Transform Domain Morphological Filters

In this thesis, we have studied the concept of mathematical morphology
and morphological operators to devise new methods to recognise and
reassemble paths and patterns through point-clouds. These are methods
which act on the local or global shape-related properties of the
components of an $n$-dimensional data set. These methods have been
applied to the data generated by a simulator for a sub-atomic
interaction detection system to reconstruct charged particle tracks
travelling through the magnetic field in three-dimensions. We showed
that application of morphological connected-filters in the
transform-domain is a candidate solution to this challenging
problem. We showed that by exclusively using the detectors' local data
and geometry, a rough estimate of the paths in 3D could be made; those
estimated paths could be used for online data reduction. Because of
the simplicity and intuitiveness of the introduced method, it could be
utilised on rather simple hardware or even on the readout system of
the tracker. The hierarchical structuring of images could also be
applied to the data in the transform-domain. The Max-Tree structure,
was applied to the data in the transform-domain after-which a number
of attributes were calculated for the tree nodes. Herewith, the effect
of processing data in the transform-domain using morphological
connected attribute-filters was explored. Specifically, we studied the
context-based morphological filtering of data in the wavelet domain.