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Sign of Gaussian curvature from eigen plane using principal components analysis

机译:主成分分析的特征面高斯曲率符号

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Describes a method to recover the sign of the local Gaussian curvature at each point on the visible surface of a 3-D object. Multiple (p<3) shaded images are acquired under different conditions of illumination. The required information is extracted from a 2-D subspace obtained by applying principal components analysis (PCA) to the p-dimensional space of normalized irradiance measurements. The number of dimensions is reduced from p to 2 by considering only the first two principal components. The sign of the Gaussian curvature is recovered based on the relative orientation of measurements obtained on a local five point test pattern to those in the 2-D subspace, called the eigen plane. The method does assume generic diffuse reflectance. The method recovers the sign of Gaussian curvature without assumptions about the light source directions or about the specific functional form of the diffuse surface reflectance. Multiple (p<3) light sources minimize the effect of shadows by allowing a larger area of visible surface to be analyzed. Results are demonstrated by experiments on synthetic and real data. The results are more accurate and more robust compared to previous approaches.
机译:描述了一种方法,用于在3-D对象的可见表面上的每个点处恢复局部高斯曲率的符号。在不同的照明条件下获取多个(P <3)阴影图像。通过将主成分分析(PCA)应用于标准化辐照度测量的P维空间而获得的二维子空间中提取所需信息。通过考虑仅考虑前两个主要组件,从P到2减少了尺寸的数量。基于在局部五点测试模式中获得的测量的相对取向来恢复高斯曲率的标志,该测量值为2-D子空间中的那些,称为eIgen平面。该方法确实假设通用漫反射率。该方法恢复高斯曲率的迹象,而不是围绕光源方向的假设或围绕漫射表面反射率的特定功能形式的假设。多个(P <3)光源通过允许分析较大的可见表面来最小化阴影的效果。结果是通过关于合成和实际数据的实验来证明的。与先前的方法相比,结果更准确,更强大。

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