On the leakage problem with the Discrete Pulse Transform decomposition

Connected operators act directly on connected components in an image, and though they present a strong framework for extraction of meaningful structures in an image, always suffer from the issue of leakage. The concept of leakage within any connectivity framework refers to situations in which two connected components are connected to each other via a thin, possibly long, pixel-sized connected component and are subsequently considered a single connected component. The LULU operators Ln and Un used to derive the Discrete Pulse Transform are also connected operators and suffer from leakage. We present the Pulse Reformation algorithm to combat leakage in the pulses extracted by the DPT, making use of erosion and subsequent restricted dilations. This enables extraction of meaningful objects consisting of partial pulses of the DPT related over various scales. The examples presented illustrate a useful technique.