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Abstract

We present a self-organizing Kohonen neural network for quantizing colour graphics images. The network is compared with existing algorithmic methods for colour quantization. It is shown experimentally that, by adjusting a quality factor, the network can produce images of much greater quality with longer running times, or slightly better quality with shorter running times than the existing methods. This confounds the frequent observation that Kohonen neural networks are necessarily slow. The continuity of the colour map produced can be exploited for further image compression, or for colour palette editing.
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a. Points Distribution
c. Median−Cut Algorithm d. Sophisticated Median−Cut
e. Oct−Trees (Quadtrees) f. Kohonen Neural Network
b. Equal−sized clusters
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Radius = 2 Radius = 2
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... Vector algorithms, on the other hand, treat the input image as a true vector image by taking into account the spectral correlations. • Pre-clustering vs. post-clustering (Dekker 1994): Pre-clustering algorithms first divide the input color space into K regions and then compute a representative for each region. Post-clustering algorithms, on the other hand, first select K representatives and then cluster the input colors around these representatives. ...
... The first rigorous application of the som algorithm to the cq problem was proposed by Dekker (1994). The author employs a 1d som 64 , initialized with centers spread evenly along the main diagonal of the rgb cube, that is, ...
... From a cq perspective, the advantages of som are (i) its biologically-inspired formulation is appealing to researchers; (ii) thanks to its soft-competitive design, the algorithm is less sensitive to initialization and the dead unit problem; and (iii) the final palette is somewhat contiguous (i.e., adjacent colors are similar), which can be exploited for postquantization image processing operations such as edge detection (Mojsilović and Soljanin 2001) and compression (Dekker 1994;Pei and Lo 1998;Mojsilović and Soljanin 2001;Chang et al. 2005;Pei et al. 2006). ...
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Color quantization (cq), the reduction of the number of distinct colors in a given image with minimal distortion, is a common image processing operation with various applications in computer graphics, image processing/analysis, and computer vision. The first cq algorithm, median-cut, was proposed over 40 years ago. Since then, many clustering algorithms have been applied to the cq problem. In this paper, we present a comprehensive overview of the cq algorithms proposed in the literature. We first examine various aspects of cq, including the number of distinguishable colors, cq artifacts, types of cq, applications of cq, data structures, data reduction, color spaces and color difference equations, and color image fidelity assessment. We then provide an overview of image-independent cq algorithms, followed by a detailed survey of image-dependent ones. After presenting a brief discussion of pixel mapping, we conclude our survey with an outline of the open problems in cq.
... Splitting methods are iterative approaches that divide the color space into sub-prisms. Median Cut (MC) [8], Center-Cut (CC) [9], Octree (OCT) [10], Variance Cut (VC), Variance Cut with Lloyd-Max (VCL), Variance-Based (WAN) [17,18], Popularity (POP) and Modified Popularity (MPOP) [19,20], Greedy Orthogonal bi-Partitioning (WU) [12], Radius-Weighted Mean-Cut (RWM) [21], Split and Merge (SAM) [20], Self-Organization Map (SOM) [22], and Modified Max-Min (MMM) [23] are commonly used quantization methods. The MC method [8] repeatedly separates the three-dimensional color space into smaller regions. ...
... The disadvantages of the method are the use of a uniform structure and its user-dependent nature. SOM [22] is a model proposed for artificial neural networks. SOM is an effective color reduction approach that is used in many fields. ...
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In this study, a novel color quantization approach which automatically estimates the number of colors by multi-level thresholding based on the histogram is proposed. The method consists of three stages. First, red–green–blue is clustered by threshold values. Thus, the pixels are positioned in a cluster or sub-prism. Second, the color palette is produced by determining the centroids of the clusters. Finally, the pixels are reassigned to clusters based on their distance from each centroid. The average of the pixels included in each cluster also represents the color of that cluster. While conventional methods are user-dependent, the proposed algorithm automatically generates the number of colors by considering the pixels assigned to the clusters. Additionally, the multi-level thresholding approach is also a solution to the initialization problem, which is another important issue for quantization. Consequently, the experimental results of the method tested with various images show better performance than many frequently used quantization techniques.
