Set Of Colors Research Articles

Inclusion total chromatic number

Let G=(V,E) be a graph and c:(V∪E)→C be a proper total colouring of G, where C is a set of colours. We call c inclusion-free if for each vertex, the set of colours appearing on the vertex and the incident edges is not a subset of the respective sets of its neighbours. With a probabilistic argument we show that the minimum number of colours for inclusion-free total colouring, denoted by χ⊂″(G), is bounded from above by Δ+150log⁡Δ for any graph G with large enough maximum degree Δ. Then we prove that χ⊂″(G)≤6 for any subcubic graph G, which meets the bound for adjacent vertex distinguishing total colouring.

On indicated coloring of lexicographic product of graphs

Indicated coloring is a graph coloring game in which two players collectively color the vertices of a graph in the following way. In each round the first player (Ann) selects a vertex, and then the second player (Ben) colors it properly, using a fixed set of colors. The goal of Ann is to achieve a proper coloring of the whole graph, while Ben is trying to prevent the realization of this project. The smallest number of colors necessary for Ann to win the game on a graph G (regardless of Ben’s strategy) is called the indicated chromatic number of G , denoted by χ i ( G ) . In this paper, we show that for any graphs G and H , G [ H ] is k -indicated colorable for all k ≥ col ( G ) col ( H ) . Also, we show that for any graph G and for some classes of graphs H with χ ( H ) = χ i ( H ) = ℓ , G [ H ] is k -indicated colorable if and only if G [ K ℓ ] is k -indicated colorable. As a consequence of this result, we show that if G ∈ G = { Chordal graphs, Cographs, Complement of bipartite graphs, { P 5 , C 4 } -free graphs, Connected { P 6 , C 5 , P 5 ¯ , K 1 , 3 } -free graphs which contain an induced C 6 , Complete multipartite graphs } and H ∈ F = { Bipartite graphs, Chordal graphs, Cographs, { P 5 , K 3 } -free graphs, { P 5 , p a w } -free graphs, Complement of bipartite graphs, { P 5 , K 4 , k i t e , b u l l } -free graphs, Connected { P 6 , C 5 , P 5 ¯ , K 1 , 3 } -free graphs which contain an induced C 6 , { P 5 , C 4 } -free graphs, K [ C 5 ] ( m 1 , m 2 , … , m 5 ) , Connected { P 5 , P 2 ∪ P 3 ¯ , P 5 ¯ , d a r t } -free graphs which contain an induced C 5 } , then G [ H ] is k -indicated colorable for every k ≥ χ ( G [ H ] ) . This serves as a partial answer to one of the questions raised by A. Grzesik in Grzesik (2012). In addition, if G ∈ { Bipartite graphs, { P 5 , K 3 } -free graphs, { P 5 , p a w } -free graphs } and H ∈ F , then we show that χ i ( G [ H ] ) = χ ( G [ H ] ) .

Color Harmonization, Deharmonization and Balancing in Augmented Reality

Color schemes play a crucial role in blending virtual objects with the real environment. Good color schemes improve user’s perception, which is of crucial importance for augmented reality. In this paper, we propose a set of novel methods based on the color harmonization methodology to recolor augmented reality content according to the real background. Three different strategies are proposed—harmonic, disharmonic, and balance—that allow for satisfying different needs in different settings depending on the application field. The first approach aims to harmonize the colors of virtual objects to make them consistent with the colors of the real background and reach a more pleasing effect to a human eye. The second approach, instead, can be adopted to generate a set of disharmonious colors with respect to real ones to be associated with the augmented virtual content to improve its distinctiveness from the real background. The third approach balances these goals by achieving a compromise between harmony and good visibility among virtual and real objects. Furthermore, the proposed re-coloring method is applied to three different case studies by adopting the three strategies to meet three different objectives, which are specific for each case study. Several parameters are calculated for each test, such as the covered area, the color distribution, and the set of generated colors. Results confirm the great potential of the proposed approaches to improve the AR visualization in different scenarios.

