Color Quantization Research Articles

Color Quantization by Modified K-Means Algorithm

Color Quantization by Modified K-Means Algorithm

Computing Color Categories from Statistics of Natural Images

This article presents a framework for understanding, modeling, and computing color categories on the basis of knowledge from the color imaging science. One of the main assumptions advocated in this article is that the structure of color categories originates from the statistical structure of the perceived color environment that was observed throughout an individual's life. The perceived color environment can be modeled as color statistics of natural images in some perceptual and approximately uniform color space (e.g., the CIELUV color space). The process of color categorization can be modeled as the grouping of the color statistics by clustering algorithms (e.g., K-means). The proposed computational model enables one to predict the location, rank, and number of color categories. The model is examined on the basis of K-means clustering analysis of statistics of 630 natural images in the CIELUV color space. In general, the model predictions are consistent with data from psycholinguistic studies. The model might be applied in different areas of imaging science such as color quantization, image quality, and gamut mapping.

Fuzzy algorithms for combined quantization and dithering

Color quantization reduces the number of the colors in a color image, while the subsequent dithering operation attempts to create the illusion of more colors with this reduced palette. In quantization, the palette is designed to minimize the mean squared error (MSE). However, the dithering that follows enhances the color appearance at the expense of increasing the MSE. We introduce three joint quantization and dithering algorithms to overcome this contradiction. The basic idea is the same in two of the approaches: introducing the dithering error to the quantizer in the training phase. The fuzzy C-means (FCM) and the fuzzy learning vector quantization (FLVQ) algorithms are used to develop two combined mechanisms. In the third algorithm, we minimize an objective function including an inter-cluster separation (ICS) term to obtain a color palette which is more suitable for dithering. The goal is to enlarge the convex hull of the quantization colors to obtain the illusion of more colors after error diffusion. The color contrasts of images are also enhanced with the proposed algorithm. We test the results of these three new algorithms using quality metrics which model the perception of the human visual system and illustrate that substantial improvements are achieved after dithering.

A fast and novel technique for color quantization using reduction of color space dimensionality

This paper describes a fast and novel technique for color quantization using reduction of color space dimensionality. The color histogram is repeatedly sub-divided into smaller and smaller classes. The colors of each class are projected on a carefully selected line, such that the color dis-similarities are preserved. Instead of using the principal axis of each class, the line is defined by the mean color vector and the color of the largest distance away from the mean color. The vector composed of the projection values for each class is then used to cluster the colors into two representative palette colors. As a result, the computation in the quantization process is fast. A fast pixel mapping algorithm based on the proposed data clustering algorithm is also presented in this paper. Experimental results show that the proposed algorithms quantize images with high image quality efficiently.

Color quantization by pairwise clustering using a reduced graph

Abstract Abstract The aim of this work is to investigate an improvement in the performance of the pairwise clustering algorithm (PCA) for color quantization of images, that algorithm uses a local error optimization strategy to generate near optimal quantization levels. We investigate the behavior of the accumulated error in the final images when, instead of computing distances between all pairs of colors, a reduced graph is used. We take advantage of a sorted vector of colors to reduce the number of neighbors considered by each node of the graph of distances.

Color quantization and processing by Fibonacci lattices

Color quantization is sampling of three-dimensional (3-D) color spaces (such as RGB or Lab) which results in a discrete subset of colors known as a color codebook or palette. It is extensively used for display, transfer, and storage of natural images in Internet-based applications, computer graphics, and animation. We propose a sampling scheme which provides a uniform quantization of the Lab space. The idea is based on several results from number theory and phyllotaxy. The sampling algorithm is very much systematic and allows easy design of universal (image-independent) color codebooks for a given set of parameters. The codebook structure allows fast quantization and ordered dither of color images. The display quality of images quantized by the proposed color codebooks is comparable with that of image-dependent quantizers. Most importantly, the quantized images are more amenable to the type of processing used for grayscale ones. Methods for processing grayscale images cannot be simply extended to color images because they rely on the fact that each gray-level is described by a single number and the fact that a relation of full order can be easily established on the set of those numbers. Color spaces (such as RGB or Lab) are, on the other hand, 3-D. The proposed color quantization, i.e., color space sampling and numbering of sampled points, makes methods for processing grayscale images extendible to color images. We illustrate possible processing of color images by first introducing the basic average and difference operations and then implementing edge detection and compression of color quantized images.

Unsupervised segmentation of color-texture regions in images and video

A method for unsupervised segmentation of color-texture regions in images and video is presented. This method, which we refer to as JSEG, consists of two independent steps: color quantization and spatial segmentation. In the first step, colors in the image are quantized to several representative classes that can be used to differentiate regions in the image. The image pixels are then replaced by their corresponding color class labels, thus forming a class-map of the image. The focus of this work is on spatial segmentation, where a criterion for "good" segmentation using the class-map is proposed. Applying the criterion to local windows in the class-map results in the "J-image," in which high and low values correspond to possible boundaries and interiors of color-texture regions. A region growing method is then used to segment the image based on the multiscale J-images. A similar approach is applied to video sequences. An additional region tracking scheme is embedded into the region growing process to achieve consistent segmentation and tracking results, even for scenes with nonrigid object motion. Experiments show the robustness of the JSEG algorithm on real images and video.

