The Embedded Morphological Dilation Coding (EMDC) algorithm, recently proposed by the author of this work, implements a direct coding of the wavelet coefficients significance map that is based on the action of a new kind of multiresolution binary (bit-plane) morphological operator. EMDC actually includes the most part of existing morphological wavelet codecs, it produces a fully progressive bitstream with low complexity and has demonstrated competitive coding performances. A peculiar feature of EMDC is the adaptive and the extended connectivity nature of the morphological analysis of the subband coefficients. In this paper we give a detailed description of this feature and quantify the related performance improvements. We conclude that the considered pattern analysis and coding technique allow an increased reduction of the data redundancy and fills the gap between existing morphological dilation techniques and state-of-the-art wavelet coders

A. SIGNORONI

LAZZARONI F

LEONARDI R

Lazzaroni, Fabio

Leonardi, Riccardo

Signoroni, Alberto

Archivio istituzionale della ricerca - Università di Brescia

Adaptive dilation analysis for wavelet coding with EMDC

LAZZARONI, Fabio

LEONARDI, Riccardo

SIGNORONI, Alberto

ADAPTIVE DILATION ANALYSIS FOR WAVELET CODING WITH EMDCF. Lazzaroni, R. Leonardi and A. Signoroni*Signals and Communications Lab. - DEA - University of Brescia, Italyvia Branze, 38 - I25123 Brescia, ItalyTel.* +39 030 3715432; Fax.+39 030 380014; *E-mail: signoron@ing.unibs.itABSTRACTThe Embedded Morphological Dilation Coding (EMDC) al-gorithm, recently proposed by the author of this work, im-plements a direct coding of the wavelet coefficients signi-ficance map that is based on the action of a new kind ofmultiresolution binary (bit-plane) morphological operator.EMDC actually includes the most part of existing morpho-logical wavelet codecs, it produces a fully progressive bit-stream with low complexity and has demonstrated compet-itive coding performances. A peculiar feature of EMDCis the adaptive and the extended connectivity nature of themorphological analysis of the subband coefficients. In thispaper we give a detailed description of this feature and quan-tify the related performance improvements. We concludethat the considered pattern analysis and coding technique al-low an increased reduction of the data redundancy and fillsthe gap between existing morphological dilation techniquesand state-of-the-art wavelet coders.1. THE MORPHOLOGICAL APPROACH TOWAVELET CODINGThe structural and statistical properties of the wavelet trans-form coefficients has been increasingly recognized and ex-ploited in various visual data processing applications.Such properties play a key role both in the quantizationand in the entropy coding stages of current wavelet cod-ing techniques. In particular the insignificant coefficientspredictability, in terms of subband zerotree or zeroblocks,is the common denominator of a family of techniques (e.g.SPIHT[1], EZBC[2]) which present state-of-the-art Rate-Distortion (R–D) coding performance. However zerotreebased techniques only indirectly exploit a salient propertyof wavelet-transformed natural images: the clustering trendof most significant coefficients [3]. A possible approach todirectly exploit this behavior has been introduced with themorphological conditioned dilation coding [3, 4, 5], wherethe significant coefficients (i.e. set to 1 in the significance-map) already detected are used as a basis for the searchof new significant ones in a progressive bit-plane quanti-zation framework. This approach is justified by observ-ing that clusters tend to grow both in spatial and in fre-quency domain when crossing successive bit-planes. Thework of Servetto et al. [3] first justifies the morphologi-cal approach to better represent significance maps, but useit in an intra-band mode only, letting the entropy coder ex-ploit some inter-band statistical dependencies. Chai et al.[4] define a bit-saving inter-band linking mechanism amongsubband clusters. However, this codec architecture does notproduce an embedded bit-stream, since good R–D perfor-mance are also due to a pre-processing stage which elim-inates all isolated significant coefficients, whose positionsare too expensive to code; moreover, in [4], the assessmentaccuracy of cluster boundaries is conceived as a static trade-off between structuring element extent and related bit cost.The extent of the structuring elements is also an issue re-lated to the performance of the embedded approaches pro-posed by Zhong et al. in [5, 6, 7].In [8] we presented a coding technique called EmbeddedMorphological Dilation Coding for 2D and 3D data that werefined in [9]. The main innovations introduced in EMDCwith respect to the previous morphological approaches arethe subdivision of a single morphological dilation in differ-ent layers ordered according to their expected R–D perfor-mance, and an original method for the analysis of the clusterboundaries by performing an adaptive search around eachfound cluster. The first aspect is representative of the ac-tion and interaction of the morphological dilation within thecoding process. The second aspect is better analyzed in thiswork and represents an example of the benefits that the di-rect access to the significant coefficient patterns could givein terms of coding performance. EMDC goes beyond thesimple duality with respect to the insignificant coefficientsprediction; in fact, it