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.