Nonrepetitive List Colorings of the Integers

A coloring of the integers is nonrepetitive if no two adjacent intervals have the same color sequence. A beautiful theorem of Thue asserts that there exists a nonrepetitive coloring of {mathbb {N}} using only three colors. We obtain some generalizations of this result in which the adjacency of intervals is specified by more general graphs. We focus on the list variant of the problem, in which every integer gets a color from its own set of colors. For instance, we prove that there exists a coloring of {mathbb {N}} from arbitrary lists of size 8, such that the following property holds for every nge 1: among any 2^n consecutively adjacent intervals, each of length n, no two have the same color sequence. Another result is related to the possible extension of the famous Dejean’s conjecture to the list setting. It asserts that for every kge 1, there is a coloring of {mathbb {N}} from lists of size k+2sqrt{k}, such that no two among any k consecutively adjacent intervals have the same color sequence.

Connected Components-based Colour Image Representations of Vibrations for a Two-stage Fault Diagnosis of Roller Bearings Using Convolutional Neural Networks

Roller bearing failure is one of the most common faults in rotating machines. Various techniques for bearing fault diagnosis based on faults feature extraction have been proposed. But feature extraction from fault signals requires expert prior information and human labour. Recently, deep learning algorithms have been applied extensively in the condition monitoring of rotating machines to learn features automatically from the input data. Given its robust performance in image recognition, the convolutional neural network (CNN) architecture has been widely used to learn automatically discriminative features from vibration images and classify health conditions. This paper proposes and evaluates a two-stage method RGBVI-CNN for roller bearings fault diagnosis. The first stage in the proposed method is to generate the RGB vibration images (RGBVIs) from the input vibration signals. To begin this process, first, the 1-D vibration signals were converted to 2-D grayscale vibration Images. Once the conversion was completed, the regions of interest (ROI) were found in the converted 2-D grayscale vibration images. Finally, to produce vibration images with more discriminative characteristics, an algorithm was applied to the 2-D grayscale vibration images to produce connected components-based RGB vibration images (RGBVIs) with sets of colours and texture features. In the second stage, with these RGBVIs a CNN-based architecture was employed to learn automatically features from the RGBVIs and to classify bearing health conditions. Two cases of fault classification of rolling element bearings are used to validate the proposed method. Experimental results of this investigation demonstrate that RGBVI-CNN can generate advantageous health condition features from bearing vibration signals and classify the health conditions under different working loads with high accuracy. Moreover, several classification models trained using RGBVI-CNN offered high performance in the testing results of the overall classification accuracy, precision, recall, and F-score.

Design and validation of tailored colour reference charts for monitoring cultural heritage degradation

Colour changes of cultural heritage objects can be related with degradation of materials, thus a proper colour monitoring system can be used to detect conservation problems. With this purpose, a monitoring methodology for cultural heritage preventive conservation based on tailored colour reference charts and image analysis is proposed.Reference colour charts have been designed and tested for use in museums. Charts containing 64 colour patches have been printed using high-stability inks on 4 different substrates: Acid-free paper SkyLight, Acid-free paper covered with a propylene film, FOREX® and GlassPack. The stability has been studied by accelerated ageing in an UV chamber, and the harmlessness of the materials by Oddy Test. The final selection of material, laminated paper, is a balance between the colour change upon ageing and the performance in the Oddy Test. Using this material and the proposed design, colour change of copper and silver coupons has been assessed using images that are adjusted and calibrated by an adaptive calibration framework employing a given set of reference colours which homogenises the visual information in the supplied images. Thus, regardless of the camera of origin, any processed picture will deliver reliable information of the state of the colour in the metal surfaces at the moment it was taken.Results demonstrate the adequacy of the approach and the design for colour calibration, so these charts can be used to monitor colour change of sensitive materials –metal coupons– using photographs. As colour change of reference metals is a consequence of corrosion by environmental factors this may be used as a measure of air quality in museum environments. This methodology can be used to design a low-cost preventive conservation tool, where colour change of metal coupons –or other reference materials– can be followed through image analysis of pictures taken periodically by conservators or visitors, introducing citizen science in the conservation strategy.

