A scalable parallel algorithm for edge detection and surface reconstruction is presented. The algorithm is based on fitting a weak membrane to the pixel gray values by minimizing the associated energy functional. The edge detection process is modeled as a line process and used as a constraint in minimizing the energy functional of the image. The optimal edge assignment cannot be obtained directly as the energy function is non-convex. Using graduated non-convexity (GNC) approach, the energy is minimized. The proposed parallel algorithm has been implemented on a cluster of workstations using the PVM communication library. The results of parallel implementation on synthetic and natural images are presented. The speedup is observed to be near-linear, thus providing scalability with the problem size. The parallel processing approach presented here can be extended to solve similar problems (e.g., image restoration, and image compression) which use regularization techniques.