Center for Multimedia Signal Processing, Department of Electronic and Information EngineeringRefereed conference paper2006-2007 > Academic research: refereed > Refereed conference paperVersion of RecordPublishe

Chan, YH

Lui, KC

PolyU Institutional Repository

An adaptive palette reordering method forcompressing color-indexed imageKa-Chun Lui and Yuk-Hee ChanDepartment of Electronic and Information EngineeringThe Hong Kong Polytechnic University, Hong KongAbstract - An adaptive palette reordering method isproposed in this paper to reshape the statistical properties ofthe color index map of a color-indexed image with adynamic palette. Unlike other reordering methods, theproposed method extracts information from both the colorindex map and the palette to achieve the objective. Thecompression performance of JPEG-LS can be significantlyimproved when the proposed method is used.I. INTRODUCTIONColor-quantized images [1] are widely used in variousapplications especially Internet applications nowadays toreduce communication bandwidth and storage requirement.A color-quantized image is generally represented with acolor index map each element of which serves as an index toselect a color from a predefined set of colors to represent thecolor of a pixel in the image. The predefined set of colors iscalled a palette.To reduce the size of a color-indexed image further,lossless compression techniques are generally used becausethe index used to pick a particular palette color must beexact in decoding. A minor difference between two indexvalues may result in a serious color shift.Predictive coding technique is widely used in losslesscompression. In fact, most lossless coding algorithms suchas CALIC [2] and JPEG-LS [3] are based on predictivecoding and entropy coding techniques. CALIC and JPEG-LS raster-scan an image and use the intensity values of someencoded local pixels to predict the intensity value of thepixel being encoded. The estimation error between theactual value and the estimated value is then encoded withentropy coding algorithms to compress the image. Inparticular, the predictors used in CALIC and JPEG-LS are,respectively, Gradient Adaptive Predictor (GAP) andMedian Edge Detection (MED) predictor. Both predictorsmake use of the high spatial correlation in a natural image.In general, the smaller the average prediction error over theimage, the higher compression ratio can be achieved.Predictive coding techniques do not perform wellwhen they are used to encode a color-quantized image.Encoding a color-quantized image implies encoding itscolor index map. In general, a palette is generated in a waywithout concerning the order of the colors in the resultantpalette. Accordingly, the numerical values of two indicesthat point to similar colors may be very different. Mostpredictors assume that neighboring pixels have similarattributes and, when these attributes are quantitativelymeasured, their values are similar. This assumption is validfor the intensity values of an image, but not for the indexvalues in a color index map due to the aforementionedreason.Palette reordering is a remedial process aiming atfinding a permutation of the color palette to make theresulting color index map more suitable for predictivecoding. In general, palette reordering attempts to minimizethe index difference between adjacent pixels such that theprediction error would be as small as possible. Variousreordering methods were proposed for this purpose. Some ofthem assign indices to palette colors based on the attributesof the palette colors [4] or the distance among the palettecolors [5]. Some of them assign indices to palette colorsbased on the number of occurrences of having two particularpalette colors in two spatially adjacent pixels[6-9]. All ofthem can effectively improve the compression rate whentheir outputs are encoded with JPEG-LS.However, after studying these algorithms, we havetwo observations. First, these methods