Edge Suppression by Gradient Field Transformation Using Cross-Projection Tensors

We propose a new technique for edge-suppressing operations on images. We introduce cross projection tensors to achieve affine transformations of gradient fields. We use these tensors, for example, to remove edges in one image based on the edge-information in a second image. Traditionally, edge suppression is achieved by setting image gradients to zero based on thresholds. A common application is in the Retinex problem, where the illumination map is recovered by suppressing the reflectance edges, assuming it is slowly varying. We present a class of problems where edge-suppression can be a useful tool. These problems involve analyzing images of the same scene under variable illumination. Instead of resetting gradients, the key idea in our approach is to derive local tensors using one image and to transform the gradient field of another image using them. Reconstructed image from the modified gradient field shows suppressed edges or textures at the corresponding locations. All operations are local and our approach does not require any global analysis. We demonstrate the algorithm in the context of several applications such as (a) recovering the foreground layer under varying illumination, (b) estimating intrinsic images in non-Lambertian scenes, (c) removing shadows from color images and obtaining the illumination map, and (d) removing glass reflections.