Unbiased Finite Element Mesh Delaunay Constrained Triangulation Applied to 2D Images with High Morphological Complexity Using Mathematical Morphology Tools Part 1: Binary Images

Abstract

We propose a method for establishing a Constrained Delaunay Triangulation CDT applied to 2D binary images of high morphological complexity. A prerequisite for CDT is the unbiased definition of the Planar Straight-Line Graph PSLG, which must respect the injective nature of Jordan’s Curve whatever the topology of the image objects. Mathematical morphology provides tools for extracting the image contour, on which points will be judiciously placed at particular points to construct the vector path of the PSLG. Finally, these tools will enable us to implement a judicious pointing process in the image to guarantee the relative equivalence of triangles. The deterministic and rigorous procedure detailed in this article will be generalized in a second article, Part 2, to the case of labeled images for which the definition of the PSLG is more complex to define, since the contour of objects in the image is defined by the set of contours of adjacent objects.

Keywords

• mathematical morphology
• 2D binary images
• delaunay triangulation
• geodesic vectors
• complex shapes
• image contouring