Roadmakers pavage, pulse reformation framework and image segmentation in the discrete pulse transform

Abstract

The Discrete Pulse Transform (DPT) is a hierarchical decomposition of a signal in ndimensions, built by iteratively applying the LULU operators. The DPT is a fairly new mathematical framework, with few applications, and is prone to leakage within the domain, as are most other connected operators. Leakage is the unwanted union of two sets after the DPT is applied. Leakage thus provides false information regarding the data. A solution to the leakage is proposed. Implementing the DPT in n-dimensions is not a trivial task and a platform to aid the research effort was required. The search for applications of the DPT is extended to image segmentation, where the potential was measured in a quantitative way. The DPT was implemented by presenting a new algorithm, the Roadmakers Pavage based on the Roadmakers algorithm. The algorithm utilizes graph theory as a basis and is packaged in the DPT Library, created to assist other researchers. The Roadmaker’s Pavage is currently the fastest available algorithm and presents the extracted pulses in a a more suitable manner. The Pulse Reformation framework was developed to address the leakage problem within the DPT. It was specifically tested with circular probes and showed successful object extraction of red blood cells. Additionally, by utilising the LULU scale-space, similar performance to the Difference of Gaussians method in detecting mRNA in fluorescence microscopy was demonstrated. The DPT was also utilized in image segmentation. Using Iterated Conditional Modes and k-means, the DPT segmentation was compared to the other segmentation methods, such as the Gaussian scale-space. The DPT showed potential in image segmentation and it is recommended that further research be conducted with the DPT in image segmentation.