Degen Generalized Cylinders and Their Properties

  • Liangliang Cao
  • Jianzhuang Liu
  • Xiaoou Tang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3951)


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.


Computer Vision Tangent Plane Machine Intelligence Invariant Property Projective Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Liangliang Cao
    • 1
  • Jianzhuang Liu
    • 1
  • Xiaoou Tang
    • 1
    • 2
  1. 1.Department of Information EngineeringThe Chinese University of Hong KongHong KongChina
  2. 2.Microsoft Research AsiaBeijingChina

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