Nonlinear Multiresolution: A Shape-from-Shading Example

Multiresolution methods are often used in computer vision to speed up computationally intensive tasks. An approximate solution computed for a reduced image is used to guide the algorithm towards the complete solution on a larger image. Whenever the image is a nonlinear function of the parameters to be computed, multiresolution should be used with special care. The obvious image reduction is incorrect, and the solution on the reduced image is a bad estimate of the higher resolution solution. Shape-from-shading is treated in this correspondence as an example of such difficulties. Reduction of the gray level resolution of an image, as often done in image “pyramids,” does not correspond to images obtained by reducing the shape resolution: the 3-D resolution of an object The correspondence between gray level and shape resolutions is therefore discussed, and a method is proposed for using multiresolution approach in the case of shape-from-shading. It is concluded that a study of the relation between image resolution and estimated-parameter resolution should be done before using any multiresolution approach.