Edge Coloring Research Articles

Enhancing Underwater Images through Multi-Frequency Detail Optimization and Adaptive Color Correction

This paper presents a novel underwater image enhancement method addressing the challenges of low contrast, color distortion, and detail loss prevalent in underwater photography. Unlike existing methods that may introduce color bias or blur during enhancement, our approach leverages a two-pronged strategy. First, an Efficient Fusion Edge Detection (EFED) module preserves crucial edge information, ensuring detail clarity even in challenging turbidity and illumination conditions. Second, a Multi-scale Color Parallel Frequency-division Attention (MCPFA) module integrates multi-color space data with edge information. This module dynamically weights features based on their frequency domain positions, prioritizing high-frequency details and areas affected by light attenuation. Our method further incorporates a dual multi-color space structural loss function, optimizing the performance of the network across RGB, Lab, and HSV color spaces. This approach enhances structural alignment and minimizes color distortion, edge artifacts, and detail loss often observed in existing techniques. Comprehensive quantitative and qualitative evaluations using both full-reference and no-reference image quality metrics demonstrate that our proposed method effectively suppresses scattering noise, corrects color deviations, and significantly enhances image details. In terms of objective evaluation metrics, our method achieves the best performance in the test dataset of EUVP with a PSNR of 23.45, SSIM of 0.821, and UIQM of 3.211, indicating that it outperforms state-of-the-art methods in improving image quality.

Tuning the Optical Absorption Edge of Vacancy-Ordered Double Perovskites through Metal Precursor and Solvent Selection.

Vacancy-ordered double perovskites with the formula A 2 MX 6 (where A is a +1 cation, M is a +4 metal, and X is a halide ion) offer improved ambient stability over other main-group halide AMX 3 perovskites and potentially reduced toxicity compared to those containing lead. These compounds are readily formed through a number of synthetic routes; however, the manner in which the synthetic route affects the resulting structure or optoelectronic properties has not been examined. Here, we investigate the role of distinct precursors and solvents in the formation of the indirect band gap vacancy-ordered double perovskite Cs2TeBr6. While Cs2TeBr6 can be synthesized from TeBr4 or TeO2, we find that synthesis from TeBr4 is more sensitive to solvent selection, requiring a polar solvent to enable the conversion of TeBr4. Synthesis from TeO2 proceeds in all of the organic solvents tested, provided that HBr is added to solubilize TeO2 and enable the formation of [TeBr6]2-. Furthermore, the choice of metal precursor and solvent impacts the product color and optical absorption edge, which we find arises from particle size effects. The emission energy remains unaffected, consistent with the idea that emission in these zero-dimensional structures arises from the isolated [TeBr6]2- octahedra, which undergo dynamic Jahn-Teller distortion rather than band-edge recombination. Our work highlights how even minor changes in synthetic procedures can lead to variability in metrics such as the absorption edge and emission lifetime and sheds light on how the optical properties of these semiconductors can be controlled for light-emitting applications.

Breaking small automorphisms by list colourings

AbstractFor a graph , we define a small automorphism as one that maps some vertex into its neighbour. We investigate the edge colourings of that break every small automorphism of . We show that such a colouring can be chosen from any set of lists of length 3. In addition, we show that any set of lists of length 2 on both edges and vertices of yields a total colouring which breaks all the small automorphisms of . These results are sharp, and they match the known bounds for the nonlist variant.

