Charalampidis Dimitrios
Department of Electrical Engineering, University of New Orleans, 2000 Lakeshore Dr., New Orleans, LA 70148, USA.
IEEE Trans Pattern Anal Mach Intell. 2005 Dec;27(12):1856-65. doi: 10.1109/TPAMI.2005.230.
Several important pattern recognition applications are based on feature vector extraction and vector clustering. Directional patterns are commonly represented by rotation-variant vectors Fd formed from features uniformly extracted in M directions. It is often desirable that pattern recognition algorithms are invariant under pattern rotation. This paper introduces a distance measure and a K-means-based algorithm, namely, Circular K-means (CK-means) to cluster vectors containing directional information, such as Fd, in a circular-shift invariant manner. A circular shift of Fd corresponds to pattern rotation, thus, the algorithm is rotation invariant. An efficient Fourier domain representation of the proposed measure is presented to reduce computational complexity. A split and merge approach (SMCK-means), suited to the proposed CK-means technique, is proposed to reduce the possibility of converging at local minima and to estimate the correct number of clusters. Experiments performed for textural images illustrate the superior performance of the proposed algorithm for clustering directional vectors Fd, compared to the alternative approach that uses the original K-means and rotation-invariant feature vectors transformed from Fd.
几个重要的模式识别应用基于特征向量提取和向量聚类。方向模式通常由在M个方向上均匀提取的特征形成的旋转可变向量Fd表示。模式识别算法通常希望在模式旋转下具有不变性。本文介绍了一种距离度量和一种基于K均值的算法,即循环K均值(CK均值),以循环移位不变的方式对包含方向信息的向量(如Fd)进行聚类。Fd的循环移位对应于模式旋转,因此该算法是旋转不变的。提出了一种有效的傅里叶域表示方法来降低计算复杂度。提出了一种适用于所提出的CK均值技术的分裂合并方法(SMCK均值),以降低在局部最小值处收敛的可能性并估计正确的聚类数。对纹理图像进行的实验表明,与使用原始K均值和从Fd变换而来的旋转不变特征向量的替代方法相比,所提出的算法在聚类方向向量Fd方面具有优越的性能。