AI 中文总结
本文提出结合热传导与明暗线索的新理论，在不依赖平滑先验且光源未知时，解决形状恢复中的局部凸凹模糊，并通过仿真和真实热视频验证。
AI 中文摘要
利用朗伯表面的单幅图像进行明暗恢复形状（Shape from Shading）本质上具有模糊性。当光源方向已知时，表面法线估计存在锥形模糊，而当光源未知时，该模糊会加剧。近年来，基于热传导的形状恢复（Shape from Heat Conduction）作为一种方法出现，它利用热传导方程来估计形状拉普拉斯算子（Shape Laplacian operator），这是一种形状的内在度量。然而，从拉普拉斯算子推导表面法线会遇到局部的二值凸/凹模糊。我们的贡献在于提出一种新理论，在不依赖平滑性等先验的情况下，通过结合明暗和热传导的线索来解决这些局部形状模糊（排除少数退化情况）。我们的方法确保明暗和拉普拉斯算子的数学约束同时得到满足，即使光源未知也是如此。我们通过复杂形状的仿真验证了我们的理论，并分析了其在存在噪声时的性能，以及在一个包含复杂形状和材料属性（包括变化的反照率）的真实世界物体的带噪单热视频上的表现。
英文摘要
Shape from shading using a single image of a Lam- bertian surface is inherently ambiguous. When the light source direction is known, the surface normal estimation has a cone- ambiguity, which worsens when the source is unknown. Recently, shape from heat conduction has emerged as an approach that leverages heat transport equations to estimate the Shape Lapla- cian operator, an intrinsic measure of shape. However, deriving surface normals from the Laplacian operator encounters a local binary convex/concave ambiguity. Our contribution introduces a novel theory to resolve these local shape ambiguities (excluding a few degeneracies) without relying on priors like smoothness, by combining the cues from shading and heat conduction. Our method ensures the mathematical constraints of both shading and the Laplacian are satisfied simultaneously, even with an unknown light source. We validate our theory through simulations of complex shapes and analyze its performance in the presence of noise, as well as on a noisy single thermal video of real-world objects with complex shapes and material properties, including varying albedo.
CommentsProject Page: https://shape-from-heat-and-shading.github.io/