An efficient corn leaf disease prediction using Adaptive Color Edge Segmentation with Resnext101 model

Corn leaf disease prediction is essential in ensuring agricultural productivity and food security. Although classical segmentation and classification techniques have been used to identify diseases, they often fail to deal with complex leaf structures. Thus, deep learning has attracted growing attention for automatically learning discriminative features from data. This paper proposes a new approach to predicting corn leaf disease using deep learning and classical segmentation techniques for improved accuracy and efficiency. The proposed work presents an adaptive colour edge segmentation method improved by a hill-climbing search for robust feature extraction according to the diversified nature of corn leaves. With the help of stochastic hill climbing, the segmentation process is optimized by adaptively changing parameters to get better segmentation accuracy. After that, features are extracted and provided as input into a ResNeXt-101 model for disease classification. The novel activation function in ResNeXt-101 combines the Adam optimizer with a Gaussian-based GELU to enhance nonlinearity to the smooth activation of GELU. The results obtained from experiments show that the proposed approach is practical. The ResNeXt-101 model has achieved overwhelming performance, with 99% for testing accuracy and a minimum loss of 0.01, proving its superior generalization capability and robustness. The proposed work was performed with no overfitting and free from local minima during the training process.

Online size Ramsey numbers: Path vs C4

Given two graphs G and H, a size Ramsey game is played on the edge set of KN. In every round, Builder selects an edge and Painter colours it red or blue. Builder's goal is to force Painter to create a red copy of G or a blue copy of H as soon as possible. The online (size) Ramsey number r˜(G,H) is the number of rounds in the game provided Builder and Painter play optimally. We prove that r˜(C4,Pn)≤2n−2 for every n≥8. The upper bound matches the lower bound obtained by J. Cyman, T. Dzido, J. Lapinskas, and A. Lo, so we get r˜(C4,Pn)=2n−2 for n≥8. Our proof for n≤13 is computer-assisted. The bound r˜(C4,Pn)≤2n−2 solves also the “all cycles vs. Pn” game for n≥8 – it implies that it takes Builder 2n−2 rounds to force Painter to create a blue path on n vertices or any red cycle.

Proper edge colorings of planar graphs with rainbow C4 ${C}_{4}$‐s

AbstractWe call a proper edge coloring of a graph a B‐coloring if every 4‐cycle of is colored with four different colors. Let denote the smallest number of colors needed for a B‐coloring of . Motivated by earlier papers on B‐colorings, here we consider for planar and outerplanar graphs in terms of the maximum degree . We prove that for planar graphs, for bipartite planar graphs, and for outerplanar graphs with . We conjecture that, for sufficiently large, for planar , and for outerplanar .

Borel edge colorings for finite-dimensional groups

AbstractWe study the potential of Borel asymptotic dimension, a tool introduced recently in [2], to help produce Borel edge colorings of Schreier graphs generated by Borel group actions. We find that it allows us to recover the classical bound of Vizing in certain cases, and also use it to exactly determine the Borel edge chromatic number for free actions of abelian groups.

Furniture design based on image color extraction algorithm

With the increasing demand for personalized and customized home products, how to realize the innovative design of furniture and improve the design efficiency has become a research hotspot for related professionals. Aiming at these problems, the study extracts the main color of furniture images by optimizing the K-mean clustering algorithm, uses the simulated annealing algorithm to color-match the furniture, and reconstructs the image by edge detection to design a furniture design method based on image color extraction. The results revealed that in the foreground part, the correct rate of color match based on the design method was 95.7%, and in the background part, the correct rate of color match based on the design method was 94.81 %, which proved its effectiveness. The average feature point extraction time and the average feature point matching time of the design-based algorithm were 5.45 ms and 9.83 ms, respectively, which proved its high computational efficiency. In furniture color edge detection and overall color match, the image obtained based on the design method was significantly clearer, and the overall coherence, saturation and brightness were closer to the input image. In addition to raising the standard of furniture design, the study's design methodology increases design efficiency and offers solid technical support for the area.

Coloring Groups

We introduce coloring groups, which are permutation groups obtained from a proper edge coloring of a graph. These groups generalize the generalized toggle groups of Striker (which themselves generalize the toggle groups introduced by Cameron and Fon-der-Flaass). We present some general results connecting the structure of a coloring group to the structure of its graph coloring, providing graph-theoretic characterizations of the centralizer and primitivity of a coloring group. We apply these results particularly to generalized toggle groups arising from trees as well as coloring groups arising from the independence posets introduced by Thomas and Williams.