Comparison of sum choice number with chromatic sum

Let G=(V,E) be a simple graph and for every vertex v∈V let L(v) be a set (list) of available colors. The graph G is called L-colorable if there is a proper coloring φ of the vertices with φ(v)∈L(v) for all v∈V. A function f:V→N is called a choice function of G if G is L-colorable for every list assignment L with |L(v)|=f(v) for all v∈V. Let size(f)=∑v∈Vf(v) and define the sum choice number χsc(G) as the minimum of size(f) over all choice functions f of G.The chromatic sum Σ(G) of G is the minimum sum of colors taken over all possible proper colorings of G.In this paper we consider the functions g(n)=max{χsc(G)∕Σ(G):Σ(G)=n} and h(n)=max{χsc(G)∕Σ(G):|V(G)|=n}. We conjecture g(n)=Θ(logn), h(n)=Θ(logn), and g(n)≤h(n) for all n. We present lower and upper bounds for g(n) and h(n) and partial proofs of the conjectures.

Visibility Restoration Using Generalized Haze-Lines

Haze reduces the perceived scene radiance and limits the visibility in outdoor images. The visibility is different for each scene point and is proportional to haze thickness, and distance from the camera. Transmission map represents percentage of scene radiance captured by the camera and is unknown for every pixel. This work generalizes the concept of haze-lines, and presents an algorithm to estimate transmission map and restore scene radiance accurately. The proposed technique depends on the perception that the colors of haze-free natural images can be well approximated by a set of distinct colors and their shades (natural color-palette) that can be learned beforehand. In presence of haze, the pixels forming a cluster in haze-free image, make a line (haze-line) in RGB color space. The two endpoints of this haze-line are the haze-free color and the airlight. We propose that these haze-lines can be generalized, with one end as learned color-palette of natural images and the other as airlight. Hence the scene radiance end can be made independent of underlying image. The algorithm recovers the transmission map, by determining membership of each pixel to a given haze-line and finding how far-off it is from its learned color-palette. The algorithm is linear to the size of image, and requires just a collection of haze-free natural images for training. The results obtained on a diverse range of images demonstrate the efficiency of proposed algorithm.

Evaluation of four different methods for assessing bee diversity as ecological indicators of agro-ecosystems

Monitoring of wild bees is becoming more and more popular in nature conservation because of the high indicator value of this insect group. However, uncertainties about the sampling performance of different methods still exist, especially in areas of limited accessibility. We therefore compared four commonly applied sampling methods across vineyard fallows in a species diverse study area over two successive years: hand netting along variable transects (HN), pan traps (PT), trap nests (TN) and Malaise traps (MT). The chosen method significantly affects the number of sampled bee species and individuals, with PT sampling by far the largest number of species and individuals, and HN sampling the most diverse bee fauna. HN samples contained a significantly higher proportion of males, red-listed, large and social Bombus species than PT, but HN and PT samples contained a significantly lower proportion of male individuals compared to MT and TN. PT colour had a significant effect on the number of sampled individuals and species, with yellow PT sampling the largest numbers, while blue PT sampled the largest number of individuals of social Bombus species. The HN sampling results of an experienced and a less-experienced observer differed remarkably, with the turnover component of the Jaccard distance being significantly higher compared to the nestedness component. Our findings indicate that PT was the most efficient method for sampling bees in our study system. Due to species-specific differences in attractivity, sets of different PT colours should be used. However, if the study focus is on red-listed species or male individuals, HN represents a more efficient method. When HN is applied, observer bias should be considered as much as possible, especially with regard to differences in sampling experience. Due to different shortcomings, MT and TN cannot be seen as appropriate methods for standard monitoring of bees.

