Needle map recovery using robust regularizers

Abstract

This article describes how robust error-kernels can be used as smoothness priors in recovering shape-from-shading (SFS). Conventionally, the smoothness error is added to the data-closeness (or brightness-error) as a quadratic regularizer. This leads to over-smoothing of the recovered needle-map or surface, and the loss of important detail provided by surface discontinuities. To solve this problem, we investigate the use of robust regularizers to reduce the smoothening by treating rapid changes in surface orientation as outliers in the calculation of the smoothness error. In particular, we study an existing continuous approximation to the Tukey bi-weight as a robust regularizer, and introduce a novel regularizer of the form log cosh η, which approximates the Huber estimator. The latter regularizer has a sigmoidal derivative and offers a compromise between premature outlier rejection and smoothening. Experiments on synthetic and real-world data reveal that this robust regularizer enhances needle-map recovery, without sacrificing robustness to noise or becoming over-sensitive to numerical instabilities.