从二维轮廓线重构三维二次曲面形状

由轮廓形状是计算机视觉研究的一个重要问题，通常Ｏｃｃｌｕｄｉｎｇ轮廓线用来恢复三维表面朝向、高斯曲率的符号等局部性质，本文则直接利用Ｏｃｃｌｕｄｉｎｇ轮廓线全避地恢复二次曲面形状，我们证明了两视图轮廓包含的信息不足以重构二次曲面，三幅视图对于恢复二次曲面三维表面是充分而且必要的。我们利用导出的不变量来建立二次曲面轮廓线夺不同视图的对应关系，最后我们给出线性最小二乘重建算法以及实验结果。

ON THE GLOBAL QUADRIC SHAPE FROM CONTOUR

Shape from contour is a very important problem in computer vision. Occluding contour is usually used to recover local properties of 3D visual surface, like orientation and the sign of Gaussian curvature. This paper recovers quadric shape globally from its Occluding contour. It is proved that two images of the quadric surface is not enough to reconstruct the quadric surface. Three images from different viewpoints are necessary and sufficient to uniquely recover the quadric surface. This paper also shows that the contours in images of the same quadric surface correspond to one another through invariants. Another important feature of our algorithm is that the quadric shape can be recovered linearly. The algorithm has been successfully tested by synthesized data.