use the informationextracted from either the palette or the index mapexclusively to assign indices to palette colors. Second, theassignment is based on the global characteristics or statisticsof the image and it is non-adaptive.In this paper, we proposed a new reordering method.This method adaptively reorders the palette based on boththe palette and the index map to produce an index map oflower zero-order entropy and higher spatial correlation. Theresultant index distribution is very biased. By so doing, theindex map can be encoded with JPEG-LS more efficientlyas compared with the outputs of other reordering methods.II. PROPOSED ALGORITHMUnlike conventional palette reordering methods[4-9]in which the palette is reordered based on some globalproperties of the input image, the proposed approachreorders the palette adaptively according to the currentstatistics and local characteristics of the image such thatmore spatial redundancy can be removed in the producedindex map.The proposed method pre-processes a given colorindex map to generate an input to a JPEG-LS codec and, atthe receiver, post-processes the output from a JPEG-LSdecoder to reconstruct the original color-quantized image. Itis fully compatible with JPEG-LS in a way that nomodification to the JPEG-LS codec is required to compressan image when the proposed reordering method is exploited.1-4244-0549-1/06/$20.00 (2006 IEEE.Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on July 27, 2009 at 21:53 from IEEE Xplore.  Restrictions apply. In the pre-processing stage, the input image is rasterscanned and pixels are processed sequentially. For eachpixel, its color is predicted with its processed neighboringpixels. The prediction error is recorded for future reference.Based on the prediction errors of all previously processedpixels and the Euclidean distance between the predictedcolor and each palette color, all palette colors are sorted toform a queue. The position of the real color in the queue isthen used as the new index for the pixel in the output.Similar approach is realized in the post-processing stage togenerate a transient color queue for each pixel to determinethe original pixel color with the received index.A. Core of the methodLet the input color-indexed image be X and theassociated palette be Q= 5 i i=O,1...N-1 }, where N is thesize of the palette. Without lose of generality, we assume allji in Q are sorted according to their luminance and jo isthe one of the minimum luminance. Note that this criterioncan be easily satisfied through an initialization process. Thissorted palette is used as a reference palette in the codec.Based on the index map of X, a full-color image canbe constructed with palette Q. In the proposed method, thethree color planes of the constructed full-color image areseparated and each of them is treated as a grey-level imagefor prediction. The three color planes are raster scanned andprocessed in parallel synchronously. For each pixel, theintensity values of its three color components areindividually predicted with their corresponding color planesby using a MED predictor. Note that some other predictorssuch as GAP can also be used for the prediction. In fact, oursimulation results show that both MED and GAP canprovide a good prediction performance in this application.That MED is suggested in the method is because thereordering method is proposed to support JPEG-LS andMED is used in JPEG-LS.Suppose the prediction result of the three colorcomponents of the current pixel is 5 = (re, g , bp) isthen quantized with palette Q. Let the quantization result becIp. cp could be different from the real color of the pixel,cr. The occurrence of this discrepancy is recorded andcumulated for improving the prediction performance in thefuture as history is useful in predicting an event. Inparticular, in the proposed scheme, a table is constructed forstoring the values of {H(m,n)jm,n=O,1 .. .N- I }, where H(m,n)is defined as