On Machine-Learning Morphological Image Operators

Nina S T Hirata,George A Papakostas

doi:10.3390/math9161854

Nina S T Hirata, George A Papakostas

Open Access

https://doi.org/10.3390/math9161854

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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.

Highlights

Images are a rich source of information
We present an overview of these recent models, the deep morphological neural networks (DMNN) (Deep Morphological Neural Networks), which take advantage of modern deep-learning frameworks to implement morphological layers
With the current deep-learning frameworks, we are already able to build deep morphological neural network architectures (i.e., DMNNs) consisting of layers of morphological processing units, more precisely erosions and dilations, and take advantage of automatic gradient computation and weight optimization to learn the shape of the structuring functions

Summary

Introduction

Images are a rich source of information. To extract useful information, images are usually carefully processed to highlight or segment objects or other information of interest. To cope with processing limitations of these devices, a traditional approach is to rely on centralized data centers with processing servers, such as cloud computing platforms, for data processing. This arrangement enables devices to relocate most of the heavy processing to these centers. Edge computing pushes to the surface the need for boosting computing capabilities and intelligent processing in hardware constrained devices [4] These limitations can be mitigated by improving processing capabilities on the hardware side, but at the same time improvements can be sought on the software side, by developing well designed and customized algorithms that take advantage of specific characteristics of the hardware as well as are efficient in terms of memory usage and processing

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