Digital Object Identifier 10.1109/LSP.2010.2040925We recognize that the key challenge in image
compression is to efficiently represent and encode high-frequency image structure components, such as edges, patterns, and textures. In this work, we develop an efficient lossless image compression scheme called super-spatial structure prediction. This super-spatial prediction is motivated by motion prediction in video coding, attempting to find an optimal prediction of structure components within previously encoded image regions. We find that this super-spatial prediction is very efficient for image regions with significant structure components. Our extensive experimental results demonstrate that the proposed scheme is very competitive and even outperforms the state-of-the-art lossless image compression methods

He, Zhihai, 1973-

Zhao, Xiwen Owen

IEEE Signal Processing Letters

University of Missouri: MOspace

IEEE SIGNAL PROCESSING LETTERS, VOL. 17, NO. 4, APRIL 2010 383Lossless Image Compression UsingSuper-Spatial Structure PredictionXiwen OwenZhao, Student Member, IEEE, and Zhihai HenryHe, Senior Member, IEEEAbstract—We recognize that the key challenge in imagecompression is to efficiently represent and encode high-frequencyimage structure components, such as edges, patterns, and textures.In this work, we develop an efficient lossless image compressionscheme called super-spatial structure prediction. This super-spatialprediction is motivated by motion prediction in video coding,attempting to find an optimal prediction of structure compo-nents within previously encoded image regions. We find that thissuper-spatial prediction is very efficient for image regions with sig-nificant structure components. Our extensive experimental resultsdemonstrate that the proposed scheme is very competitive andeven outperforms the state-of-the-art lossless image compressionmethods.Index Terms— Context-based adaptive lossless image coding(CALIC), lossless image compression, structure components,super-spatial structure prediction.I. INTRODUCTIONS PATIAL image prediction has been a key component in ef-ficient lossless image compression [1], [2]. Existing loss-less image compression schemes attempt to predict image datausing their spatial neighborhood. We observe that this will limitthe image compression efficiency. A natural image often con-tains a large number of structure components, such as edges,contours, and textures. These structure components may repeatthemselves at various locations and scales. Therefore, there isa need to develop a more efficient image prediction scheme toexploit this type of image correlation.The idea of improving image prediction and coding efficiencyby relaxing the neighborhood constraint can be traced back tosequential data compression [3], [4] and vector quantizationfor image compression [5]. In sequential data compression, asubstring of text is represented by a displacement/length ref-erence to a substring previously seen in the text. Storer ex-tended the sequential data compression to lossless image com-pression [6]. However, the algorithm is not competitive with thestate-of-the-art such as context-based adaptive lossless imagecoding (CALIC) [1] in terms of coding efficiency. During vectorquantization (VQ) for lossless image compression, the inputimage is processed as vectors of image pixels. The encoder takesManuscript received November 11, 2009; revised January 11, 2010. First pub-lished January 22, 2010; current version published February 24, 2010. The as-sociate editor coordinating the review of this manuscript and approving it forpublication was Prof. Lisimachos Paul Kondi.The authors are with Department of Electrical and Computer Engineering,University of Missouri, Columbia, MO 65203 USA (e-mail: xzc33@mail.mis-souri.edu; HeZhi@missouri.edu).Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/LSP.2010.2040925in a vector and finds the best match from its stored codebook.The address of the best match, the residual between the originalvector and its best match are then transmitted to the decoder.The decoder uses the address to access an identical codebook,and obtains the reconstructed vector. Recently, researchers haveextended the VQ method to visual pattern image coding (VPIC)[7] and visual pattern vector quantization (VPVQ) [8]. The en-coding performance of VQ-based methods largely depends onthe codebook design. To our best knowledge, these methods stillsuffer from lower coding efficiency, when compared with thestate-of-the-art image coding schemes.In the intra prediction scheme proposed by Nokia [9], thereare ten possible prediction methods: DC prediction, directionalextrapolations, and block matching. DC and directional predic-tion methods are very similar with those of H.264 intra predic-tion [10]. The block matching tries to find the best match of thecurrent block by searching within a certain range of its neigh-boring blocks. As mentioned earlier, this neighborhood con-straint will limit the image compression efficiency since imagestructure components may repeat themselves at various loca-tions.In fractal image compression [11], the self-similarity be-tween different parts of an image is used for image compressionbased on contractive mapping fixed point theorem. However,the fractal image compression focuses on contractive transformdesign, which makes it usually not suitable for lossless imagecompression. Moreover, it is extremely computationally ex-pensive due to the search of optimum transformations. Evenwith high complexity, most fractal-based schemes are notcompetitive with the current state of the art [12].In this work, we develop an efficient image compressionscheme based on super-spatial prediction of structure units.This so-called super-spatial structure prediction breaks theneighborhood constraint, attempting to find an optimal predic-tion of structure components within the previously encodedimage regions. It borrows the idea of motion prediction fromvideo coding, which predicts a block in the current frame usingits previous encoded frames. In order to “enjoy the best of bothworlds”, we also propose a classification scheme to partitionan image into two types of regions: structure regions (SRs) andnonstructure regions (NSRs). Structure regions are encodedwith super-spatial prediction while NSRs can be efficientlyencoded with conventional image compression methods, suchas CALIC. It is also important to point out that no codebookis required in this compression scheme, since the best matchesof structure components are simply searched within encodedimage regions. Our extensive experimental results demonstratethat the proposed scheme is very competitive and even outper-forms the state-of-the-art lossless image compression methods.1070-9908/$26.00 © 2010 IEEE384 IEEE SIGNAL PROCESSING LETTERS, VOL. 17, NO. 4, APRIL 2010Fig. 1. (a) Barbara image. (b) Four image blocks extracted from Barbara.Fig. 2. (a) Super-spatial prediction. (b) Motion prediction in video coding.II. SUPER-SPATIAL STRUCTURE PREDICTIONFOR EFFICIENT IMAGE COMPRESSIONIn this section, we explain the basic idea of super-spatial pre-diction and how it can be used for efficient image compression.We observe that a real world scene often consists of variousphysical objects, such as buildings, trees, grassland, etc. Eachphysical object is constructed from a large number of struc-ture components based upon some predetermined object char-acteristics. These structure components may repeat themselvesat various locations and scales. For example, Fig. 1(a) showsthe image Barbara and Fig. 1(b) shows four patches (32 32blocks) extracted from different locations of the image. It can beseen that they share very similar structure characteristics. There-fore, it is important to exploit this type of data similarity andredundancy for efficient image coding.The proposed super-spatial prediction borrows the idea ofmotion prediction from video coding, as illustrated in Fig. 2. Inmotion prediction, we search an area in the reference frame tofind the best match of the current block, based on some distor-tion metric. The chosen reference block becomes the predictorof the current block. The prediction residual and the motionvector are then encoded and sent to the decoder. In super-spatialprediction, we search within the previously encoded image re-gion to find the prediction of an image block. In order to findthe optimal prediction, at this moment, we apply brute-forcesearch. The reference block that results in the minimum blockdifference is selected as the optimal prediction. For simplicity,we use the sum of absolute difference (SAD) to measure theblock difference. Besides this direct block difference, we canalso introduce additional H.264-like prediction modes, such ashorizontal, vertical, and diagonal prediction [10], as illustratedin Fig. 3. Here, block B is the current block to be encoded andblock A is the reference block from the previous reconstructedFig. 