A note on the k-colored crossing ratio of dense geometric graphs

A geometric graph is a graph whose vertex set is a set of points in general position in the plane, and its edges are straight line segments joining these points. We show that for every integer k≥2, there exists a constant c>0 such that the following holds. The edges of every dense geometric graph, with sufficiently many vertices, can be colored with k colors, such that the number of pairs of edges of the same color that cross is at most (1/k−c) times the total number of pairs of edges that cross. The case when k=2 and G is a complete geometric graph, was proved by Aichholzer et al. (2019) [2].

Segmentation Method of Concrete Small Cracks Based on UAV Images

Introduction:: Cracks are one of the major problems in modern concrete buildings, especially in locations that are difficult to map manually, such as bridges and high-rise buildings. Accurate analysis of unmanned aerial vehicle (UAV) images has become the key to determining whether a building needs maintenance. Methods:: Traditional image processing methods are easily interfered by high-frequency background. Neural network methods need fine datasets, which increase labor costs. Therefore, this paper proposes a segmentation algorithm based on UNet3+ network. After obtaining the UAV image, the rough location of the crack can be obtained by only rough labeling. And then, the sample balance can be carried out by clipping the target area. The UNet3+ network is used to train the processed datasets and extract the region of interest to ignore the non-target texture. Finally, the region of interest is further segmented by color clustering and edge detection methods. Results:: The proposed method can detect the cracks accurately. In all test images, the relative errors are less than 13%. Especially in test images whose width is less than 0.2mm, the maximum absolute error is only 0.0237mm, which is completely acceptable in actual production. The proposed method has higher practicability in the detection of concrete crack images taken by UAV. The results show that the proposed method outperforms the cutting-edge method published in the journal "Sensor", when the background is complex. Conclusion:: The proposed method can segment and detect cracks effectively, which can remove the high-frequency interference region from the images.

On Strong Regal and Strong Royal Colorings

Two colorings have been introduced recently where an unrestricted coloring c assigns nonempty subsets of [ k ] = { 1 , … , k } to the edges of a (connected) graph G and gives rise to a vertex-distinguishing vertex coloring by means of set operations. If each vertex color is obtained from the union of the incident edge colors, then c is referred to as a strong royal coloring. If each vertex color is obtained from the intersection of the incident edge colors, then c is referred to as a strong regal coloring. The minimum values of k for which a graph G has such colorings are referred to as the strong royal index of G and the strong regal index of G respectively. If the induced vertex coloring is neighbor distinguishing, then we refer to such edge colorings as royal and regal colorings. The royal chromatic number of a graph involves minimizing the number of vertex colors in an induced vertex coloring obtained from a royal coloring. In this paper, we provide new results related to these two coloring concepts and establish a connection between the corresponding chromatic parameters. In addition, we establish the royal chromatic number for paths and cycles.

Interval colourable orientations of graphs

A graph is interval colourable if it admits a proper edge colouring in which for each vertex the set of colours of edges that are incident with the vertex is an interval of integers. An oriented graph is interval colourable if it admits a proper arc colouring in which for each vertex the set of colours of in-arcs and the set of colours of out-arcs that are incident with the vertex are both intervals of integers. In this paper we apply a classical approach and a new special trail technique to confirm the existence of interval colourable orientations of graphs from three classes: i) all k-trees with Δ(G)≤2k and k∈{2,3,4} and all k-paths with arbitrary k∈N; ii) graphs in which the length of every even closed trail is at least 2s and each such a trail has common edges with no more than d other even closed trails and 21−2se(d+1)≤1; iii) graphs that are decomposable into a bipartite interval colourable graph and a graph whose each connected component has at most one cycle that, if it exists, has odd length. Consequently, cactus graphs, graphs that are homeomorphic to Halin graphs, full subdivision graphs and others have interval colourable orientations.

