We develop a powerful probabilistic framework for the local characterization of surfaces and edges in range images. We use the geometrical nature of the data to derive an analytic expression for the joint probability density function (pdf) for the random variables used to model the ranges of a set of pixels in a local neighborhood of an image. We decompose this joint pdf by considering independently the cases where two real world points corresponding to two neighboring pixels are locally on the same real world surface or not. In particular, we show that this joint pdf is linked to the Voigt pdf and not to the Gaussian pdf as it is assumed in some applications. We apply our framework to edge detection and develop a locally adaptive algorithm that is based on a probabilistic decision rule. We show in an objective evaluation that this new edge detector performs better than prior art edge detectors. This proves the benefits of the probabilistic characterization of the local neighborhood as a tool to improve applications that involve range images.

中文翻译：

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用于表征范围图像中的表面和边缘的概率框架及其在边缘检测中的应用


我们开发了一个强大的概率框架，用于范围图像中表面和边缘的局部表征。我们利用数据的几何性质来推导出用于对图像局部邻域中一组像素的范围进行建模的随机变量的联合概率密度函数 (pdf) 的解析表达式。我们通过独立考虑对应于两个相邻像素的两个现实世界点局部位于同一现实世界表面上或不在同一现实世界表面上的情况来分解该联合概率密度函数。特别是，我们表明该联合 pdf 与 Voigt pdf 相关，而不是像某些应用中假设的那样与高斯 pdf 相关。我们将我们的框架应用于边缘检测，并开发一种基于概率决策规则的局部自适应算法。我们在客观评估中表明，这种新的边缘检测器比现有技术的边缘检测器表现更好。这证明了局部邻域的概率表征作为改进涉及范围图像的应用的工具的好处。