Bézier Curves in the Space of Images
Bézier Curves in the Space of Images
复制标题
图像空间中的贝塞尔曲线
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
B. Wirth
中科院分区：
文献类型：
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作者：
Alexander Effland;M. Rumpf;Stefan Simon;Kirsten Stahn;B. Wirth
贝塞尔曲线是欧几里得空间中曲线设计的常用工具。本文将贝塞尔曲线的概念推广到图像的无限维空间。为此，图像空间配备了黎曼度量，该度量在变形模型[MY01]的意义上测量图像传输的成本和强度变化。然后通过 de Casteljau 算法的黎曼版本计算贝塞尔曲线，该算法基于沿测地线凸组合的分层方案。使用黎曼路径能量的变分离散化来近似测地线。这导致了一种广义的 de Casteljau 方法来计算图像空间中合适的离散贝塞尔曲线。选定的测试用例展示了该方法的定性特性。此外，还提出了一种通过图像草图调制面部插值和形状动画的贝塞尔方法。
Bezier curves are a widespread tool for the design of curves in Euclidian space. This paper generalizes the notion of Bezier curves to the infinite-dimensional space of images. To this end the space of images is equipped with a Riemannian metric which measures the cost of image transport and intensity variation in the sense of the metamorphosis model [MY01]. Bezier curves are then computed via the Riemannian version of de Casteljau’s algorithm, which is based on a hierarchical scheme of convex combination along geodesic curves. Geodesics are approximated using a variational discretization of the Riemannian path energy. This leads to a generalized de Casteljau method to compute suitable discrete Bezier curves in image space. Selected test cases demonstrate qualitative properties of the approach. Furthermore, a Bezier approach for the modulation of face interpolation and shape animation via image sketches is presented.
影响因子：
2.1
作者：
Berkels, B.;Effland, A.;Rumpf, M.
通讯作者：
Rumpf, M.