Consistent parameter clustering: Definition and analysis

Parameter clustering is a popular robust estimation technique based on location statistics in a parameter space where parameter samples are obtained from data samples. A problem with clustering methods is that they produce estimates not invariant to transformations of the parameter space. This article presents three contributions to the theoretical study of parameter clustering. First, it introduces a probabilistic formalization of parameter clustering. Second, it uses the formalism to define consistency in terms of a symmetry requirement and to derive criteria for a consistent choice of parameterization. And third, it applies the criteria to the practically relevant cases of motion and pose estimation of three-dimensional shapes. Bias and error statistics on random data sets demonstrate a significant advantage of using a consistent parameterization for rotation clustering. Moreover, clustering parameters of analytic shapes is discussed and a real application example of circle estimation given.