An efficient color quantization based on generic roughness measure
Introduction
In a high quality color image, there are millions of different colors. Color quantization is a process that reduces the number of distinct colors in a digital image, usually with the intention that the reconstructed image should be as visually similar as possible to the original image. By reducing the complexity of color space, color quantization will benefit image storage and image transfer on the internet. Moreover, color quantization also simplifies feature spaces, which is helpful for image recognition and retrieval.
A color quantization algorithm generally consists of two parts. The first is color palette design and the second part is pixel mapping. There are two kinds of methods for creating color palette: image-independent methods and image-dependent methods. Image-independent methods determine a generic palette without considering any specific image contents, while image-dependent methods generate palettes based on the color distribution of images. Although it is fast, the image-independent method often produces poor results because of not considering image contents. To maintain a quality of image representation, most of the recent works on color quantization rely on image-dependent methods. For image-dependent methods, there are two different strategies to build up color palette: preclustering and postclustering [1]. The preclustering strategy partitions the original image colors into multiple subspaces based on the statistics of color distribution [7], [9], [11], [19], [26], [39], [47], [48]. Because palette construction is an once-off procedure, the preclustering strategy usually has low computational complexity while sacrificing quantization quality in some degree. The postclustering strategy starts color quantization with an initial palette and improves it iteratively [3], [13], [27], [35], [36], [38], [49]. Since this strategy involves an objective function to minimize color distortion through stochastic optimization, it has better quality than preclustering strategy. However, it greatly increases the computational complexity.
From the discussion above, the challenge to color image quantization is to balance the quantization quality and computational complexity. To achieve this balance, the postclustering quantization methods have been improved in different ways. Puzicha et al. proposed a color quantization method incorporating spatial and contextual information, in which the quantization was performed by an efficient multi-scale procedure to alleviate the computational burden [34]. Mojsilović and Soljanin proposed another quantization approach based on Fibonacci numbers and spiral lattices, in which the sampling scheme was used to generate color palettes [23]. Computational intelligence theories such as neural networks [29], PSO [25], GA [37], SOM [4] and competitive learning [2], [45] were also used to optimize the color quantization process. Zhou et al. proposed an algorithm to adjust the color quantization results which tuned the palette by assigning weights to pixel clusters and color distances [50]. For the postclustering quantization based on clustering strategies, the quantization efficiency was improved by reducing the computational cost of pixel clustering. The modifications focused on speeding up clustering process, in the meantime, optimizing the clustering initialization [3], [12], [27], [42]. The above improvements of postclustering methods could produce the higher quality of quantization results and alleviate the computational burden to some degree. However, these methods needed to heavily traverse pixels iteratively thus computational complexity was still high.
To tackle the problem above, we propose a two-stage color quantization framework based on Generic Roughness measure, which is abbreviated as GR framework. The basic idea of this framework is to integrate the low complexity of the histogram-based color space segmentation and the high quality of the clustering-based color quantization. First, the original image color is initially compressed to a condensed color space through thresholding color components. It is very important to form precise segmentation of color space to avoid the severe color distortion in final quantization results. However, the traditional histogram-like statistics cannot guarantee the segmentation precision. We propose generic roughness measure for color segmentation in the initial compression stage. Generic roughness can represent the spatial color homogeneity and thus generate the delicate color segmentation results. In the second stage, the initially compressed colors are further merged to a palette using clustering methods. Carrying out clustering in a compressed color space rather than on the pixel level, merging color in the second stage is very fast. Thus the computational cost of the framework mainly depends on the roughness thresholding in the first stage. The efficiency of the framework is analyzed in Section 5.3. Meanwhile, because of the precise segmentation of color space through generic roughness, the proposed framework causes little color distortion in the initial compression stage and guarantees the quantization quality. Therefore, the proposed framework can well balance the quantization quality and computational cost. The contributions of this paper are summarized as follows:
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Propose a postclustering quantization strategy at color space level: Common postclustering quantization methods are implemented at the pixel level. The proposed strategy applies the postclustering quantization in a precisely compressed color space. At this level, the quantization efficiency is greatly improved. In the meantime, the quantization quality is maintained.
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Propose a generic roughness measure for color space segmentation: Generic roughness measure is the key to precise color space compression. It can tolerate the disturbance of imbalanced color distribution and thus produces the accurate segmentation of image color space.
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Design an efficient two-stage quantization framework: In the first stage, a self-adaptive algorithm is designed to threshold roughness on color components to compress color space. In the second stage, the Rough K-means algorithm [18], [33] is modified by integrating the color weights to merge the compressed colors to obtain the final quantization result.
The rest of this paper is organized as follows: Section 2 reviews the related work and analyzes the existing problems. Section 3 describes the basic framework and workflow of the roughness-based quantization. Section 4 introduces the construction of generic roughness measure. Section 5 presents the specific quantization method which includes the roughness thresholding algorithm and color merging algorithm. In Section 6, the comprehensive experimental results validate the high efficiency of the proposed color quantization framework. The work is concluded in Section 7.