A Blind Color Separation Model for Faithful Palette-Based Image Recoloring

Palette-based image recoloring provides a simple yet effective way for color adjustment, which allows users to interactively manipulate the color of an image by editing a compact color palette. While remarkable progress has been made by previous methods, they have the common limitations that may produce unfaithful image recoloring results i.e., the obtained result does not respond faithfully to the palette adjustment, and tend to induce visual artifacts such as color bleeding and distortion. To address these limitations, we in this paper present a novel color separation model for palette-based recoloring. Akin to previous methods, our color separation model is built upon the assumption that color of each pixel in an image can be formulated as a linear combination of a small set of same basis colors. However, different from previous palette-based recoloring methods which typically rely on heuristic rules to build the color separation model, we experimentally reveal the underlying relationship between the color separation and the palette-based recoloring, and summarize three specialized color separation priors that allow more faithful palette-based recoloring. Based on these priors, we devise a blind color separation model that not only does not require known palette as input as done in previous methods, but also enables more effective palette-based recoloring with much less visual artifacts. Experiments on two datasets demonstrate that our method outperforms the state-of-the-art palette-based recoloring methods. In addition, we show some applications enabled by the proposed color separation model, including automatic pattern coloring generation, green screen keying and region-controllable color transfer.

Partially normal 5-edge-colorings of cubic graphs

In a proper edge-coloring of a cubic graph, an edge e is normal if the set of colors used by the five edges incident with an end of e has cardinality 3 or 5. The Petersen coloring conjecture asserts that every bridgeless cubic graph has a normal 5-edge-coloring, that is, a proper 5-edge-coloring such that all edges are normal. In this paper, we prove a result related to the Petersen coloring conjecture. The parameter μ3 is a measurement for cubic graphs, introduced by Steffen in 2015. Our result shows that every bridgeless cubic graph G has a proper 5-edge-coloring such that at least |E(G)|−μ3(G) (which is no less than 2735|E(G)|) edges are normal. This result improves on some earlier results of Bílková and Šámal.

Quantarctica, an integrated mapping environment for Antarctica, the Southern Ocean, and sub-Antarctic islands

Quantarctica (https://www.npolar.no/quantarctica) is a geospatial data package, analysis environment, and visualization platform for the Antarctic Continent, Southern Ocean (>40oS), and sub-Antarctic islands. Quantarctica works with the free, cross-platform Geographical Information System (GIS) software QGIS and can run without an Internet connection, making it a viable tool for fieldwork in remote areas. The data package includes basemaps, satellite imagery, terrain models, and scientific data in nine disciplines, including physical and biological sciences, environmental management, and social science. To provide a clear and responsive user experience, cartography and rendering settings are carefully prepared using colour sets that work well for typical data combinations and with consideration of users with common colour vision deficiencies. Metadata included in each dataset provides brief abstracts for non-specialists and references to the original data sources. Thus, Quantarctica provides an integrated environment to view and analyse multiple Antarctic datasets together conveniently and with a low entry barrier.

The set chromatic numbers of the middle graph of graphs

For a simple connected graph G, let c : V(G) → ℕ be a vertex coloring of G, where adjacent vertices may be colored the same. The neighborhood color set of a vertex v, denoted by NC(v), is the set of colors of the neighbors of v. The coloring c is called a set coloring provided that NC(u) ≠ NC(v) for every pair of adjacent vertices u and v of G. The minimum number of colors needed for a set coloring of G is referred to as the set chromatic number of G and is denoted by χs(G). In this work, the set chromatic number of graphs is studied in relation to the graph operation called middle graph. Our results include the exact set chromatic numbers of the middle graph of cycles, paths, star graphs, double-star graphs, and some trees of height 2. Moreover, we establish the sharpness of some bounds on the set chromatic number of general graphs obtained using this operation. Finally, we develop an algorithm for constructing an optimal set coloring of the middle graph of trees of height 2 under some assumptions.