On spatial quantization of color images

Image quantization and digital halftoning, two fundamental image processing problems, are generally performed sequentially and, in most cases, independent of each other. Color reduction with a pixel-wise defined distortion measure and the halftoning process with its local averaging neighborhood typically optimize different quality criteria or, frequently, follow a heuristic approach without reference to any quantitative quality measure. In this paper, we propose a new model to simultaneously quantize and halftone color images. The method is based on a rigorous cost-function approach which optimizes a quality criterion derived from a simplified model of human perception. It incorporates spatial and contextual information into the quantization and thus overcomes the artificial separation of quantization and halftoning. Optimization is performed by an efficient multiscale procedure which substantially alleviates the computational burden. The quality criterion and the optimization algorithms are evaluated on a representative set of artificial and real-world images showing a significant image quality improvement compared to standard color reduction approaches. Applying the developed cost function, we also suggest a new distortion measure for evaluating the overall quality of color reduction schemes.

An adaptive clustering algorithm for color quantization

In this paper, a novel adaptive clustering algorithm for color image quantization is presented. In our approach, a superposed 3D histogram is calculated first. Then, the sorted histogram list is fed into an adaptive clustering algorithm to extract the palette colors in the image. Finally, a destined pixel-mapping algorithm is applied to classify pixels into their corresponding palette colors. The quantized error of our proposed algorithm is very small due to the combination of the reduced RGB color space utilization and the adaptive clustering algorithm. Besides, the executing speed of our proposed algorithm is also quite fast due to the reduced RGB color space, sorted histogram list, suitable color design and destined pixel mapping. Experimental results reveal the feasibility and superiority of our proposed approach in solving color quantization problem.

A near real-time Evolution-based Adaptation Strategy for dynamic Color Quantization of image sequences

Color Quantization of still images can be easily stated as a Clustering problem. Color Quantization of sequences of images becomes a Non-stationary Clustering Problem. In this paper we propose a very simple and effective Evolution-based Adaptive Strategy to perform the adaptive computation of the color representatives for each image in the sequence. Salient features of the algorithm proposed here are: individuals correspond to individual cluster centers, to approach real-time response we impose one-generation adaptation for each image, mutation operators are guided by the actual covariance matrices of the clusters. Experimental results on a sequence of indoor images are presented.

Color quantization using the fast K-means algorithm

Many color images use 24 bits for color information. However, this number of colors is not always necessary. In this paper, an algorithm that quantizes a full-color image from about 17 million to 256 colors is proposed. The quantized colors are calculated so that the sum of squared quantization errors is minimized. To quantize the color image, the fast K-means algorithm is proposed. This algorithm classifies K clusters into groups. These groups are used to decrease the number of calculations and the execution time. The fast K-means algorithm is effective when K is large. The results show that for K = 256 the execution time is less than a quarter of that for the K-means algorithm. © 2000 Scripta Technica, Syst Comp Jpn, 31(8): 33–40, 2000

Basic Competitive Neural Networks as Adaptive Mechanisms for Non-Stationary Colour Quantisation

In this paper we consider the application of two basic Competitive Neural Networks (CNN) to the adaptive computation of colour representatives on image sequences that show non-stationary distributions of pixel colours. The tested algorithms are the Simple Competitive Learning (SCL) algorithm and the Frequency-Sensitive Competitive Learning (FSCL) algorithm. Both, SCL and FCSL are the simplest adaptive methods based, respectively, on minimising the distortion and on the search for a uniform quantisation. The aim of this paper is to study several computational properties of these methods when applied to non-stationary clustering as adaptive vector quantisation algorithms. Non-stationary colour quantisation is, therefore, representative of the more general class of non-station-ary clustering problems. We expect our results to be meaningful for other algorithms that involve either the minimisation of the distortion or the search for uniform quantisers. We study experimentally the effect of the size of the image sample employed in the one-pass adaptation, their robustness to initial conditions, and the effect of local versus global scheduling of the learning rate.

Color quantization by preserving color distribution features

A color quantization method is proposed. The method hierarchically uses a bisection tool that preserves certain color-distribution features. The preserved features are average color, variance in each color dimension, and average color radius. An algorithm is given that includes the histogram simplification procedure, color palette generation, and pixel mapping. Experiments show that the proposed method usually obtains acceptable quantized images with competitive speed.

3D visualization of color image histograms

Color quantization is a useful method for obtaining high-quality compressed images for storage and subsequent distribution via the World Wide Web. The first step of most color quantization techniques is to create a histogram of the colors in the truecolor image. The dramatic differences in time and space efficiency of various data structures used to represent truecolor image histograms are visually explored in 3D. Spatial subdivisions use buckets to store colors in a portion of the RGB cube. Linked lists are the typical data structure used for buckets; we propose using red-black trees and treaps. Our visualizations highlight the clustering property of spatial subdivision methods.