Infrared and Visible Image Fusion Algorithm Based on Double-Domain Transform Filter and Contrast Transform Feature Extraction

Current challenges in visible and infrared image fusion include color information distortion, texture detail loss, and target edge blur. To address these issues, a fusion algorithm based on double-domain transform filter and nonlinear contrast transform feature extraction (DDCTFuse) is proposed. First, for the problem of incomplete detail extraction that exists in the traditional transform domain image decomposition, an adaptive high-pass filter is proposed to decompose images into high-frequency and low-frequency portions. Second, in order to address the issue of fuzzy fusion target caused by contrast loss during the fusion process, a novel feature extraction algorithm is devised based on a novel nonlinear transform function. Finally, the fusion results are optimized and color-corrected by our proposed spatial-domain logical filter, in order to solve the color loss and edge blur generated in the fusion process. To validate the benefits of the proposed algorithm, nine classical algorithms are compared on the LLVIP, MSRS, INO, and Roadscene datasets. The results of these experiments indicate that the proposed fusion algorithm exhibits distinct targets, provides comprehensive scene information, and offers significant image contrast.

Extending partial edge colorings of iterated cartesian products of cycles and paths

We consider the problem of extending partial edge colorings of iterated cartesian products of even cycles and paths, focusing on the case when the precolored edges satisfy either an Evans-type condition or is a matching. In particular, we prove that if $G=C^d_{2k}$ is the $d$th power of the cartesian product of the even cycle $C_{2k}$ with itself, and at most $2d-1$ edges of $G$ are precolored, then there is a proper $2d$-edge coloring of $G$ that agrees with the partial coloring. We show that the same conclusion holds, without restrictions on the number of precolored edges, if any two precolored edges are at distance at least $4$ from each other. For odd cycles of length at least $5$, we prove that if $G=C^d_{2k+1}$ is the $d$th power of the cartesian product of the odd cycle $C_{2k+1}$ with itself ($k\geq2$), and at most $2d$ edges of $G$ are precolored, then there is a proper $(2d+1)$-edge coloring of $G$ that agrees with the partial coloring. Our results generalize previous ones on precoloring extension of hypercubes [Journal of Graph Theory 95 (2020) 410--444].

Edge incident 2-edge coloring of graphs

The edge incident 2-edge coloring of a graph [Formula: see text] is an edge coloring of the graph [Formula: see text] such that not more than two colors are assigned to the edges incident to an edge [Formula: see text] in [Formula: see text]. In other words, for every edge [Formula: see text] in [Formula: see text], the edge [Formula: see text] and all the edges that are incident to the edge [Formula: see text] is in at most two different color classes. The edge incident 2-edge coloring number [Formula: see text] is the maximum number of colors in any edge incident 2-edge coloring of [Formula: see text]. The main objective of this paper is to study the edge incident 2-edge coloring concept and apply the same to some graph classes. Besides finding the exact values of these parameters, we also obtain some bounds.

Heterogeneity constrained color ellipsoid prior image dehazing algorithm

To address the issue of inaccurate transmission estimation in areas with sudden depth changes in hazy images, the image dehazing algorithm with Heterogeneity Constrained Color Ellipsoid Prior (HC-CEP) is proposed. Firstly, a local threshold optimization quadtree search method is designed, in order to solve the problem of inaccurate global atmospheric light estimation and avoid the overall darkening of the image caused by white objects.Then, different regions are selected by a local block heterogeneity window to construct diversity prior vectors to estimate the initial transmission. Finally, by constructing neighborhood heterogeneity weighted constraints on each pixel of the initial transmission and improving the high-order differential filtering of the Scharr operator, the optimization of the transmission is achieved, eliminating halo artifacts in the depth mutation area of the image. Both qualitative and quantitative experimental results show that the proposed algorithm comprehensively considers the heterogeneity of local pixel characteristics, and the dehazing image obtained has better color fidelity and edge detail preservation ability, which can effectively eliminate halo artifacts on the edges of hazy images.The proposed method has better dehazing performance and has a 8% improvement in terms of the FADE metric compared to state-of-the-art dehazing methods.

