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In the last ten years, Convolutional Neural Networks (CNNs) have formed the basis of deep-learning architectures for most computer vision tasks. However, they are not necessarily optimal. For example, mathematical morphology is known to be…

In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…

The recent impressive results of deep learning-based methods on computer vision applications brought fresh air to the research and industrial community. This success is mainly due to the process that allows those methods to learn…

Mathematical morphology (MM) is a theory of non-linear operators used for the processing and analysis of images. Morphological neural networks (MNNs) are neural networks whose neurons compute morphological operators. Dilations and erosions…

In this paper we study an emerging class of neural networks based on the morphological operators of dilation and erosion. We explore these networks mathematically from a tropical geometry perspective as well as mathematical morphology. Our…

Convolutional Neural Networks (CNNs) have been widely applied. But as the CNNs grow, the number of arithmetic operations and memory footprint also increase. Furthermore, typical non-linear activation functions do not allow associativity of…

The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of…

Morphological neural networks, or layers, can be a powerful tool to boost the progress in mathematical morphology, either on theoretical aspects such as the representation of complete lattice operators, or in the development of image…

Convolutional neural networks are witnessing wide adoption in computer vision systems with numerous applications across a range of visual recognition tasks. Much of this progress is fueled through advances in convolutional neural network…

We present a novel framework for learning morphological operators using counter-harmonic mean. It combines concepts from morphology and convolutional neural networks. A thorough experimental validation analyzes basic morphological operators…

Morphological neurons, that is morphological operators such as dilation and erosion with learnable structuring elements, have intrigued researchers for quite some time because of the power these operators bring to the table despite their…

Dilated Convolutions have been shown to be highly useful for the task of image segmentation. By introducing gaps into convolutional filters, they enable the use of larger receptive fields without increasing the original kernel size. Even…

In this study, we build upon a previously proposed neuroevolution framework to evolve deep convolutional models. Specifically, the genome encoding and the crossover operator are extended to make them applicable to layered networks. We also…

The shapes and morphology of the organs and tissues are important prior knowledge in medical imaging recognition and segmentation. The morphological operation is a well-known method for morphological feature extraction. As the morphological…

In the paper we introduce a novel bipolar morphological neuron and bipolar morphological layer models. The models use only such operations as addition, subtraction and maximum inside the neuron and exponent and logarithm as activation…

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

Non-local self-similarity is well-known to be an effective prior for the image denoising problem. However, little work has been done to incorporate it in convolutional neural networks, which surpass non-local model-based methods despite…

Dilation and erosion are two elementary operations from mathematical morphology, a non-linear lattice computing methodology widely used for image processing and analysis. The dilation-erosion perceptron (DEP) is a morphological neural…

Mathematical morphology contributes many profitable tools to image processing area. Some of these methods considered to be basic but the most important fundamental of data processing in many various applications. In this paper, we modify…

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…