Triangle does that (assuming 2D based on OP). Nothing forces you to use it as a command line interface.

http://www.cs.cmu.edu/~quake/triangle.delaunay.html

(edit)

It comes with the source code as a zip or shar. If your project is for commercial purposes you may have to contact them to find out how you might get a license, though.

Just one question, I would like to know when boundaries are extracted from images, what is the usual way to construct surface from images, is it delaunay triangulation? Or is there any other approach? My requirement is that I need to extract 3D geometry from the images and at the same time, it is supposed to preserve color.

If you triangulate your polygons, you'll have a set of vertices and triangles you can use for a triangle mesh.