introduces an additive pattern analysiswhich allows to save a portion of bit in the coded descrip-tion.The adaptive analysis of cluster boundaries is described indetail in Sec.3 while the related performance improvementis quantified in Sec.4. In the next section the ideas and thestructure of the EMDC algorithm are briefly recalled. Algo-rithmic details can be found in [9].2. EMDC: EMBEDDED MORPHOLOGICALDILATION CODINGAs in the popular zerotree coders, our progressive EMDCalgorithm is composed of two iterative stages. The firstone is the significant coefficient map description, which isprogressively coded by means of a combination of subbandscanning, bit-plane thresholding and binary morphologicaldilations based on predictive hypothesis. After each bit-plane scanning a refinement pass adds to the precision ofthe previously marked significant coefficients.The dilation operator is conceived to work in a subband im-age structure. It is structured in different layers because ofthe different predictive hypothesis to which each layer cor-responds. The layers of this “multiresolution morphologicaloperator” are the following:– layer (a): intra-band morphological dilation– layer (b): inter-band expansion– layer (c): adaptive boundary dilationThe layer (a) exploits the clustering trend of the waveletcoefficient, the layer (b) recognizes the morphological sim-ilarities among the different scales in the multiresolutionsubband domain and authorizes to establish a linking mech-anism among different scale clusters based on some parent-child relations. The layer (a) and (b) allow to explore thealready identified clusters. The layer (c) analyzes the co-efficients on the cluster boundaries and is detailed in thefollowing section. An additional layer (d) called explicitposition coding works as a “seed layer” in order to start thedilation of unexplored significant clusters and also serves tolocate isolated significant coefficients.In this framework the cluster dilation is performed by aunique operator: this operator works during the coding pro-cessing, and it is activated by means of different codinglayers in order to guarantee an R–D optimized progressivecoded bit-stream. In previous works, the different codingsteps correspond to separate pattern dilation or linking mech-anisms. For example the algorithm described in [5] consid-ers 3 steps which correspond to our layers (a), (b) and (d).In EMDC, the layers have been ordered by decreasing ex-pected frequencies of identification of significant coefficients,corresponding to decreasing expected R–D performance [9].In addition, the four layers do not act in a strictly sequen-tial order, but layer (a), which appears the most effective,is started each time a new significant coefficient is found.The combination of bit-plane quantization with such a prior-itized multiresolution dilation, guarantees a good R–D em-bedding.The so produced progressive bit-stream is entropy coded us-ing an in-line context-based adaptive arithmetic coder. Theprobability tables are associated with the quantized bit-streamstructure and with causal contexts based on parent-childrenneighborhoods. The entropy coding is performed also onrefinement bits. Further details can be found in [9, 10].3. ADAPTIVE AND EXTENDED CONNECTIVITYPATTERN ANALYSISThe EMDC dilation strategy is able to detect multiresolu-tion clusters and to work on an extended connectivity basisin order to go beyond false cluster boundaries. This mech-anism is implemented through the iterative dilation of thecluster boundaries (insignificant-marked coefficients whichencircle a significant cluster) corresponding to the layer (c).Subband clusters presents irregular boundaries because ofthe complex nature of images and the oscillating responseof wavelet filters. In fact, on the boundary of connectedclusters, there are typically a relatively few scattered signif-icant coefficients, but it is difficult to forecast the dimensionof the area interested to this phenomenon. Such coefficientsin the vicinity of a cluster are here considered connected tothe cluster itself, like the rocks and stacks which could scat-ter an island or an archipelago. Therefore, the extent of thesearching area around a cluster should be reasonably limitedbut may not be fixed a-priori.The Fig.1 shows the way the algorithm searches aroundthe clusters of significant coefficients at increasing distanceas long as new significant coefficients are found: the widthof the scanned area is adaptively selected on the basis ofthe occurrence of newly significant coefficients. In EMDCthe searching by boundary dilation of scattered clusters isrepeated until two successive scans do not lead to new sig-nificant coefficients, this can be justified by considering thenature of the analysis filter responses, while experimentallycorresponds to the best trade-off between the ability to cap-ture significant coefficient and the related description cost.The gray line of Fig.1(a) is the boundary of a completelyexplored cluster, a first additional dilation (Fig.1(b)) allowsthe detection of the small connected components 1 and 2.The second dilation (c) doesn’t find any new significant co-efficients, thus it represents the new cluster boundary. Withanother additional dilation (d) the components 3 are foundand with (e) the component 4. Finally, the two additional di-lations which follow do not detect new components, thus thegray-white interface in Fig.1(f) is the final extended clusterboundary; components 5 and 6 are considered too much farfrom the “coast”, and will be coded as connected to anotherarchipelago or as isolated clusters. We observe that the useof a minimal 3x3 structuring element for cluster growingcombined with the “adaptive extended connectivity” boun-dary detection, actually entails an adaptive morphologicalanalysis, and allows to overcome the static trade-off, men-tioned in Sec.1, which limits others morphological dilationFig. 