Mean shift clustering is a powerful nonparametric technique that does not require prior knowledge of the number of clusters and does not constrain the shape of the clusters. However, being completely unsupervised, its performance suffers when the original distance metric fails to capture the underlying cluster structure. Despite recent advances in semi-supervised clustering methods, there has been little effort towards incorporating supervision into mean shift. We propose a semi-supervised framework for kernel mean shift clustering (SKMS) that uses only pairwise constraints to guide the clustering procedure. The points are first mapped to a high-dimensional kernel space where the constraints are imposed by a linear transformation of the mapped points. This is achieved by modifying the initial kernel matrix by minimizing a log det divergence-based objective function. We show the advantages of SKMS by evaluating its performance on various synthetic and real datasets while comparing with state-of-the-art semi-supervised clustering algorithms.

We propose a novel robust estimation algorithm—the generalized projection-based M-estimator (gpbM), which does not require the user to specify any scale parameters. The algorithm is general and can handle heteroscedastic data with multiple linear constraints for single and multicarrier problems. The gpbM has three distinct stages—scale estimation, robust model estimation, and inlier/outlier dichotomy. In contrast, in its predecessor pbM, each model hypotheses was associated with a different scale estimate. For data containing multiple inlier structures with generally different noise covariances, the estimator iteratively determines one structure at a time. The model estimation can be further optimized by using Grassmann manifold theory. We present several homoscedastic and heteroscedastic synthetic and real-world computer vision problems with single and multiple carriers.

We introduce a robust estimator called generalized projection based M-estimator (gpbM) which does not require the user to specify any scale parameters. For multiple inlier structures, with different noise covariances, the estimator iteratively determines one inlier structure at a time. Unlike pbM, where the scale of the inlier noise is estimated simultaneously with the model parameters, gpbM has three distinct stages-scale estimation, robust model estimation and inlier/outlier dichotomy. We evaluate our performance on challenging synthetic data, face image clustering upto ten different faces from Yale Face Database B and multi-body projective motion segmentation problem on Hopkins155 dataset. Results of state-of-the-art methods are presented for comparison.

Following work of Stroud and Saeger and Anand et al., we formulate a port of entry inspection sequencing task as a problem of finding an optimal binary decision tree for an appropriate Boolean decision function. We report on new algorithms that are more efficient computationally than those presented by Stroud and Saeger and Anand et al. We achieve these efficiencies through a combination of specific numerical methods for finding optimal thresholds for sensor functions and a novel binary decision tree search algorithm that operates on a space of potentially acceptable binary decision trees.