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A continuous Formulation of intrinsic Dimension

The intrinsic dimension (see, e.g., [29, 11]) has proven to be a suitable descriptor to distinguish between different kind of image structures such as edges, junctions or homogeneous image patches. In this paper, we will show that the intrinsic dimension is spanned by two axes: one axis represents the variance of the spectral energy and one represents the a weighted variance in orientation. Moreover, we will show in section that the topological structure of instrinsic dimension has the form of a triangle. We will review diverse definitions of intrinsic dimension and we will show that they can be subsumed within the above mentioned scheme. We will then give a concrete continous definition of intrinsic dimension that realizes its triangular structure.