This paper presents a generalization of Kokaram's model for scratch lines detection on digital film materials. It is based on the assumption that scratch is not purely additive on a given image but shows also a destroying effect. This result allows us to design a more efficacious scratch detector which performs on a hierarchical representation of a degraded image, i.e., on its cross section local extrema. Thanks to Weber's law, the proposed detector even works well on slight scratches resulting completely automatic, except for the scratch color (black or white). The experimental results show that the proposed detector works better in terms of good detection and false alarms rejection with a lower computing time.

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The separation of overlapping components is a well-known and difficult problem in multicomponent signals analysis and it is shared by applications dealing with radar, biosonar, seismic, and audio signals. In order to estimate the instantaneous frequencies of a multicomponent signal, it is necessary to disentangle signal modes in a proper domain. Unfortunately, if signal modes supports overlap both in time and frequency, separation is only possible through a parametric approach whenever the signal class is a priori fixed. In this work, time-frequency analysis and Radon transform are jointly used for the unsupervised separation of modes of a generic frequency modulated signal in noisy environment. The proposed method takes advantage of the ability of the Radon transform of a proper time-frequency distribution in separating overlapping modes. It consists of a blind segmentation of signal components in Radon domain by means of a near-to-optimal threshold operation. The inversion of the Radon transform on each detected region allows us to isolate the instantaneous frequency curves of each single mode in the time-frequency domain. Experimental results performed on constant amplitudes chirp signals confirm the effectiveness of the proposed method, opening the way for its extension to more complex frequency modulated signals.