An Edge Detection Method for Three-dimensional Gray Images Using Optimum Surface Fitting

The optimum surface-fitting method for binary images is extended in order to treat gray images, and a new method to extract edges in three-dimensional gray images is proposed. If voxels that have similar values to the voxel of interest (VOI) are distributed like a two-dimensional curved surface, it is thought that there would be a curved surface at the VOI. To apply the fitting method to gray images, voxels in the neighborhood region are moved according to their voxel values, and only relative coordinates of voxels are used. Using the surface fitting method, the proposed method can provide coefficients of optimum surface and goodnessof-fit (GoF) on each voxel. This makes it possible to extract voxels on edges according to the shape of the surface and/or GoF. High GoF means high probability of the existence of edges. It is confirmed that there are voxels with high GoF at the edges.