Analysis of planar shapes using geodesic paths on shape spaces
Analysis of planar shapes using geodesic paths on shape spaces
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DOI：
10.1109/tpami.2004.1262333
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发表时间：
2004-03-01
影响因子：
23.6
通讯作者：
Joshi, SH
中科院分区：
文献类型：
--
作者：
Klassen, E;Srivastava, A;Joshi, SH
为了分析平面闭合曲线的形状，我们使用其方向函数和曲率函数提出曲线的微分几何表示。形状被表示为无限维空间的元素，并且使用在这些空间上连接它们的测地线的长度来量化它们的成对差异。我们使用傅立叶基来表示形状空间的切线，然后使用基于梯度的射击方法来求解通过测地线连接任意两个形状的切线。使用萨里鱼数据库，我们演示了这种方法的一些应用：1）形状变化的插值和外推，2）根据对象的形状进行聚类，3）形状空间的统计，以及4）低质量图像中形状的贝叶斯提取。
For analyzing shapes of planar, closed curves, we propose differential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinite-dimensional spaces and their pairwise differences are quantified using the lengths of geodesics connecting them on these spaces. We use a Fourier basis to represent tangents to the shape spaces and then use a gradient-based shooting method to solve for the tangent that connects any two shapes via a geodesic. Using the Surrey fish database, we demonstrate some applications of this approach: 1) interpolation and extrapolations of shape changes, 2) clustering of objects according to their shapes, 3) statistics on shape spaces, and 4) Bayesian extraction of shapes in low-quality images.