On the Link between Gaussian Homotopy Continuation and Convex Envelopes

Abstract. The continuation method is a popular heuristic in computer vision for nonconvex optimization. The idea is to start from a simpli-fied problem and gradually deform it to the actual task while tracking the solution. It was first used in computer vision under the name of graduated nonconvexity. Since then, it has been utilized explicitly or im-plicitly in various applications. In fact, state-of-the-art optical flow and shape estimation rely on a form of continuation. Despite its empirical success, there is little theoretical understanding of this method. This work provides some novel insights into this technique. Specifically, there are many ways to choose the initial problem and many ways to progres-sively deform it to the original task. However, here we show that when this process is constructed by Gaussian smoothing, it is optimal in a specific sense. In fact, we prove that Gaussian smoothing emerges from the best affine approximation to Vese’s nonlinear PDE. The latter PDE evolves any function to its convex envelope, hence providing the optimal convexification

PS-FCN: A Flexible Learning Framework for Photometric Stereo

This paper addresses the problem of photometric stereo for non-Lambertian surfaces. Existing approaches often adopt simplified reflectance models to make the problem more tractable, but this greatly hinders their applications on real-world objects. In this paper, we propose a deep fully convolutional network, called PS-FCN, that takes an arbitrary number of images of a static object captured under different light directions with a fixed camera as input, and predicts a normal map of the object in a fast feed-forward pass. Unlike the recently proposed learning based method, PS-FCN does not require a pre-defined set of light directions during training and testing, and can handle multiple images and light directions in an order-agnostic manner. Although we train PS-FCN on synthetic data, it can generalize well on real datasets. We further show that PS-FCN can be easily extended to handle the problem of uncalibrated photometric stereo.Extensive experiments on public real datasets show that PS-FCN outperforms existing approaches in calibrated photometric stereo, and promising results are achieved in uncalibrated scenario, clearly demonstrating its effectiveness.Comment: ECCV 2018: https://guanyingc.github.io/PS-FC

Calibrating photometric stereo by holistic reflectance symmetry analysis

10.1109/CVPR.2013.197Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition1498-1505PIVR

制約付き回帰に基づく照度差ステレオ

学位の種別: 課程博士審査委員会委員 : (主査)東京大学准教授 山﨑 俊彦, 東京大学教授, 相澤 清晴, 東京大学教授 池内 克史, 東京大学教授 佐藤 真一, 東京大学教授 佐藤 洋一, 東京大学教授 苗村 健University of Tokyo(東京大学