the number of occurrences when the quantizedpredicted color and the real color of a pixel are, respectively,cm and ., All H(m,n) values are initialized to zero at thevery beginning and the table is updated whenever a pixel isprocessed. For reference, this table is referred to asdiscrepancyfrequency table (DFT) hereafter.After fP and cp are determined, the colors in paletteQ are adaptively reordered based on {H(p,i)ji=O,1.. N-I}and 11 ji - Vp, 12 .In particular, ,i 's are sorted according tothe values of {H(p,i)li=O,l...N-I} in descending order. Ifthere exist two different colors cl and C such thatH(p,/)=H(pj), C, and Cj will be sorted according to theirEuclidean distances to v-P. The closer one is in front of theother. If they are still not distinguishable, their order will bedetermined by their ranking in reference palette Q.The position of cr in the newly reordered queue canbe used as an index to the queue and is used to represent thepixel in the output of the reordering method. Note the queueforms a transient version of palette Q. After processing thispixel, H(p,r) is incremented by 1 to update the frequencycount of this event.Figure 1 shows an example of how an index isadaptively determined for a pixel when the current status ofH(m,n) is shown in Fig. la. In this example, the palette Q isof size 8. Assume that the quantized predicted color and thereal color of the pixel are, respectively, C4 and c3{I 5i i=0,1...7} are then sorted by H(4,i) and then byc1-V4 2. The position of Q in the sorted sequence is 2and hence the output index for C3 is 2.In the decoder, to decode a pixel, the same process iscarried out to determine a transient version of palette Q. Assoon as the index for the pixel is received, it can be used tofetch the corresponding color in the transient version ofpalette Q to reconstruct (i) a static color-index map whichuses a fixed palette such as Q to generate a full-color image,or even (ii) the full-color image directly.B. DFT MergingThe DFT helps to improve the performance of palettereordering. Based on the values of {H(m,n)jn=0,l..N-l}, itshows how likely that CJ is the real color when cm is thequantized predicted color. This statistical information isuseful for the codec to assign indices to palette colors. In ourcase, the color which is more likely to occur is assigned asmaller index. Eventually, the indices of the output indexmap are highly biased to zero. This helps to reduce the zero-order entropy of the index map.At the early stage of palette reordering, most ofH(m,n) entries are of zero values. Working with a prematureDFT degrades the reordering performance. As it takes timeto process sufficient pixels for building up a meaningfulDFT, a DFT merging scheme is exploited in the proposedreordering method to solve this problem.In the proposed method, by making use of LBGalgorithm[10], a palette of a size smaller than palette Q isgenerated with all colors in Q as the training vectors. Allcolors in Q are then color quantized with this smallerpalette. In consequence, all 5i in Q are clustered into a fewgroups.Let cP be the quantized predicted color for the pixelbeing processed and Hm = E H(m, n) for m=O,1 ... N-1.When c- is determined, Hp is checked against a predefinedthreshold value T. If it is smaller than T, which impliesinsufficient samples were collected for predicting the realcolor cr based on cP, the statistics of all colors in the sameAuthorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on July 27, 2009 at 21:53 from IEEE Xplore.  Restrictions apply. group with cJ will be merged to determine the new indexof cr. For instance, if CJp and Ck belong to the samegroup, Ci 's will be sorted according to the values of{H(p,i)+H(k,i) i=0,1...N-1} in descending order. If thereexist two different colors c, and Cj such that H(p,l)+H(k,l)= H(pj)+H(kj), Cl and Cj will be sorted according to theirEuclidean distance to vip.Let's consider the example shown in Figure 1 again.Assume that C4 and C7 belong to the same group and H4 isnow smaller than the threshold. After sorting { ,i Ii=0,1... 