Section snippets
Related work
The clustering technique is a key component in postclustering color quantization. To accelerate the clustering for quantization, Celebi proposed an improved K-means algorithm which simplified distance calculation and comparison in the clustering procedure through sorting cluster means [3]. Using partition indices, Özdemir and Akarun proposed a variant of fuzzy C-means algorithm to reduce the computational cost of the quantization based on soft clustering [27]. The initialization strategies
Framework
Our objective is to design a hybrid quantization framework to balance the quantization quality and computational complexity. The solution involves two stages. In the first stage, the color space of original image is segmented based on the histogram-like thresholding to form the initial color compression. In the second stage, the initially compressed colors are merged using clustering to form a palette for quantization. The key of this solution is to guarantee the precision of color space
Generic roughness measure
Roughness measure is obtained according to the boundary between lower approximation and upper approximation. Histogram represents certain pixels distribution in terms of intensity values of color component. From the view of rough sets, it is considered as the lower approximation of color component. By measuring the spatial color homogeneity, histogram of every color component is extended to form the upper approximation. Upper approximations of all color components represent the color
Initial color compression
In the first stage of GR quantization framework, the original image color is compressed based on the color space segmentation induced by generic roughness measure. Algorithm 1 Adaptive roughness thresholding. Input: roughness indices on each color component r(l), Output: band cuts on color component Find all peaks of roughness indices ; Compute the threshold of peak heights Th; ; ; ; ; ; Select peaks
Experimental results
The experiments include the tests of roughness measure, quantization quality and quantization efficiency. In the test of roughness measure, we demonstrate the ability of generic roughness measure to represent color homogeneity. In the tests of quantization quality and efficiency, through comparing with other hybrid quantization methods, we demonstrate that GR quantization framework can achieve a good balance between quantization quality and computational complexity. All the testing images are
Conclusions
Although many postclustering quantization methods can achieve high quality results, they always suffer from heavy computational cost. To improve the efficiency of postclustering quantization, a two-stage color quantization framework based on generic roughness measure (GR framework) is investigated in this paper. The basic idea of this novel framework is to synthesize the techniques of roughness-based color space segmentation and clustering-based quantization. In the first stage, through
Conflict of interest statement
None declared.
Acknowledgment
This work was supported by National Natural Science Foundation of China (Serial Nos. 61103067, 61273304) and Innovation Foundation of Shanghai University.
Xiaodong Yue is presently a Research Fellow in the Advanced Analytic Institute (AAI) at University of Technology Sydney (UTS), supervised by Prof. Longbing Cao. Before this postdoctoral period, he received the Ph.D. degree from Tongji University in 2010. From October 2008 to April 2009, he was a research assistant in the Department of Computer Science at Hong Kong Baptist University, supervised by Prof. Jiming Liu. His research topics include pattern recognition, soft computing and multimedia.
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Xiaodong Yue is presently a Research Fellow in the Advanced Analytic Institute (AAI) at University of Technology Sydney (UTS), supervised by Prof. Longbing Cao. Before this postdoctoral period, he received the Ph.D. degree from Tongji University in 2010. From October 2008 to April 2009, he was a research assistant in the Department of Computer Science at Hong Kong Baptist University, supervised by Prof. Jiming Liu. His research topics include pattern recognition, soft computing and multimedia.
Duoqian Miao received his Ph.D. degree in Pattern Recognition and Intelligent System at Institute of Automation, Chinese Academy of Sciences in 1997. He is a Professor and Vice dean of the School of Electronics and Information Engineering of Tongji University. Prof. Miao's present research interests include Soft Computing and Data Mining. Prof. Miao has published over 160 scientific articles in international journals, books, and conferences, such as Pattern Recognition, Pattern Recognition Letters and Information Sciences. He is a committee member of International Rough Sets Society, a senior member of the China Computer Federation (CCF), a committee member of the CCF Artificial Intelligence and Pattern Recognition and a vice chair of the CAAI Rough Set and Soft Computing Society.
Longbing Cao is a professor of information technology at the University of Technology Sydney (UTS). He got one Ph.D. in Pattern Recognition and Intelligent Systems and another in Computing Science. He is the Director of the Advanced Analytics Institute at UTS. He is also the Research Leader of the Data Mining Program at the Australian Capital Markets Cooperative Research Centre. He is a Senior Member of IEEE, SMC Society and Computer Society. His primary research interests include data analysis and machine learning. He works/worked with several major organizations on enterprise data mining, such as Australian Commonwealth Government Agency Centrelink, ATO, Westpac Banking Group, Qantas and Shanghai Stock Exchange.
Qiang Wu received the Ph.D. degree in computing science from the University of Technology Sydney, Australia, in 2004. He is currently a Senior Lecturer with the School of Computing and Communications, University of Technology Sydney. His major research interests include computer vision, image processing, pattern recognition and multimedia. He has published more than 70 refereed papers in these areas, including those published in prestigious journals and top international conferences. Dr. Wu has been a Guest Editor of several international journals, such as Pattern Recognition Letters. He has served as a Chair and/or a Program Committee Member for a number of international conferences. He has also served as a Reviewer for several international journals, such as the IEEE Transactions on Systems, Man, and Cybernetics Part B, the IEEE Transactions on Circuits and Systems for Video Technology, Pattern Recognition, Pattern Recognition Letters.
Yufei Chen is presently a senior lecturer in the School of Electronics and Information Engineering of Tongji University. She received Ph.D. degree from Tongji University in 2010. She was also a research fellow in Darmstadt University of Technology in 2009. Her research topics include pattern recognition and medical image analysis.