Constructing the Electronic Countermeasures System Architecture Based on Case-Based Reasoning and Bayesian Inference

In order to promote the quality of electronic countermeasures system architecture, this paper present a methodology for constructing the electronic countermeasures system architecture based on case-based reasoning and Bayesian inference. The methodology described history cases by CPN model, established the largest similarity case and feasibility space by combining the CPN color set and k-means algorithm, and then proposed the optimizing orderings of variables of Bayesian by the LFS (Legal Firing Sequence) of CPN model and maximum information entropy, learned the Bayesian networks structure by K2 algorithm using the result of orderings of variables. At last, this paper concluded the electronic countermeasures system architecture tactics and discussed the way of reasoning for constructing the electronic countermeasures system architecture.

The eternal game chromatic number of random graphs

The eternal vertex colouring game, recently introduced byKlostermeyer and Mendoza (2018), is a version of the vertex colouring game, a well studied graph game. The game is played by two players, Alice and Bob on a graph G with a set of colours {1,…,k}. The game consists of rounds, such that in each round, every vertex is coloured exactly once. In the first round, players alternate turns with Alice playing first. During their turn, each player first picks yet uncoloured vertex and then colours it by any colour so that the resulting partial colouring of the graph is proper (if at least one such colour exists). During all further rounds, players keep choosing vertices alternately. After choosing a vertex, the player assigns a colour to the vertex which is distinct from its current colour such that the resulting colouring is still proper. Each vertex retains its colour between rounds until it is recoloured. Bob wins if at any point the chosen vertex does not have a legal recolouring, while Alice wins if the game is continued indefinitely. The eternal game chromatic number χg∞(G) is the smallest number k such that Alice has a winning strategy.In this note, we study the eternal game chromatic number of random graphs. We show that with high probability χg∞(Gn,p)=(p2+o(1))n for odd n, and also for even n when p=1k for some k∈N. The upper bound applies for even n and any other value of p as well, but we conjecture in this case this upper bound is not sharp. Finally, we answer a question posed by Klostermeyer and Mendoza.

Emotions on pictures in motion

Movies are stories that convey the viewer to intensely experiment deep-rooted emotional messages. Film contents are predominantly delivered through vision and audition perceptive channel senses, with a wide gamma of colour sets and sound atmospheres managed to create moods, able as well to generate equilibrium awareness effects, as motion pictures glide through our attention. They can trigger emotions, thoughts and memories, derived of personal ecosystem attention structures. Distinct behaviours at the message interpretation are predisposed by cultural antecedents, validation associations and a reflection of individual emotions. Communication is a process of interaction, that leads the individual to establish perceptual and cognitive relationships with the transmitted message, such as: sensing, selecting and signifying. Therefore, meanings generated by the movie scene unravelling can be enhanced by detailed scenic cinema photography composition, as well through electing specific hue palette, saturation and brightness on image implementation, features that drive to conform an involving narrative, modulating the communication space mediation on movie creation. The semiotic field understanding, at cinema photography aesthetics and color-grading, bring about new insights of how to achieve meaningful messages, that can produce enjoyment and connection between people, within the cinematic masterpiece.

A new interpretation of nonpulmonary vein substrates of the left atrium in patients with atrial fibrillation.

