Continuous Surface Normal Integration
Keywords: normal integration, shape modelling, shape recovery
Abstract: We address a novel task for monocular explicit surface reconstruction that extends traditional surface normal integration over measurements on a regular grid to direct continuous surface depth estimation. Our solution accepts coordinates as queries and predicts both the normal and depth of an arbitrary query point by its relative locations and orientations to the points distributed in its vicinity. In general, all points are regarded by our model as random samples drawn from an underlying continuous gradient field of a surface which we parameterize using a field of polynomials to establish its topology. We establish a mapping from coordinates to a sequence of learnable polynomial coefficients to model a continuous surface and train a neural network to approximate it. We decompose a continuous surface representation into two components: (1) a set of grid points of unknown orientations whose locations are picked by a quadtree and (2) a set of sample points whose orientations are directly observable. Our training workflow estimates the normal of grid points and the locations of depth discontinuities iteratively. During each iteration, we generate a normal map of grid points for it to be processed by a standard bilateral normal integrator to identify the locations of depth discontinuities, which we use to refine the estimation for grid-based normal map in the subsequent iteration. As a result, the learned model generates both normal and depth for arbitrary coordinates accurately in a continuous field. We provide both theoretical formulation for our design and extensive empirical evidence to demonstrate that our proposed method not only delivers a performance as effective as its grid-based counterpart approaches but also flexibly and accurately addresses the continuous cases that existing methods are unable to handle.
Primary Area: applications to computer vision, audio, language, and other modalities
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Submission Number: 2697
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