Approximation methods for the recovery of shapes and images from gradients

Recovery of shapes and images from gradients is an important problem in many fields such as computer vision, computational photography, and remote sensing. For instance, techniques such as photometric stereo and shape from Shading recover the underlying 3D shape by integrating an estimated surface gradient field or surface normals. In applications such as image stitching and image editing, gradients of given images are first manipulated. The final image is then reconstructed from the modified gradient field. The estimated or modified gradient field is usually nonintegrable due to the presence of noise, outliers in the estimation process, and inherent ambiguities. This chapter reviews some approximation-based methods for surface reconstruction from the given nonintegrable gradient field with applications to 3D modeling and image reconstruction.