Integrating Surface Normal Vectors Using Fast Marching Method

Abstract. Integration of surface normal vectors is a vital component in many shape reconstruction algorithms that require integrating surface normals to produce their final outputs, the depth values. In this paper, we introduce a fast and efficient method for computing the depth val-ues from surface normal vectors. The method is based on solving the Eikonal equation using Fast Marching Method. We introduce two ideas. First, while it is not possible to solve for the depths Z directly using Fast Marching Method, we solve the Eikonal equation for a function W of the form W = Z+λf. With appropriately chosen values for λ, we can ensure that the Eikonal equation for W can be solved using Fast March-ing Method. Second, we solve for W in two stages with two different λ values, first in a small neighborhood of the given initial point with large λ, and then for the rest of the domain with a smaller λ. This step is needed because of the finite machine precision and rounding-off errors. The proposed method is very easy to implement, and we demonstrate experimentally that, with insignificant loss in precision, our method is considerably faster than the usual optimization method that uses conju-gate gradient to minimize an error function.

Solving the Uncalibrated Photometric Stereo Problem using Total Variation

International audienceIn this paper we propose a new method to solve the problem of uncalibrated photometric stereo, making very weak assumptions on the properties of the scene to be reconstructed. Our goal is to solve the generalized bas-relief ambiguity (GBR) by performing a total variation regularization of both the estimated normal field and albedo. Unlike most of the previous attempts to solve this ambiguity, our approach does not rely on any prior information about the shape or the albedo, apart from its piecewise smoothness. We test our method on real images and obtain results comparable to the state-of-the-art algorithms

Solving Uncalibrated Photometric Stereo using Total Variation

International audienceEstimating the shape and appearance of an object, given one or several images, is still an open and challenging research problem called 3D-reconstruction. Among the different techniques available, photometric stereo (PS) produces highly accurate results when the lighting conditions have been identified. When these conditions are unknown, the problem becomes the so-called uncalibrated PS problem, which is ill-posed. In this paper, we will show how total variation can be used to reduce the ambiguities of uncalibrated PS, and we will study two methods for estimating the parameters of the generalized bas-relief ambiguity. These methods will be evaluated through the 3D-reconstruction of real-world objects