Invariant Properties of Straight Homogeneous Generalized Cylinders and Their Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
Finding and recovering SHGC objects in an edge image
CVGIP: Image Understanding
Recovery of 3-D objects with multiple curved surfaces from 2-D contours
Artificial Intelligence
Segmentation and recovery of SHGCs from a real intensity image
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recovery of SHGCs From a Single Intensity View
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Applied Geometry for Computer Graphics
Applied Geometry for Computer Graphics
Perception of 3-D Surfaces from 2-D Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recovering Generalized Cylinders by Monocular Vision
ECCV '96 Proceedings of the International Workshop on Object Representation in Computer Vision II
Transitions of the 3D Medial Axis under a One-Parameter Family of Deformations
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Proceedings of the 5th IMA Conference on the Mathematics of Surfaces
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Vision: A Computational Investigation into the Human Representation and Processing of Visual Information
The ACRONYM model-based vision system
IJCAI'79 Proceedings of the 6th international joint conference on Artificial intelligence - Volume 1
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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.