论文标题
在任意域上的最小二乘表面重建
Least squares surface reconstruction on arbitrary domains
论文作者
论文摘要
在计算机视觉中，几乎普遍使用表面导数时，仅使用一阶准确的有限差近似值计算它们。我们提出了一种基于2D Savitzky-Golay过滤器和K-Nearest邻居内核的数值衍生物的新方法。在存在大噪声的情况下，可以将所得的衍生矩阵用于任意（甚至是断开）域的最小二乘表面重建，并允许高阶多项式局部表面近似值。它们对于一系列任务很有用，包括正常的深度（即表面差异），高度 - 正常值（即表面积分）和形状 - from-X。我们展示了如何使用相同的公式将拼字法或透视高范围作为线性最小二乘问题，并避免在透视案例中避免变量的非线性变化。我们证明了相对于合成和真实数据的这些任务的最新任务的性能提高，并提供了我们方法的开源实现。
Almost universally in computer vision, when surface derivatives are required, they are computed using only first order accurate finite difference approximations. We propose a new method for computing numerical derivatives based on 2D Savitzky-Golay filters and K-nearest neighbour kernels. The resulting derivative matrices can be used for least squares surface reconstruction over arbitrary (even disconnected) domains in the presence of large noise and allowing for higher order polynomial local surface approximations. They are useful for a range of tasks including normal-from-depth (i.e. surface differentiation), height-from-normals (i.e. surface integration) and shape-from-x. We show how to write both orthographic or perspective height-from-normals as a linear least squares problem using the same formulation and avoiding a nonlinear change of variables in the perspective case. We demonstrate improved performance relative to state-of-the-art across these tasks on both synthetic and real data and make available an open source implementation of our method.
