从光滑曲面图像恢复对极几何
Recovering Epipolar Geometry from Images of Smooth Surfaces
摘要：
我们提出了四种方法来恢复核几何从图像的光滑表面。在用于恢复对极几何的现有方法中，使用在这样的图像中找不到的对应特征点。第一种方法是基于找到由照明创建的对应特征点（ICPM -照明特征点方法（PM））。第二种方法是基于相应的切点创建的切线从核线的光滑体（OTPM -轮廓切线PM）。这两种方法都是精确的，对真实图像给出正确的结果，因为相应的照明特征点的位置和相应的轮廓是已知的，误差很小。但是第二种方法要么局限于特殊类型的场景，要么局限于受限的相机运动。我们还考虑了两种方法，被称为CCPM（曲线特征PM）和CTPM（曲线切线PM），用于搜索对极几何的图像的光滑体的基础上的一组水平曲线与恒定的照明强度。CCPM方法是基于等照度曲线上的对应点的搜索与这些线之间的曲率的相关性的帮助。CTPM方法是根据等照度曲线的切线核线的性质，将其映射为对应等照度曲线的切线核线。标准方法（SM）基于几乎精确对应点对的知识。该方法已实施和测试SM对真实图像。不幸的是，最后两种方法只给我们一个有限的子集的解决方案，包括“好”的解决方案。例外是“无穷远的核线”。其主要原因是光滑天体的等亮度假设不准确。但轮廓和光照特征点不受此误差的影响。因此，第一对方法给出了精确的结果。
英文摘要：
We present four methods for recovering the epipolar geometry from images of smooth surfaces. In the existing methods for recovering epipolar geometry corresponding feature points are used that cannot be found in such images. The first method is based on finding corresponding characteristic points created by illumination (ICPM - illumination characteristic points' method (PM)). The second method is based on correspondent tangency points created by tangents from epipoles to outline of smooth bodies (OTPM - outline tangent PM). These two methods are exact and give correct results for real images, because positions of the corresponding illumination characteristic points and corresponding outline are known with small errors. But the second method is limited either to special type of scenes or to restricted camera motion. We also consider two more methods which are termed CCPM (curve characteristic PM) and CTPM (curve tangent PM), for searching epipolar geometry for images of smooth bodies based on a set of level curves with constant illumination intensity. The CCPM method is based on searching correspondent points on isophoto curves with the help of correlation of curvatures between these lines. The CTPM method is based on property of the tangential to isophoto curve epipolar line to map into the tangential to correspondent isophoto curves epipolar line. The standard method (SM) based on knowledge of pairs of the almost exact correspondent points. The methods have been implemented and tested by SM on pairs of real images. Unfortunately, the last two methods give us only a finite subset of solutions including "good" solution. Exception is "epipoles in infinity". The main reason is inaccuracy of assumption of constant brightness for smooth bodies. But outline and illumination characteristic points are not influenced by this inaccuracy. So, the first pair of methods gives exact results.
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