A PARALLEL LEAP-FROG ALGORITHM FOR 3-SOURCE PHOTOMETRIC STEREO

Abstract

Existing Photometric Stereo methods provide reasonable surface reconstructions unless the irradiance image is corrupted with noise and effects of digitisation. However, in real world situations the measured image is almost always corrupted, so an efficient method must be formulated to denoise the data. Once noise is added at the level of the images the noisy Photometric Stereo problem with a least squares estimate is transformed into a non-linear discrete optimization problem depending on a large number of parameters. One of the computationally feasible methods of performing this non-linear optimization is to use many smaller local optimizations to find a minimum (called 2D Leap-Frog). However, this process still takes a large amount of time using a single processor, and when realistic image resolutions are used this method becomes impractical. This paper presents a parallel implementation of the 2D Leap-Frog algorithm in order to provide an improvement in the time complexity. While the focus of this research is in the area of shape from shading, the iterative scheme for finding a local optimum for a large number of parameters can also be applied to any optimization problems in Computer Vision. The results presented herein support the hypothesis that a high speed up and high efficiency can be achieved using a parallel method in a distributed shared memory environment.