7}by H(4,i)+H(7,i) and then by II Ci -V4 112, the new queue isI Z3 I 5 I 7 I 4 I 6 I l ICo 2 } andthe new index of j3 iS 0.A merged DFT can further be merged into an evensmaller DFT in the same manner when it is necessary. Thecodec can use a smaller DFT whenever a large DFT has notyet been mature. As it needs fewer samples to build up asmaller DFT, the proposed palette reordering method canprovide a reasonable and steady performance afterprocessing a few samples and its advantage can be seeneven at a very early stage of the index reordering process.C. Preparation for JPEG-LSWith the proposed palette reordering method, theindices of the output index map are highly biased to zeroand the zero-order entropy of the output index map islowered. For example, the zero-order entropy of the indexmap of a 256-color color-quantized 'Lena' can be reducedfrom 7.7756 to 4.0217 bits per pixel (bpp) with the proposedreordering method. In contrast, other reordering methods[4-9,1 1] cannot reduce the zero-order entropy of an index mapas they exploit bijective mappings to reindex the palettecolors.However, the index map obtained at this stage is stillnot good enough for JPEG-LS to encode. To further reducethe index difference between adjacent pixels, the indices ofthe index map are remapped to other values with a bijectivemapping M(p) as follows.M(i) {(N- 2-i) 2 fori =0,2...N-2 ifNis even(N -+i) 12 fori =1,3 ...N -1M(i) =(Nli)2 fori 0,2...N- ifNis odd (1)(N+ i)l/ 2 for i = 1,3 ...N- 2This mapping shifts the bias of the index from 0 toFN/21]1.III. EXPERIMENTAL RESULTSSimulations were carried out to evaluate theperformance of the proposed reordering method. A numberof standard full-color testing images including computergraphic images and natural images were color-quantized to256-color images with MathLab function RGB2IND. Nodithering was performed in the quantization. The resultantcolor quantized images were then processed with differentindex reordering methods. Finally, the reordered index mapswere encoded with JPEG-LS.Table 1 lists the compression ratios achieved byJPEG-LS when encoding the outputs of various reorderingmethods [4-9,12]. The proposed method boosts up morecompression performance than the others.Figure 2 shows the histograms of the color index mapsobtained with different reordering methods. One can see thatour result is very biased while the others are not. Thisexplains why the zero-order entropy of our result is lowerthan the others.Table of {H(m,n)}Index m Index n0 1 2 3 4 5 6 70 29 7 6 5 4 3 2 11 0 88 1 2 0 0 0 12 0 2 65 1 2 1 0 03 0 2 10 56 1 1 0 14 3 1 0 8 8 8 0 05 0 0 3 2 3 23 S 16 0 0 0 1 1 2 23 27 0 2 0 3 0 2 6 9(a)| Index i 0 1 2Prediction Error 0.6 0.2 0.3(b)| Index i 0 1 2New index | 3 | 4 7(c)Index i 0 1 2H(4,i)+H(7,i) 3 3 0New index 6 5 7(d)4 5 6 70.2 0.1 0.2 0.14 5 6 711 0 6 554 5 6 78 10 6 93 1 4 2Refer to the reference palette c4 and c7 are in the same group.Fig. 1 Example of how to assign indices to a dynamic palettewhen V4, C4 and c3 are, respectively, the predicted, thequantized predicted and the real colors: (a) current statusof the DFT, (b) prediction error ci v4 2 (c) indexassignment without DFT merging, and (d) indexassignment with DFT merging.0C30InduexFig. 2 Histograms of color index maps ofLenaIV. CONCLUSIONAn adaptive palette reordering method is proposed inthis paper to reshape the statistical properties of a colorindex map such that, when the index map is encoded withAuthorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on July 27, 2009 at 21:53 from IEEE Xplore.  