3. Additional prediction modes.image region. The best prediction mode will be encoded andsent to the decoder.As in video coding, we need to encode the position informa-tion of the best matching reference block. To this end, we simplyencode the horizontal and vertical offsets, , between thecoordinates of the current block and the reference block usingcontext-adaptive arithmetic encoder.We observe that the size of the prediction unit is an importantparameter in the super-spatial prediction. When the unit size issmall, the amount of prediction and coding overhead will be-come very large. However, if we use a larger prediction unit,the overall prediction efficiency will decrease. In this work, weattempt to find a good tradeoff between these two and propose toperform spatial image prediction on block basis. For example,in our experiments, we set the block size to be 4 4.We can see that, when compared to VQ-based image en-coders, the proposed super-spatial prediction scheme hasthe flexibility to incorporate multiple H.264-style predictionmodes. When compared to other neighborhood-based predic-tion methods, such as gradient-adjusted prediction (GAP) [1]and H.264 Intra prediction, it allows the block to find the bestmatch from the whole image which will significantly reducesthe prediction residual.III. IMAGE BLOCK CLASSIFICATIONFrom the experimental results in Section V, we will see thatsuper-spatial prediction works very efficiently for image regionswith a significant amount of structure components. However,due to its large overhead and high computational complexity,its efficiency will degrade in nonstructure or smooth image re-gions. Therefore, we propose a block-based image classificationscheme. More specifically, we partition the image into blocks(e.g. 4 4 blocks). We then classify these blocks into twocategories: structure and nonstructure blocks. Structure blocksare encoded with super-spatial prediction. Nonstructure blocksare encoded with conventional lossless image compressionmethods, such as CALIC. CALIC is a spatial prediction basedscheme, in which GAP is used for adaptive image prediction[1]. We propose to explore two classification methods. In thefirst method (denoted by Method_A), we compare the GAPprediction against the super-spatial prediction. Our basic ideais that, if a block can be predicted more efficiently by GAPthan super-spatial prediction, we classify it into NSRs. Forsimplicity, we use SAD to measure the prediction performance.Otherwise, we classify it into structure regions. In the secondmethod (denoted by Method_B), we simply perform GAPprediction on the original image and compute the predictionerror for each block. If the prediction error is larger than aZHAO AND HE: LOSSLESS IMAGE COMPRESSION USING SUPER-SPATIAL STRUCTURE PREDICTION 385Fig. 4. (a) Barbara image. (b) Classification result using Method_A.Fig. 5. (a) Original Barbara image. (b) Nonstructure regions. (c) Structure re-gions.Fig. 6. Nine test images from USC and Kodak image databases.given threshold, then it is considered as a structure block. Oth-erwise, it is classified as a nonstructure block. We can see thatMethod_A has a much higher computational complexity thanMethod_B since it needs to perform super-spatial prediction foreach block. Fig. 4 shows a classification result for the Barbaraimage using Method_A. The white pixels in Fig. 4(b) indicatestructure blocks.IV. IMAGE CODING BASED ON SUPER-SPATIALSTRUCTURE PREDICTIONBased on the super-spatial prediction and image content sep-aration proposed in previous sections, we develop a losslessimage coding system. The proposed image coding system hasthe following major steps. First, using the method described inSection III, we classify the image into NSRs and structure re-gions as shown in Fig. 5(b) and (c), respectively. The classifica-tion map is encoded with arithmetic encoder. Second, based onthe classification map, our encoder switches between super-spa-tial prediction scheme to encode structure regions and CALICscheme to encode NSRs.We observe that the super-spatial prediction has relativelyhigh computational complexity because it needs to find the bestmatch of the current block from previous reconstructed imageTABLE IPREDICTION PERFORMANCE COMPARISON ON THE STRUCTURE REGIONSregions. Using the Method_B classification, we can classify theimage into structure and NSRs and then apply the super-spatialprediction just within the structure regions since its predictiongain in the nonstructure smooth regions will be very limited.This will significantly reduce overall computational complexity.V. EXPERIMENTAL RESULTSWe have implemented the proposed super-spatial predic-tion scheme in CALIC [1], a very efficient lossless imagecompression scheme which outperforms other state-of-the-artcoding