On Machine-Learning Morphological Image Operators

Nina S. T. Hirata and George A. Papakostas
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Nina S. T. Hirata: Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, São Paulo 05508-090, Brazil
George A. Papakostas: HUMAIN-Lab, Department of Computer Science, International Hellenic University, 65404 Kavala, Greece

Mathematics, 2021, vol. 9, issue 16, 1-22

Abstract: Morphological operators are nonlinear transformations commonly used in image processing. Their theoretical foundation is based on lattice theory, and it is a well-known result that a large class of image operators can be expressed in terms of two basic ones, the erosions and the dilations. In practice, useful operators can be built by combining these two operators, and the new operators can be further combined to implement more complex transformations. The possibility of implementing a compact combination that performs a complex transformation of images is particularly appealing in resource-constrained hardware scenarios. However, finding a proper combination may require a considerable trial-and-error effort. This difficulty has motivated the development of machine-learning-based approaches for designing morphological image operators. In this work, we present an overview of this topic, divided in three parts. First, we review and discuss the representation structure of morphological image operators. Then we address the problem of learning morphological image operators from data, and how representation manifests in the formulation of this problem as well as in the learned operators. In the last part we focus on recent morphological image operator learning methods that take advantage of deep-learning frameworks. We close with discussions and a list of prospective future research directions.

Keywords: mathematical morphology; lattice theory; image operator; erosion; dilation; boolean function; deep learning; image-to-image transformation; deep morphological network (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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