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Two new data structures are defined for use in multidimensional histogramming. Their purpose is to cover a parameter space with a limited number of histogram bins so that fine precision is maintained where it is needed. The original motivation for these data structures was to implement Hough-like transforms in high-dimensional parameter spaces. The two data structures share the ability to adapt to distributions that change with time.

A convenient representation for blob-like figures in an image consists of the orientation, length, and width of a bounding rect-angle. One fast algorithm for producing such a bounding rectangle is based upon a dot product space. The analysis of the dot product space shape representation is improved to handle certain pathological cases, and it is shown how to generalize this analysis to accommodate different criteria for the goodness of the representation.