Active contour methods on arbitrary graphs based on partial differential equations
| Autor: | Nikos Kolotouros, Kimon Drakopoulos, Christos Sakaridis, Petros Maragos |
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| Rok vydání: | 2019 |
| Předmět: |
Active contour model
Partial differential equation Discretization Geodesic Computer science ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION Finite difference Applied mathematics Image segmentation Curvature Finite element method ComputingMethodologies_COMPUTERGRAPHICS MathematicsofComputing_DISCRETEMATHEMATICS |
| DOI: | 10.1016/bs.hna.2019.07.002 |
| Popis: | This chapter formulates and compares two approaches that have been developed to discretize over arbitrary graphs the partial differential equations (PDEs) of classical active contour models with level sets, which have been widely used in image analysis and computer vision. The first approach takes a finite difference path and proposes geometric approximations of the fundamental continuous differential operators that are involved in active contour PDEs, namely gradient and curvature, on graphs with arbitrary vertex and edge configuration. The second approach leverages finite elements to approximate the solution of these PDEs on graphs with arbitrary vertex configuration that constitute a triangulation. We present numerical algorithms and compare both approaches while using them to successfully apply the popular models of geodesic active contours (GACs) and active contours without edges (ACWE) to arbitrary 2D graphs for graph cluster detection and image segmentation. |
| Databáze: | OpenAIRE |
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