Accurate subvoxel location and characterization of edges in 3D images based on the Partial Volume Effect

An accurate estimation of the position, orientation, principal curvatures, and change in intensity of the edges in a 3D image provides highly useful information for many applications. The use of derivative operators to compute the gradient vector and the Hessian matrix in each voxel usually generates inaccurate results. This paper presents a new edge detector which is derived from the Partial Volume Effect (PVE). Instead of assuming continuity in the image values, edge features are extracted from the distribution of intensities within a neighborhood of each edge voxel. First, the influence of the intensities of the voxels in first-and second-order edges is analyzed to demonstrate that these types of edges can be precisely characterized from the intensity distribution. Afterward, this approach is extended to especially demanding situations by considering how adverse conditions can be tackled. This extension includes filtering noisy images, characterizing edges in blurred regions, and using windows with floating limits for close edges. The proposed technique has been tested on synthetic and real images, including some particularly difficult objects, and achieving a highly accurate subvoxel characterization of the edges. An open source implementation of our method is provided.