Nonlinear Eigenproblems in Image Processing and Computer Vision by Guy Gilboa

Author:Guy Gilboa
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

We can now consider filterings of the inverse scale space flow representation, again by formal integration by parts

where T is the finite extinction time stated by Proposition 5.5. The last line can be used to define filterings in the inverse scale space flow setting. Note that for all t leads to a reconstruction of the , i.e.,

(5.25)

5.4.4 Definitions of the Power Spectrum

As in the linear case, it is very useful to measure in some sense the “activity” at each frequency (scale). This can help identify dominant scales and design better the filtering strategies (either manually or automatically). Moreover, one can obtain a notion of the type of energy which is preserved in the new representation using an analog of Parseval’s identity. While the amount of information on various spatial scales in linear and nonlinear scale spaces has been analyzed using Renyi’s generalized entropies in [9], we will focus on defining a spectral power spectrum. As we have seen above, at least for an orthogonal spectral definition there is a natural definition of the power spectrum as the measure

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