... More recent hierarchical CQ algorithms include variance-cut and Ueda et al.'s algorithm (Ueda et al., 2017). Partitional algorithms adapted to CQ include maximin (Xiang, 1997), k-means (Celebi, 2009(Celebi, , 2011Hu & Lee, 2007;Hu & Su, 2008;Huang, 2021;Thompson et al., 2020;Valenzuela et al., 2018), self-organizing maps (Dekker, 1994;Park et al., 2016), fuzzy c-means (Schaefer, 2014;Szilágyi et al., 2016;Wen & Celebi, 2011), k-harmonic means (Frackiewicz & Palus, 2011), rough c-means (Schaefer et al., 2012), and competitive learning . ...
... Celebi Fig. 2. Baboon output images ( = 32). (Heckbert, 1982), modified popularity (MPOP) (Braudaway, 1987), octree (OCT) (Gervautz & Purgathofer, 1988), variance-based algorithm (WAN) (Wan et al., 1990), greedy orthogonal bipartitioning (WU) (Wu, 1991), center-cut (CC) (Joy & Xiang, 1993), self-organizing map (SOM) (Dekker, 1994), radius-weighted mean-cut (RWM) (Yang & Lin, 1996), modified maximin (MMM) (Xiang, 1997), split and merge (SAM) (Brun & Mokhtari, 2000), variance-cut (VC) , and variance-cut with Lloyd iterations (VCL) . ...
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Color quantization is a common image processing operation with various applications in computer graphics, image processing, and computer vision. Color quantization is essentially a large-scale combinatorial optimization problem. Many clustering algorithms, both of hierarchical and partitional types, have been applied to this problem since the 1980s. In general, hierarchical color quantization algorithms are faster, whereas partitional ones produce better results provided that they are initialized properly. In this paper, we propose a novel partitional color quantization algorithm based on a binary splitting formulation of MacQueen’s online k-means algorithm. Unlike MacQueen’s original algorithm, the proposed algorithm is both deterministic and free of initialization. Experiments on a diverse set of public test images demonstrate that the proposed algorithm is significantly faster than two popular batch k-means algorithms while yielding nearly identical results. In other words, unlike previously proposed k-means variants, our algorithm addresses both the initialization and acceleration issues of k-means without sacrificing the simplicity of the algorithm. The presented algorithm may be of independent interest as a general-purpose clustering algorithm.
... Su and Hu (2013) proposed a self-adaptive differential evolution-based CQ algorithm. Artificial neural networks have been applied to obtain color quantized images by several authors, such as Pei and Lo (1998) and Dekker (1994), who used Kohonen neural networks with this purpose. The Ant colony algorithm was proposed by Ghanbarian, Kabir, and Charkari (2007) for CQ. ...
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Color Quantization (CQ) is a complex and hard problem because selecting the best set of colors from many available colors and using that set to obtain a good quality image is an NP-complete problem. The use of evolutionary computation and swarm-based methods to solve search and optimization problems has increased dramatically in recent years. This article compares some of these methods in order to solve the CQ problem. The following methods were used to generate CQ images: Particle swarm optimization, Artificial bee colony, Adaptive differential evolution, Success-history based adaptive differential evolution (with and without linear population size reduction), Cuckoo search, Firefly algorithm and Shuffled-frog leaping algorithm. For the first two methods, two variants were considered. Thus, a total of ten metaheuristics were compared with four classical CQ methods (Variance-based, Median-cut, Binary splitting and Wu’s methods) applying them to a set of benchmark images and considering four different palette sizes (32, 64, 128, and 256 colors). Three error measures were considered to compare the methods: the mean squared error, the mean absolute error and the peak signal-to-noise ratio. Some of the swarm-based methods analyzed include a recently proposed CQ method using ants. Although they have a slow computational speed in the experimental studies, the ant-based methods are significantly better than all other methods according to the Wilcoxon signed rank test. In general, despite their speed, classical methods underperform the other ten methods both qualitatively and quantitatively
... SOM has also been used in color related applications: in binarization [16], segmentation [12] and CQ [7][8][9]15] where author presents FS-SOM a frequency sensitive learning scheme including neighborhood adaptation that achieves similar results to SOM, but less sensitive to the training parameters. One variant of special interest is the neural network Self-Growing and Self-Organized Neural Gas (SGONG) [2], an hybrid algorithm using the GNG mechanism for growing the neural lattice and the SOM leaning adaptation mechanism. ...
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... The third group of methods consists of additional CQ techniques that primarily exist within the field of artificial intelligence. These techniques include neural networks, such as the Kohonen network NeuQuant [11] and Neural Gas [12], and metaheuristic methods based on the flocking behavior of animals, such as ants [13,14], bees [2], fireflies [15], and frogs [16]. Typically, the use of these techniques for CQ is somewhat time consuming. ...
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