Related papers: A Unified Algebraic Framework for Fuzzy Image Comp…
Existing compression methods typically focus on the removal of signal-level redundancies, while the potential and versatility of decomposing visual data into compact conceptual components still lack further study. To this end, we propose a…
Astronomical objects frequently exhibit structure over a wide range of scales whereas many telescopes, especially interferometer arrays, only sample a limited range of spatial scales. In order to properly image these objects, images from a…
We summarize a unified and computationally efficient treatment of Fierz identities for form-valued pinor bilinears in various dimensions and signatures, using concepts and techniques borrowed from a certain approach to spinors known as…
Adaptive binarization methodologies threshold the intensity of the pixels with respect to adjacent pixels exploiting the integral images. In turn, the integral images are generally computed optimally using the summed-area-table algorithm…
We describe a construction of fuzzy spaces which approximate projective toric varieties. The construction uses the canonical embedding of such varieties into a complex projective space: The algebra of fuzzy functions on a toric variety is…
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…
In this work we focus on the problem of colorization for image compression. Since color information occupies a large proportion of the total storage size of an image, a method that can predict accurate color from its grayscale version can…
In recent years, deep learning has become a very active research tool which is used in many image processing fields. In this paper, we propose an effective image fusion method using a deep learning framework to generate a single image which…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
Let $S$ be a rational projective surface given by means of a projective rational parametrization whose base locus satisfies a mild assumption. In this paper we present an algorithm that provides three rational maps $f,g,h:\mathbb{A}^2 --\to…
The success of deep learning is inseparable from normalization layers. Researchers have proposed various normalization functions, and each of them has both advantages and disadvantages. In response, efforts have been made to design a…
Aim. This paper (Paper D) unifies the ideal-theoretic, computational, and homological layers developed in Papers A (Rao 2025), B (Rao 2025), and C (Rao 2025) into a geometric framework that includes fuzzy and computational geometries on the…
For natural and artificial systems with some symmetry structure, computational understanding and manipulation can be achieved without learning by exploiting the algebraic structure. Here we describe this algebraic coordinatization method…
In this paper we demonstrate that the framework of nonlinear spectral decompositions based on total variation (TV) regularization is very well suited for image fusion as well as more general image manipulation tasks. The well-localized and…
This paper describes a novel approach to unsupervised learning that has been developed within a framework of "information compression by multiple alignment, unification and search" (ICMAUS), designed to integrate learning with other AI…
Image fusion aims to integrate structural and complementary information from multi-source images. However, existing fusion methods are often either highly task-specific, or general frameworks that apply uniform strategies across diverse…
We develop a general framework for working with structured lifting problems, establishing closure and uniqueness properties of their solutions. In a subsequent paper, we apply these results to axiomatize computation rules of cubical type…
An orthogonal approach to the fuzzification of both multisets and hybrid sets is presented. In particular, we introduce L-multi-fuzzy and L-fuzzy hybrid sets, which are general enough and in spirit with the basic concepts of fuzzy set…
Current distributed data fabrics lack a rigorous mathematical foundation, often relying on ad-hoc architectures that struggle with consistency, lineage, and scale. We propose a mathematical framework for data fabrics, unifying heterogeneous…
Multi-sentence summarization is a well studied problem in NLP, while generating image descriptions for a single image is a well studied problem in Computer Vision. However, for applications such as image cluster labeling or web page…