal_Title :
Pattern Analysis and Machine Intelligence, IEEE Transactions on
DOI :
10.1109/TPAMI.2013.106