Restrictions apply. JPEG-LS, the compression ratio can be significantlyimproved. Unlike other reordering methods, this methodadaptively reorders the palette based on both the palette andthe index map to produce a new index map of very lowzero-order entropy and high spatial correlation. Simulationresults reveal that its performance is better than other JPEG-LS-compatible reordering methods.ACKNOWLEDGEMENTThis work was supported by a grant from The HongKong Polytechnic University (G-YE90).REFERENCE[1] Orchard, M.T. and Bouman, C.A. "Color quantization ofimages," IEEE Trans. Signal Processing, Dec 1991, Vol.39,No.12, pp.2677-2690.[2] X. Wu and N. D. Memon, "Context-based adaptive losslessimage coding," IEEE Trans. Commun., Vol. 45, Apr. 1997,pp. 437-444.[3] ISO/JEC JTC 1/SC 29/WG 1 JPEG LS image codingsystem, ISO Working Document ISO/JEC JTC1/SC29/WG1N399 -WD14495, July 1996.[4] A. Zaccarin and B. Liu, "A novel approach for coding colorquantized images," IEEE Trans. Image Processing, Vol. 2,Oct. 1993, pp. 442-453.Average[5] A. Spira and D. Malah, "Improved lossless compression ofcolor-mapped images by an approximate solution of thetraveling salesman problem," Proc. IEEE ICASSP'01,Vol.111, May 2001, pp.1797-1800[6] N. D. Memon and A. Venkateswaran, "On ordering colormaps for lossless predictive coding," IEEE Trans. ImageProcessing, Vol. 5, Nov. 1996, pp. 1522-1527.[7] W. Zeng, J. Li, and S. Lei, "An efficient color re-indexingscheme for palette-based compression," in Proc. 7th IEEEInt. Conf. Image Processing Vancouve, BC, Canada, vol. III,Sept. 2000, pp. 476-479.[8] A. J. Pinho and A. J. R. Neves, "A note on Zeng's techniquefor color reindexing of palette-based images," IEEE SignalProcessing Letter, Vol. 11, Feb. 2004, pp. 232-234.[9] S. Battiato, G. Gallo, G. Impoco and F. Stanco, "AnEfficient Re-Indexing Algorithm for Color-MappedImages," IEEE Trans. Image Processing, Vol.13, Nov 2004,pp.1419-1423[10] Y. Linde, A. Buzo, and R. M. Gray, "An algorithm forvector quantizer design," IEEE Trans. Commun., Vol.COM-28, Jan. 1980, pp. 84-95.[11] A.J. Pinho and A. J. R. Neves, "A survey on paletterecording methods for improving the compression of color-indexed images," IEEE Trans. On Image Processing,Vol.13, No.11, Nov 2004, pp.1411-1418[12]4.207 4.673 4.216 4.707 4.351 5.341 3.685Table 1. Performance of different palette reordering methods when working with JPEG-LSSize Bits per pixel(pixel2) [12] [4] [6] [7] [8] [9] Ourspool 510x383 1.563 1.965 1.464 1.560 1.462 1.786 1.402watch 1027x768 2.111 2.436 2.093 2.273 2.169 2.632 1.964water 1024x768 5.568 5.673 5.487 6.207 5.621 7.089 4.887Kodak 01 768x512 5.489 5.956 5.403 5.969 5.599 7.055 4.926Kodak 02 768x512 4.259 5.277 4.234 4.605 4.383 5.418 3.748Kodak 03 768x512 2.603 3.587 2.723 2.875 2.742 3.548 2.526Kodak 04 768x512 4.002 4.765 3.920 4.953 4.312 5.447 3.468Kodak 05 768x512 5.071 5.669 5.029 5.390 5.204 6.408 4.485Kodak 06 768x512 4.758 4.997 4.976 5.413 5.153 5.921 4.247Kodak 07 768x512 3.525 4.208 3.667 4.069 3.857 4.698 3.082Kodak 08 768x512 5.517 5.554 5.797 5.965 5.852 6.404 4.603Kodak 09 768x512 3.873 4.423 3.952 4.514 4.100 5.506 3.497Kodak 10 768x512 4.683 4.551 4.505 5.339 4.826 5.969 3.668S' Kodak 1 1 768x512 4.461 5.024 4.334 4.890 4.458 4.799 3.787FE._ Kodak 12 768x512 3.739 4.316 3.868 4.403 3.960 5.329 3.318D Kodak 13 768x512 6.009 6.482 5.968 6.509 6.203 7.016 5.608Kodak 14 768x512 4.468 5.369 4.497 5.140 4.717 6.482 4.106Kodak 15 768x512 3.397 4.089 3.537 3.883 3.636 4.332 3.060Kodak 16 768x512 4.104 4.558 4.254 4.817 4.386 5.995 3.661Kodak 17 768x512 4.654 4.510 4.335 5.526 4.818 5.763 3.733Kodak 18 768x512 5.398 5.906 5.276 5.777 5.220 6.762 4.583Kodak 19 768x512 4.565 5.018 4.656 5.104 4.845 5.987 3.988Kodak 20 768x512 3.085 3.201 3.144 3.326 3.053 3.690 2.912Kodak 21 768x512 4.509 5.231 4.422 4.916 4.544 5.563 4.012Kodak 22 768x512 5.043 5.242 4.990 5.708 5.119 5.969 4.095Kodak 23 768x512 2.926 3.489 3.091 3.252 2.890 3.297 2.448Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on July 27, 2009 at 21:53 from IEEE Xplore.  Restrictions apply. 

An adaptive palette reordering method for compressing color-indexed image

Abstract

Similar works

Full text

Available Versions

PolyU Institutional Repository