Shape from inconsistent silhouette

Shape from Silhouette (SfS) is the general term used to refer to the techniques that obtain a volume estimate from a set of binary images. In a first step, a number of images are taken from different positions around the scene of interest. Later, each image is segmented to produce binary masks, also called silhouettes, to delimit the objects of interest. Finally, the volume estimate is obtained as the maximal one which yields the silhouettes. The set of silhouettes is usually considered to be consistent which means that there exists at least one volume which completely explains them. However, silhouettes are normally inconsistent due to inaccurate calibration or erroneous silhouette extraction techniques. In spite of that, SfS techniques reconstruct only that part of the volume which projects consistently in all the silhouettes, leaving the rest unreconstructed. In this paper, we extend the idea of SfS to be used with sets of inconsistent silhouettes. We propose a fast technique for estimating that part of the volume which projects inconsistently and propose a criteria for classifying it by minimizing the probability of miss-classification taking into account the 2D error detection probabilities of the silhouettes. A number of theoretical and empirical results are given, showing that the proposed method reduces the reconstruction error.