methods, such as JPEG-LS and LOCO-I. In this work,we choose a block size of 4 4. The output bit stream ofthe proposed encoder consists of bits for the following majorsyntax components: image classification map, bits for NSRs,bits for prediction residual of structure blocks, addresses ofreference blocks, and prediction mode.Fig. 6 shows the test images. We first evaluate the predictionefficiency of the proposed super-spatial prediction scheme. Weuse Method_A to classify the image blocks. We then apply threeschemes to predict the image data within the structure regions:GAP from CALIC, H.264 Intra prediction, which is a very effi-cient spatial prediction scheme proposed in H.264 video coding,and the proposed super-spatial prediction. We measure the SADof the prediction residual. The results are summarized in Table I.Our super-spatial prediction scheme is able to significantly re-duce the prediction error. Compared with H.264 Intra predic-tion, it is able to reduce the SAD by up to 79% within thesestructure regions.In Table II, we compare the coding bit rate of the proposedlossless image coding method based on super-spatial predictionwith CALIC [1], one of the best encoders for lossless imagecompression. We can see that the proposed scheme outperformsCALIC and save the bit rate by up to 13%, especially for imageswith significant high-frequency components. Table III showsthe percentages of bits used by three major syntax components:SRs, NSRs, and overhead information (including classifi-cation map, reference block address, and prediction mode).In Table IV, we evaluate two image classification methods,Method_A and Method_B, as discussed in Section III. Wecan see that, the Method_B, although has low computationalcomplexity, its performance loss is very small, when comparedto Method_A. In Table V, we evaluate two super-spatial predic-tion methods: 1) prediction of the current block from previousreconstructed image regions and 2) prediction from previousreconstructed structure image regions. We can see that limitingthe prediction reference to structure regions only increases386 IEEE SIGNAL PROCESSING LETTERS, VOL. 17, NO. 4, APRIL 2010TABLE IICOMPRESSION PERFORMANCE COMPARISON WITH CALICTABLE IIIPERCENTAGES OF BITS OF MAJOR SYNTAX COMPONENTSTABLE IVCOMPARISON BETWEEN METHOD_A AND METHOD_BIMAGE CLASSIFICATION METHODSTABLE VIMPACT OF SEARCH RANGE OF SUPER-SPATIAL PREDICTIONthe overall coding bit rate by less than 1%. This implies moststructure blocks can find its best match in the structure regions.VI. CONCLUSIONIn this work, we have developed a simple yet efficient imageprediction scheme, called super-spatial prediction. It is moti-vated by motion prediction in video coding, attempting to findan optimal prediction of a structure components within previ-ously encoded image regions. When compared to VQ-basedimage encoders, it has the flexibility to incorporate multipleH.264-style prediction modes. When compared to other neigh-borhood-based prediction methods, such as GAP and H.264Intra prediction, it allows the block to find the best match fromthe whole image which significantly reduces the predictionresidual by up to 79%. We classified an image into structureregions and NSRs. The structure regions are encoded withsuper-spatial prediction while the NSRs are encoded withexisting image compression schemes, such as CALIC. Ourextensive experimental results demonstrated that the proposedscheme is very efficient in lossless image compression, espe-cially for images with significant structure components. In ourfuture work, we shall develop fast and efficient algorithms tofurther reduce the complexity of super-spatial prediction. Wealso notice that when the encoder switches between structureand NSRs, the prediction context is broken and it will degradethe overall coding performance. In our future work, we shallinvestigate more efficient schemes for context switching.ACKNOWLEDGMENTThe authors would like to thank X. Wu for generously pro-viding the source codes of CALIC.REFERENCES[1] X. Wu and N. Memon, “Context-based, adaptive, lossless imagecoding,” IEEE Trans. Commun., vol. 45, no. 4, pp. 437–444, Apr.1997.[2] M. J. Weinberger, G. Seroussi, and G. Sapiro, “The LOCO-I losslessimage compression algorithm: Principles and standardization intoJPEG-LS,” IEEE Trans. Image Process., vol. 9, no. 8, pp. 1309–1324,Aug. 2000.[3] J. Ziv and A. Lempel, “A universal algorithm for sequential data com-pression,” IEEE Trans. Inform. Theory, vol. 23, no. 3, pp. 337–343,May 1977.[4] J. Ziv and A. 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