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.