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A technique is presented to combine n data points, each available with point-dependent uncertainty, when only a subset of these points come from N≪n sources, where N is unknown. We detect the significant modes of the underlying multivariate probability distribution using a generalization of the nonparametric mean shift procedure. The number of detected modes automatically defines N, while the belonging of a point to the basin of attraction of a mode provides the fusion rule. The robust data fusion algorithm was successfully applied to two computer vision problems: estimating the multiple affine transformations, and range image segmentation.