Minimizing the Reprojection Error in Surface Reconstruction from Images

Abstract

This paper addresses the problem of image-based surface reconstruction. The main contribution is the computation of the exact derivative of the reprojection error functional. This allows its rigorous minimization via gradient descent surface evolution. The main difficulty has been to correctly take into account the visibility changes that occur when the surface moves. A geometric and analytical study of these changes is presented and used for the computation of derivative.Our analysis shows the strong influence that the movement of the contour generators has on the reprojection error. As a consequence, during the proper minimization of the reprojection error, the contour generators of the surface are automatically moved to their correct location in the images. Therefore, current methods adding additional silhouettes or apparent contour constraints to ensure this alignment can now be understood and justified by a single criterion: the reprojection error.

Generic Scene Recovery Using Multiple Images

“…As suggested by [20,21], to be sure that the estimated foreground surface does not shrink to an empty set, it is crucial to define and characterize the background. In this work, we assume that we have the background imagesĨ = {Ĩ 1 , · · · ,Ĩ nc } and define (Ĩ iF ,Ĩ iB ) analogously to (I iF , I iB ).…”

“…where δ(·) is the delta function andê i is an error computed by using the radiance at point X in the direction of the i th camera, which is the terminator of a horizon point X [21]. When a horizon point has no terminator point on the surface,ê i = 0 because the terminator point is from the background.…”

“…The data cost is a function of the visibility of a surface point, which is dependent on the whole surface shape. According to [20,21] for correctly dealing with the visibility of non-convex objects, S t data is given by…”

Integration of Multiview Stereo and Silhouettes Via Convex Functionals on Convex Domains

“…Alternatively, one can unify both information sources in a single formulation. Two different techniques have been proposed to achieve this goal: One can integrate in the evolution silhouette-aligning forces [13,14,15,16], or one can use predetermined surface points [17,18,19] to impose exact silhouette constraints. Both strategies have their shortcomings.…”

An Occupancy–Depth Generative Model of Multi-view Images

“…A voxel carving technique carving inside the object, or a shrinking surface evolution are consequences of this oversight. Our recent work [12] avoids these problems by explicitly taking into account the visibility changes during the surface evolution. This is nothing but the continuous version of the model presented in this paper.…”