The assumption of the smoothness constraint in the global sense using a fixed regularization parameter is one of the major problems of the algorithms based on regularization theory. Several nonstandard algorithms have been developed to overcome this problem by using a line process, but they suffer from the extensive computation required in minimizing the resulting nonconvex functionals. We present an edge detection and surface reconstruction algorithm in which the smoothness is controlled spatially over the image space. The values of parameters in the model are adaptively determined by an iterative refinement process, hence, the image-dependent parameters such as the optimum value of the regularization parameter or the filter size are eliminated. The algorithm starts with an oversmoothed regularized solution and iteratively refines the surface around discontinuities by using the structure exhibited in the error signal. The spatial control of smoothness is shown to resolve the conflict between detection and localization criteria of edge detection by smoothing the noise in continuous regions while preserving discontinuities. The performance or the algorithm is quantitatively and qualitatively evaluated on real and synthetic images, and it is compared with those or Marr-Hildreth and Canny edge detectors.