<title>Obtaining surface orientation of texture image using mathematical morphology</title>

Abstract

In this paper, we present a new morphological approach to obtain a surface orientation using the variation of texture image caused by projective distortions. The perspective effect and the foreshortening are considered as the projective distortions. Under the assumption that the surface of texture image is plane, we apply the mathematical morphology in order to compute the 3D surface orientation. Centroids of texels can be obtained from the farthest texel to the nearest texel sequentially by recursive erosions, so the entire texture image is segmented into several sub-regions. We may compute a major axis of each sub-region with centroids and an average slope with all major axes. Intersections between the line perpendicular to the average slope and the major axes are obtained. Using the relations between the intersections and the size of structuring elements in each sub-region, we can compute the vanishing point. The entire region is rearranged using the major axes of sub-regions and the lines converging to the vanishing point. We can obtain the surface orientation by using the vanishing point and the perpendicular line. We have demonstrated experimental results with the artificial image and the natural images. In the experimental results, we have ascertained the proposed algorithm was more effective than the algorithm using the aggregation transform with the texel edge.