Attribute filters are a class of connected morphological operators, widely used for their edge preserving property but have restrictions imposed from their underlying connectivity. In this work, aiming at extending their flexibility, several generalizations on the notion of connectivity are investigated. Starting from the concept of second-generation connectivity, a new type of operator is presented. Aided by mask images dictating the connectivity on the originals, this mask-based connected operator can handle clusters or contractions of binary objects or combinations of the two. This has a significant impact on filtering where desired objects previously discarded can now be preserved as members of a cluster or fine, elongated structures linking objects that should be treated individually, are removed. Contraction-based operators have certain drawbacks when extended to gray-scale. These are further investigated and a new type of connectivity, termed the partition-induced or pi-connectivity, is presented with operators countering the over-segmentation problem reported in literature. Pi-connected operators are also used for enriching feature descriptors in texture-based image classification. Both mask based and pi-connected operators make use of spatial characteristics to enhance the filters performance. Contrast information has also been studied leading to new type of hyperconnectivity based on k-flatzones. The hyperconnected operator presented, can capture high contrast but of low attribute measure structures resting on objects to be preserved while removes low contrast but of sufficient measure objects which normally rest on the background. Extensions to gray-scale and efficient algorithms for implementing the filters of all three cases of generalized connectivity, are developed. The contribution of each method is demonstrated with experiments on real biomedical data-sets followed by discussions on their performance.
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