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Mathematical morphology is a part of image processing that has proven to be fruitful for numerous applications. Two main operations in mathematical morphology are dilation and erosion. These are based on the construction of a supremum or…
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…
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…
Mathematical morphology is a theory concerned with non-linear operators for image processing and analysis. The underlying framework for mathematical morphology is a partially ordered set with well-defined supremum and infimum operations.…
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…
Mathematical morphology provides a nonlinear framework for image and spatial data processing and analysis. Although there have been many successful applications of mathematical morphology to vector-valued images, such as color and…
A general definition of mathematical morphology has been defined within the algebraic framework of complete lattice theory. In this framework, dealing with deterministic and increasing operators, a dilation (respectively an erosion) is an…
We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering…
A new set of mathematical morphology (MM) operators adaptive to illumination changes caused by variation of exposure time or light intensity is defined thanks to the Logarithmic Image Processing (LIP) model. This model based on the physics…
Colour refinement is a basic algorithmic routine for graph isomorphism testing, appearing as a subroutine in almost all practical isomorphism solvers. It partitions the vertices of a graph into "colour classes" in such a way that all…
Superpixel decomposition methods are widely used in computer vision and image processing applications. By grouping homogeneous pixels, the accuracy can be increased and the decrease of the number of elements to process can drastically…
The object recognition is a complex problem in the image processing. Mathematical morphology is Shape oriented operations, that simplify image data, preserving their essential shape characteristics and eliminating irrelevancies. This paper…
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…
We establish the link between Mathematical Morphology and the map of Asplund's distances between a probe and a grey scale function, using the Logarithmic Image Processing scalar multiplication. We demonstrate that the map is the logarithm…
In Mathematical Morphology for grey-level functions, an image is analysed by another image named the structuring function. This structuring function is translated over the image domain and summed to the image. However, in an image…
Colorization of gray-scale images relies on prior color information. Examplar-based methods use a color image as source of such information. Then the colors of the source image are transferred to the gray-scale image. In the literature,…
Sequential DeepFake detection is an emerging task that predicts the manipulation sequence in order. Existing methods typically formulate it as an image-to-sequence problem, employing conventional Transformer architectures. However, these…
State-of-the-art methods for semantic segmentation of images involve computationally intensive neural network architectures. Most of these methods are not adaptable to high-resolution image segmentation due to memory and other computational…
Creating arbitrary light patterns finds applications in various domains including lithography, beam shaping, metrology, sensing and imaging. We study the formation of high-contrast light patterns that are obtained by transmission through an…
Sampling is a basic operation in image processing. In classic literature, a morphological sampling theorem has been established, which shows how sampling interacts by morphological operations with image reconstruction. Many aspects of…