The main contribution of this paper has been to develop a general framework for applying robust statistics to the iterative recovery of needle-maps. From the theoretical perspective, our contributions have been twofold. In the first instance, we have shown how robust error-kernels can be used as smoothness regularizers. Our second contribution has been to develop a novel robust regularizer, and apply this to produce an update equation for the iterative recovery of the needle-map. We evaluate the performance of the new shape-from-shading process against the conventional iterative scheme, and demonstrate that the sigmoidal regularizer offers the dual advantages of delivering improved normal recovery and increased noise rejection.
There are a number of ways in which the work described here can be extended. Our primary motivation in embarking on this study has been to facilitate needle-map recovery without over-smoothing fine curvature detail. Although the apparatus of robust statistics provides an effective means of realising this goal, it fails to exploit the differential structure of the needle-map in a direct way. It is for this reason that our immediate goal is to develop a regularization framework which preserves consistent curvature structures. Although Legarde and Ferrie [ 4 ] have posed shape-from-shading using curvature consistency constraints, their regularizer is couched in terms of the quadratic smoothness of the principal curvature directions. Our immediate goal is therefore to explore how curvature consistency can be posed in terms of robust statistics.
Benoit Huet