A fuzzy colour quantizer for renderers

This paper presents a new colour quantization method for ray tracing. Normally, quantization is carried out by generating statistics about the colours present in the original image. Then a colour look-up table is created which contains the colours available in the quantized image. Original quantized values are mapped into the nearest colour entries in the look-up table. Although the execution time is quick using this method (histogram analysis) the cost is that the image quality is poor. The fuzzy c-means clustering algorithm (FCM) is an alternative solution to ameliorate the degradation in image quality. However, FCM introduces a considerable amount of computational burden and the process is time-consuming. This paper shows that the dominant peaks of histograms yield the fuzzy centroids needed for the first estimate in FCM. This reduces the computational burden imposed by FCM and improves the overall execution time.

Dithered Color Quantization

Image quantization and digital halftoning are fundamental problems in computer graphics, which arise when displaying high‐color images on non‐truecolor devices. Both steps are generally performed sequentially and, in most cases, independent of each other. Color quantization with a pixel‐wise defined distortion measure and the dithering process with its local neighborhood optimize different quality criteria or, frequently, follow a heuristic without reference to any quality measure.In this paper we propose a new method to simultaneously quantize and dither color images. The method is based on a rigorous cost‐function approach which optimizes a quality criterion derived from a generic model of human perception. A highly efficient algorithm for optimization based on a multiscale method is developed for the dithered color quantization cost function. The quality criterion and the optimization algorithms are evaluated on a representative set of artificial and real‐world images as well as on a collection of icons. A significant image quality improvement is observed compared to standard color reduction approaches.

Color image compression and limited display using self-organization Kohonen map

Several methods have been proposed to do color quantization for limited color displays. Self-organization of Kohonen feature maps (SOFM) is a very useful tool for data clustering. By extracting a special butterfly-jumping sequence from an image, a neural network was fed in that sequence of image data for SOFM training, and a fairly good color table was present to represent that image. The peak signal-to-noise ratio of the decoded image is high (about 35 dB in average for a 256 color image), and the perceptual quality is good as well, even with a small set of color tables (for example, 32 or 64 colors). Furthermore, the training process is fast. For encoding, we also propose an efficient algorithm based on the Kohonen map ordering property. By considering that the neighboring image pixels are closely related and by setting some acceptable thresholds, we can quickly get an encoded image. For further compression on the color indexed image with the limited color palette, we cut the indexed images into 4/spl times/4 blocks and send the block vectors into another SOFM neural network for training. Under the two-dimensional (2-D) mesh neural structure, SOFM vector quantization on an indexed image could largely reduce the color shift artifacts and avoid the requantization problem. About 0.5 b per pixel of coded image can be easily obtained with a fairly good perceptual quality. More importantly, the decoded color indexed images can be readily displayed. This will reduce the decoder complexity greatly.

An Algorithm for Dynamic Color Management

Though the problem of color quantization in static images is not completely solved, there are a few algorithms that produce good results. Color quantization with dynamic color requests is an unsolved problem. In this paper we present an algorithm that manages dynamic color allocations without advance knowledge of the sequence of color requests. It uses a dynamic color table that can be used simultaneously in multiple windows from one or more applications. Advance knowledge about color requirements will improve the results of the algorithm.

Color quantization with genetic algorithms

The need for quantization of color images arises because of limitations of image display and hardcopy, data storage and data transmission devices. Many of the present algorithms for color quantization find non-optimal solutions, giving rise to visible shifts in color and false contours when the number of quantization colors is small. This paper describes a new approach to finding the optimal solutions of the color image quantization problem using a genetic algorithm. The nature and the difficulty of the problem and its formulation are discussed. Then genetic algorithms (GAs) are presented and the representation of the problem with this method is explained. The effect of the parameters such as mutation and crossover probabilities and population size on the quality of solutions is studied. Solutions obtained with genetic algorithms are compared with those of heuristics and the K-means clustering algorithm and the superior quality of the results of the GA is shown.

Color image compression using quantization, thresholding, and edge detection techniques all based on the moment-preserving principle

A new approach to color image compression with high compression ratios and good quality of reconstructed images using quantization, thresholding, and edge detection all based on the moment-preserving principle is proposed. An input image with 24 bits per pixel is quantized into 8 bits per pixel using a new color quantization method based on the moment-preserving principle. The quantized image is then divided into n × n non-overlapping square blocks. Two representative colors for each block are computed by moment-preserving thresholding. A bit-map is then generated, consisting of 0s and 1s indicating whether the block pixels are assigned to the first color or the second according to the Euclidean distance measure. A moment-based edge detector is performed further on the bit-map of each non-uniform block. The two parameters l and θ of a line edge with the equation of x cos θ + y sin θ = l are obtained. The image is finally coded with a codebook of a 256-color palette; a 1-bit indicator for each block which specifies whether the block is uniform or not; an 8-bit color index for a uniform block, or two 8-bit color indices, a 3-bit index for θ, and a 2-bit or 3-bit index for l for a non-uniform block. An average compression ratio of 22.49 or 33.32 can be obtained for 4 × 4 or 5 × 5 image blocks, respectively. Experimental results show the feasibility and efficiency of the proposed approach for color image compression.