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Morphological filters (MFs) are composed of two basic operators: dilation and erosion, inspired by natural geometrical dilation and erosion. MFs locally modify geometrical features of the signal/image using a probe resembling a segment of a function/image that is called structuring element. This chapter analytically explains MFs and their inspirational features from natural geometry. The basic theory of MFs in the binary domain is illustrated, and at the sequence, it has been shown how it is extended to the domain of multivalued functions. Each morphological operator is clarified by intuitive geometrical interpretations. Creative natural inspired analogies are deployed to give a clear intuition to readers about the process of each of them. In this regard, binary and grayscale morphological operators and their properties are well defined and depicted via many examples.

The image perception by human brain through the eyes is not exactly what the eyes receive. In order to have an enhanced view of the received image and more clarity in detail, the brain naturally modifies the color tones in adjacent neighborhoods of colors. A very famous example of this human sight natural modification to the view is the famous Chevreul–Mach bands. In this phenomenon, every bar is filled with one solid level of gray, but human brain perceives narrow bands at the edges with increased contrast which does not reflect the physical reality of solid gray bars. This human visual system action in illusion, highlighting the edges, is inspired here in visual illusory image enhancement (VIIE). An algorithm for the newly introduced VIIE by deploying morphological filters is presented as morphological VIIE (MVIIE). It deploys morphological filters for boosting the same effect on the image edges and aiding human sight by increasing the contrast of the sight. MVIIE algorithm is explained in this chapter. Significant image enhancement, by MVIEE, is approved through the experiments in terms of image quality metrics and visual perception.

Multi-label classification has received more attention recently in the fields of data mining and machine learning. Though many approaches have been proposed, the critical issue of how to combine single labels to form a multi-label remains challenging. In this work, we propose a novel multi-label classification approach that each label is represented by two exclusive events: the label is selected or not selected. Then a weighted graph is used to represent all the events and their correlations. The multi-label learning is transformed into finding a constrained minimum cut of the weighted graph. In the experiments, we compare the proposed approach with the state-of-the-art multi-label classifier ML-KNN, and the results show that the new approach is efficient in terms of all the popular metrics used to evaluate multi-label classification performance.