Related papers: Mathematical Morphology via Category Theory
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
Integrating mathematical morphology operations within deep neural networks has been subject to increasing attention lately. However, replacing standard convolution layers with erosions or dilations is particularly challenging because the…
Category computation theory deals with a web-based systemic processing that underlies the morphic webs, which constitute the basis of categorial logical calculus. It is proven that, for these structures, algorithmically incompressible…
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…
Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades,…
This work proposes a new type of classifier called Morphological Classifier (MC). MCs aggregate concepts from mathematical morphology and supervised learning. The outcomes of this aggregation are classifiers that may preserve shape…
Semantic image segmentation is an important computer vision task that is difficult because it consists of both recognition and segmentation. The task is often cast as a structured output problem on an exponentially large output-space, which…
Connected operators are filtering tools that act by merging elementary regions of an image. A popular strategy is based on tree-based image representations: for example, one can compute an attribute on each node of the tree and keep only…
Mathematical morphology is a part of image processing that uses a window that moves across the image to change certain pixels according to certain operations. The concepts of supremum and infimum play a crucial role here, but it proves…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
Functor morphing provides a method to translate complex representations of automorphism groups of finite modules over finite rings to representations of automorphism groups of functors in some abelian category. In this paper we give an…
Mathematical morphology (MM) is a powerful and widely used framework in image processing. Through set-theoretic and discrete geometric principles, MM operations such as erosion, dilation, opening, and closing effectively manipulate digital…
The categorical distribution is a natural representation of uncertainty in multi-class segmentations. In the two-class case the categorical distribution reduces to the Bernoulli distribution, for which grayscale morphology provides a range…
The present paper develops a general methodology for the morphological segmentation of hyperspectral images, i.e., with an important number of channels. This approach, based on watershed, is composed of a spectral classification to obtain…
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…
Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image…
Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more…
The evolution of image halftoning, from its analog roots to contemporary digital methodologies, encapsulates a fascinating journey marked by technological advancements and creative innovations. Yet the theoretical understanding of…
This paper aims to establish the theoretical foundation for shift inclusion in mathematical morphology. In this paper, we prove that the morphological opening and closing concerning structuring elements of shift inclusion property would…
Image classification is an essential part of computer vision which assigns a given input image to a specific category based on the similarity evaluation within given criteria. While promising classifiers can be obtained through deep…