图 书 馆
关于射影图形的图像轮廓On Image Contours of Projective Shapes |
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| 课程网址: | http://videolectures.net/eccv2014_ponce_image_contours/ |
| 主讲教师: | Jean Ponce |
| 开课单位: | 法国国家信息与自动化研究所 |
| 开课时间: | 2014-10-29 |
| 课程语种: | 英语 |
| 中文简介: |  本文回顾了以光滑表面为边界的实体轮廓的经典属性，并表明可以在纯投影环境中建立它们，而无需使用诸如法线或曲率的欧几里得度量。特别是，我们给出了Koenderink著名的关于图像轮廓的凹凸的定理的新综合证明，以及边缘在切点的凸点处沿与视点相同的方向以及相反的方向旋转的事实在一个双曲线点。这表明射影几何不仅应视为线性化计算的分析工具（其主要作用在于运动的结构），还应视为研究实体形状与其透视投影之间关系的适当框架。与该领域以前的工作不同，该提议的方法不需要定向的设置，也不依赖于坐标系或分析考虑因素的任何选择。 |
| 课程简介: | This paper revisits classical properties of the outlines of solid shapes bounded by smooth surfaces, and shows that they can be established in a purely projective setting, without appealing to Euclidean measurements such as normals or curvatures. In particular, we give new synthetic proofs of Koenderink’s famous theorem on convexities and concavities of the image contour, and of the fact that the rim turns in the same direction as the viewpoint in the tangent plane at a convex point, and in the opposite direction at a hyperbolic point. This suggests that projective geometry should not be viewed merely as an analytical device for linearizing calculations (its main role in structure from motion), but as the proper framework for studying the relation between solid shape and its perspective projections. Unlike previous work in this area, the proposed approach does not require an oriented setting, nor does it rely on any choice of coordinate system or analytical considerations. |
| 关 键 词: | 分析工具; 欧几里得度量 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2021-01-06：zyk |
| 最后编审: | 2021-01-06：zyk |
| 阅读次数: | 40 |