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首页> 外文期刊>IEEE Transactions on Pattern Analysis and Machine Intelligence >Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation
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Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation

机译：估计由隐式方程定义的平面曲线，曲面和非平面空间曲线，并将其应用于边缘和范围图像分割

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The author addresses the problem of parametric representation and estimation of complex planar curves in 2-D surfaces in 3-D, and nonplanar space curves in 3-D. Curves and surfaces can be defined either parametrically or implicitly, with the latter representation used here. A planar curve is the set of zeros of a smooth function of two variables x-y, a surface is the set of zeros of a smooth function of three variables x-y-z, and a space curve is the intersection of two surfaces, which are the set of zeros of two linearly independent smooth functions of three variables x-y-z For example, the surface of a complex object in 3-D can be represented as a subset of a single implicit surface, with similar results for planar and space curves. It is shown how this unified representation can be used for object recognition, object position estimation, and segmentation of objects into meaningful subobjects, that is, the detection of 'interest regions' that are more complex than high curvature regions and, hence, more useful as features for object recognition.
机译：作者解决了3-D中2-D表面中的复杂平面曲线的参数表示和估计以及3-D中非平面空间曲线的参数表示和估计问题。曲线和曲面可以参数化或隐式定义，此处使用后者表示。平面曲线是两个变量xy的光滑函数的零点集，表面是三个变量xyz的光滑函数的零点集，而空间曲线是两个表面的交点，它们是零点集三个变量xyz的两个线性独立平滑函数的关系例如，3-D中复杂物体的表面可以表示为单个隐式表面的子集，对于平面和空间曲线，其结果类似。展示了如何将这种统一表示形式用于对象识别，对象位置估计以及将对象分割为有意义的子对象，即检测比高曲率区域更复杂，因此更有用的“兴趣区域”作为对象识别的功能。

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