Watershed on the holodisc distance relief

We present an original method for the reconstruction of missing grain boundary lines in metallic photomicrographs. The extraction of the joints from the grey image and the reconstruction step are performed using mathematical morphology based on geometrical considerations similar to the binary watershed segmentation, our method avoids the classical problems of over and under-segmentation. We consider a particular distance: the holodisc distance which is the Euclidean one rounded up to the next integer value. The algorithm uses template matching to detect saddle zones on the holodisc relief. Then a step by step investigation of the neighbouring relief allows one to differentiate touching grains