Rotation Invariant Kernels and Their Application to Shape Analysis
Rotation Invariant Kernels and Their Application to Shape Analysis
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DOI：
10.1109/tpami.2008.234
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发表时间：
2009-11-01
影响因子：
23.6
通讯作者：
Martinez, Aleix M.
中科院分区：
文献类型：
--
作者：
Hamsici, Onur C.;Martinez, Aleix M.
形状分析需要在翻译，比例和旋转下的不变性。翻译和比例不变性可以通过使形状向量相对于其平均值和规范来实现。这将形状特征向量映射到超晶表面。归一化后，可以通过使用复杂的超晶体上定义的复杂标量旋转不变分布来对所得数据进行建模，例如使用复杂的宾厄姆分布来使形状矢量进行旋转不变。但是，这些分布的使用受到估计其参数和表述的非线性性质的困难的阻碍。在本文中，我们展示了如何使用我们称为旋转不变内核的一组内核函数将原始的非线性问题转换为线性问题。顾名思义，这些内核被定义为提供急需的旋转属性，从而允许人们绕过使用复杂的球形分布的困难。最终的方法为2D和3D形状分析提供了一种简单，快速的机制。使用各种形状建模和分类问题的广泛验证证明了这种提出的方法的准确性。
Shape analysis requires invariance under translation, scale, and rotation. Translation and scale invariance can be realized by normalizing shape vectors with respect to their mean and norm. This maps the shape feature vectors onto the surface of a hypersphere. After normalization, the shape vectors can be made rotational invariant by modeling the resulting data using complex scalar-rotation invariant distributions defined on the complex hypersphere, e.g., using the complex Bingham distribution. However, the use of these distributions is hampered by the difficulty in estimating their parameters and the nonlinear nature of their formulation. In the present paper, we show how a set of kernel functions that we refer to as rotation invariant kernels can be used to convert the original nonlinear problem into a linear one. As their name implies, these kernels are defined to provide the much needed rotation invariance property allowing one to bypass the difficulty of working with complex spherical distributions. The resulting approach provides an easy, fast mechanism for 2D & 3D shape analysis. Extensive validation using a variety of shape modeling and classification problems demonstrates the accuracy of this proposed approach.