An Experimental Study on Light Emitting Concrete

The study of light emitting concrete which has the property of transmitting light from concrete by using optical fibers. Since years concrete has a low impression because of its dirty greyish color, opaqueness and sharp edge but this concept has been changed after the development of light emitting concrete, which gives the increased strength, better looks and light transmitting features. Plastic optical fibers are used because of its total internal reflection as its working principle as it gives maximum efficiency in transmitting light. The percentages of optical fiber added in this experimental study are 3%, 4%, 5%. This paper gives the structure a good aesthetic look without loss of strength parameters and serves as a eco-friendly building material and is also a energy efficient which reduces energy consumption by 30% by allowing the natural light by transmitting light through optical fibers and will also have a good scope in future. This experiment will be a series of initiatives to look closely at new and emerging advanced construction in future

An investigation into augmentation and preprocessing for optimising X-ray classification in limited datasets: a case study on necrotising enterocolitis

PurposeObtaining large volumes of medical images, required for deep learning development, can be challenging in rare pathologies. Image augmentation and preprocessing offer viable solutions. This work explores the case of necrotising enterocolitis (NEC), a rare but life-threatening condition affecting premature neonates, with challenging radiological diagnosis. We investigate data augmentation and preprocessing techniques and propose two optimised pipelines for developing reliable computer-aided diagnosis models on a limited NEC dataset.MethodsWe present a NEC dataset of 1090 Abdominal X-rays (AXRs) from 364 patients and investigate the effect of geometric augmentations, colour scheme augmentations and their combination for NEC classification based on the ResNet-50 backbone. We introduce two pipelines based on colour contrast and edge enhancement, to increase the visibility of subtle, difficult-to-identify, critical NEC findings on AXRs and achieve robust accuracy in a challenging three-class NEC classification task.ResultsOur results show that geometric augmentations improve performance, with Translation achieving +6.2%, while Flipping and Occlusion decrease performance. Colour augmentations, like Equalisation, yield modest improvements. The proposed Pr-1 and Pr-2 pipelines enhance model accuracy by +2.4% and +1.7%, respectively. Combining Pr-1/Pr-2 with geometric augmentation, we achieve a maximum performance increase of 7.1%, achieving robust NEC classification.ConclusionBased on an extensive validation of preprocessing and augmentation techniques, our work showcases the previously unreported potential of image preprocessing in AXR classification tasks with limited datasets. Our findings can be extended to other medical tasks for designing reliable classifier models with limited X-ray datasets. Ultimately, we also provide a benchmark for automated NEC detection and classification from AXRs.

On a class of column‐weight 3 decomposable LDPC codes with the analysis of elementary trapping sets

AbstractA column‐weight LDPC code with the parity‐check matrix is called decomposable if there exists a permutation on the rows of , such that can be decomposed into column‐weight one matrix. In this paper, some variations of edge coloring of graphs are used to construct some column‐weight three decomposable LDPC codes with girths at least six and eight. Applying the presented method on several known classes of bipartite graphs, some classes of column‐weight three decomposable LDPC codes are derived having flexibility in length and rate. Interestingly, the constructed parity‐check matrices based on the proper edge coloring of graphs can be considered as the base matrix of some high rate column‐weight three quasi‐cyclic (QC) LDPC codes with maximum‐achievable girth 20. The paper also leads to a simple characterization of elementary trapping sets of the decomposable codes based on the chromatic index of the corresponding normal graphs. This characterization corresponds to a simple search algorithm finds all possible existing elementary trapping sets in a girth‐6 or girth‐8 column‐weight 3 LDPC code which are layered super set of a short cycle in the Tanner graph of the code. Simulation results indicate that the QC‐LDPC codes with large girths lifted from the constructed base matrices have good performances over AWGN channel.