Adaptive Regularization: Towards Self-Calibrated Reconstruction

Regularization is often applied to the ill-posed problem of surface reconstruction. This implies the incorporation of a priori knowledge in the solution. The reconstruction depends strongly on this a priori information. Typically, qualitative a priori information is used, leaving it to the user to estimate parameters, (eg. the weak string \citeblake). Other methods depend strongly on assumptions of the viewing geometry and/or statistics of the scene \citebelhumeur, \citeisotrop. Neither the viewing geometry nor the scene statistics are in general known for an active observer. In dynamic vision, however, the a priori knowledge can be extracted from the reconstruction of the previous scenes. This leads to an adaptive regularization scheme capable of capturing the resulting scene statistics in the camera coordinate system. Consequently, calibration is not needed. The a priori knowledge required is the amount of noise in the data, and that the statistics of the scene is only varying slowly. It is shown that the adaptive regularization yields results which are comparable to those of the weak string if the input is piecewise planar. Inputs having only a few different surface orientations are reconstructed robustly. The adaptive system is shown to have 1 stable fixpoint.