BackgroundSubstrate analysis of the left atrium in patients undergoing atrial fibrillation ablation has limitations when performed by means of simple bipolar acquisition.ObjectiveTo evaluate the incidence of low‐voltage zones (LVZs) through maps constructed by means of various catheters: multipolar (MC), omnipolar (OC), and circular catheters (CMCs) with the 3D electro‐anatomical systems (3d‐S) CARTO3 and EnSite Precision.MethodsTo assess LVZs, we acquired maps by means of CMC and MC in the voltage range 0.05‐0.5 mV in 70 consecutive patients in sinus rhythm. In the case of OC only, we made an intra‐patient comparison of bipolar maps constructed by means of the along and across, and HD‐Wave configurations of the EnSite 3d‐S in the ranges of 0.05‐0.5 and 0.5‐1.0 mV. On the basis of this comparison, we chose the range that best identified LVZs as a set of different colors (SDC) compatible with patchy fibrosis (qualitative analysis). Subsequently, we detected the voltage values corresponding to purple and gray points, close to SDC, and the value inside corresponding to blue, green, and red colors, and we evaluated the color change in other voltage ranges. Finally, we performed a quantitative analysis of LVZs by applying the qualitative characteristics described above.ResultsOn the basis of our settings, for OC, the optimal range identifying LVZs was 0.3‐0.6 mV. OC revealed smaller LVZs than MC (P < .05 or P < .001), except in the lateral wall. No significant differences were observed between CMCs.ConclusionsIn our experience, OC does not present the limits of bipolar HD maps, though further studies are needed in order to confirm that 0.3‐0.6 mV is the optimal voltage range within which to identify LVZs.

Constrained feature selection for semisupervised color-texture image segmentation using spectral clustering

Color-texture image segmentation remains a challenging problem due to extensive color-texture variability. Thus, the limited prior knowledge that is expressed by pairwise constraints can be exploited to guide the segmentation process. We propose a new semisupervised method by combining constrained feature selection and spectral clustering (SC) to perform color-texture image segmentation. The pairwise constraints are used by the constraint feature selection to choose the most relevant features among an available set of color and texture features. For this purpose, an innovative constraint score is developed to evaluate a subset of features at one time. A specific constrained SC algorithm involving the pairwise constraints is then applied to regroup the pixels into clusters. Experimental results on four benchmark datasets show that the proposed constraint score outperforms the main state-of-the-art constraint scores and that our semisupervised segmentation method is competitive compared with supervised, semisupervised, and unsupervised state-of-the-art segmentation methods.

Braid Plot-A Mixed Palette Plotting Method as an Extension of Contour Plot.

In this article, we propose a new method of three-dimensional data plotting based on the use of mixed hue palettes, which makes it possible to distinguish simultaneously both huge and subtle changes in the value of the presented quantity at the same plot. This method called "braid plot" is based on the alternating use of multiple palettes of colors (a kind of interlacing), which greatly increases the sharpness of the graph and allows us to define areas of equal values more accurately than using traditional graphs with a single palette or contour plot. We present here an algorithm of preparing braid plot composed of any number of initial color sets. As a result of using this type of plot, it was possible to detect, e.g., weak perturbation effects or subtle oscillations of the spectral density function, which is very hard to observe using classical plots.

Candidate reference genes for quantitative gene expression analysis in Lagerstroemia indica.

Quantitative gene expression analysis by qPCR requires reference genes for normalization. Lagerstroemia indica (crape myrtle) is a popular ornamental plant in the world, but suitable endogenous reference genes are lacking. To find suitable reference genes, we evaluated the stabilities of nine candidate genes in six experimental data sets: six different tissues, three leaf colors, nine flower colors, and under three abiotic stresses (salt, drought, cold) using four statistical algorithms. A target gene LiMYB56 (homolog of Arabidopsis MYB56) was used to verify the authenticity and accuracy of the candidate reference genes. The results showed that the combination of two stably expressed reference genes, rather than a single reference gene, improved the accuracy of the qPCR. LiEF1α-2 + LiEF1α-3 was best for the tissue, salt treatment, and drought treatment sets; LiEF1α-2 + LiEF1α-1 was optimal for leaf color; LiEF1α-2 + LiACT7 was optimal for cold treatment; and LiUBC + LiEF1α-1 was best for the flower color set. Notably, LiEF1α-2 had high expression stability in all six experimental sets, implying it may be a good reference gene for expression studies in L. indica. Our results will facilitate future gene expression studies in L. indica.