Nonlinear scale-space

We propose a generalisation of scale-space theory for scalar images. The starting point is the assumption that the conventional Gaussian model constitutes an unbiased (that is, task independent), multiscale image representation. A generalised scale-space is then considered as a conventional scale-space “in disguise”, representing the data in a format that is more convenient for specific applications. Although formally equivalent to the conventional representation (at least locally), a generalised representation may be more apt for a dedicated task. In particular, it may potentially solve the so-called “localisation problem” of linear scale-space. Several models based on nonlinear diffusion have emerged by the desire to deal with this problem. The proposed theory provides a unifying framework for a variety of such models that can be related to conventional scale-space in a one-to-one way.

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