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首页> 外文会议>European Conference on Computer Vision(ECCV 2006) pt.1; 20060507-13; Graz(AT) >Degen Generalized Cylinders and Their Properties
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Degen Generalized Cylinders and Their Properties

机译：简并广义圆柱及其性质

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摘要

Generalized cylinder (GC) has played an important role in computer vision since it was introduced in the 1970s. While studying GC models in human visual perception of shapes from contours, Marr assumed that GC's limbs are planar curves. Later, Koenderink and Ponce pointed out that this assumption does not hold in general by giving some examples. In this paper, we show that straight homogeneous generalized cylinders (SHGCs) and tori (a kind of curved GCs) have planar limbs when viewed from points on specific straight lines. This property leads us to the definition and investigation of a new class of GCs, with the help of the surface model proposed by Degen for geometric modeling. We call them Degen generalized cylinders (DGCs), which include SHGCs, tori, quadrics, cyclides, and more other GCs into one model. Our rigorous discussion is based on projective geometry and homogeneous coordinates. We present some invariant properties of DGCs that reveal the relations among the planar limbs, axes, and contours of DGCs. These properties are useful for recovering DGC descriptions from image contours as well as for some other tasks in computer vision.
机译：自从1970年代问世以来，广义圆柱（GC）在计算机视觉中起着重要作用。在研究人眼从轮廓形状感知GC模型时，Marr认为GC的四肢是平面曲线。后来，Koenderink和Ponce给出了一些示例，指出了这种假设通常并不成立。在本文中，我们显示了从特定直线上的点看时，直的均质广义圆柱（SHGC）和tori（一种弯曲的GC）具有平坦的分支。这一特性使我们能够借助Degen提出的用于几何建模的表面模型来定义和研究一类新的GC。我们称它们为Degen广义圆柱体（DGC），其中将SHGC，花托，二次曲面，环化物和更多其他GC包含在一个模型中。我们的严格讨论基于射影几何和齐次坐标。我们提出了DGC的一些不变性质，揭示了DGC的平面肢体，轴和轮廓之间的关系。这些属性对于从图像轮廓中恢复DGC描述以及计算机视觉中的其他一些任务很有用。

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