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.