1. Adaptive boundary analysiscoding approaches.In the next section we evaluate the validity of our sourcemodel, based on the definition of the above multiresolutionmorphological operator. In particular we quantify the ad-ditional dilation layer (c) contribution in terms of codingperformance improvement.4. PERFORMANCE ANALYSISQuantitative coding performance results are here presentedfor the Lena, Barbara and Goldhill test images. The wavelettransform is implemented on a five-level decomposition withthe popular 9/7-tap filters. To highlight the ovarall good per-formance of EMDC, PSNR coding results has been com-pared with respect to the progressive SPIHT [1] algorithm(the original software available on the SPIHT web site1 hasbeen used). As shown in Fig.2 the EMDC algorithm reachesfor all bit-rates the best PSNR performance for the consid-1http://www.cipr.rpi.edu/research/SPIHT/ered images.In order to quantify the contribution of the adaptive boun-dary dilation to the above performance, Fig.2 shows the R–D curves obtained by the implementation of EMDC withoutthe layer (c). A coding gain of about 0.15dB at 0.5bpp and0.3dB at 1bpp due to the adaptive boundary dilation layerdemonstrates that the adopted solution is effective.5. CONCLUSIONSThis work dealt with the adaptive analysis of the boundaryof significant coefficient clusters, in order to improve thewavelet subband description in a more synthetic significance-map coding. Such morphological analysis has been imple-mented as a layer of EMDC, a recently proposed codingtechnique, and the actual contribution of this layer with re-spect to the overall EMDC performance has been quanti-fied here. The experimental results actually show an over-all R–D performance improvement due to the cluster boun-dary analysis. We conclude that thanks to its particularmorphological analysis, EMDC goes beyond a mere dualitywith respect zerotree based techniques, in addition, the ad-ditional boundary dialtion is a simple but effective analysisstep in terms of significance-map description. For these rea-sons, this kind of significance-map coding approach seemsto be an interesting field for further investigations: more ad-vanced morphological subband analyses could be designedto capture other coefficient features and to be embedded inthe coding algorithm causing a bit-saving description of thesignificance-map. Moreover, investigations should be di-rected not only towards objective quality improvements, butalso by considering perceptual quality criteria.6. REFERENCES[1] A. Said and W. A. Pearlman, “A new fast and efficientimage codec based on set partitioning in hierarchi-cal trees,” IEEE Trans. Circuits Syst. Video Technol.,vol. 6, pp. 243–250, June 1996.[2] S.-T. Hsiang and J. W. Woods, “Embedded image cod-ing using zeroblocks of subband/wavelet coefficientsand context modeling,” in Proc. MPEG-4 Workshopand Exhibition at ISCAS 2000, Geneva, Switzerland,May 2000.[3] S. D. Servetto, K. Ramchandran, and M. T. Orchard,“Image coding based on a morphological representa-tion of wavelet data,” IEEE Trans. Image Processing,vol. 8, pp. 1161–1174, Sept. 1999.[4] B. B. Chai, J. Vass, and X. Zhuang, “Significance-linked connected component analysis for wavelet im-age coding,” IEEE Trans. Image Processing, vol. 8,pp. 774–784, June 1999.[5] J. M. Zhong, C. H. Leung, and Y. Y. Tang, “Waveletimage coding based on significance extraction usingmorphological operations,” IEE Proc.-Vis. Image Sig-nal Process., vol. 146, no. 4, pp. 206–210, Aug. 1999.[6] ——, “Image compression based on energy clusteringand zero-quadtree representation,” IEE Proc.-Vis. Im-age Signal Process., vol. 147, no. 6, pp. 564–570, Dec.2000.[7] ——, “An improved embedded zerotree wavelet im-age coding method based on coefficient partitioningusing morphological operation,” Int. Journal. Patt.Recog. Artif. Intell., vol. 14, no. 6, pp. 795–807, 2000.[8] F. Lazzaroni, A. Signoroni, and R. Leonardi, “Embed-ded morphological dilation coding for 2d and 3d im-ages,” in VCIP 2002, vol. SPIE(4671), San Jose´, Cali-fornia, Jan. 2002, pp. 923–934.[9] F. Lazzaroni, R. Leonardi, and A. Signoroni, “High-performance embedded morphological wavelet cod-ing,” in IWDC 2002. Capri, Italy: CNIT, Sept. 2002,pp. 319–326.[10] A. Signoroni, M. Arrigoni, F. Lazzaroni, andR. Leonardi, “Improving SPIHT-based compressionof volumetric medical data,” in PCS 2001, Seoul, Ko-rea, Apr. 2001, pp. 187–190.0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 13435363738394041Bit rate (bpp)PSNR (dB)EMDC               EMDC without a.b.d.SPIHT              –a–0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 126283032343638Bit rate (bpp)PSNR (dB)EMDC               EMDC without a.b.d.SPIHT              –b–0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 13031323334353637Bit rate (bpp)PSNR (dB)EMDC               EMDC without a.b.d.SPIHT              –c–Fig. 2. PSNR curves for EMDC, EMDC without the addi-tional boundary dilation (layer (c)), and SPIHT[1] on three512x512 test images: -a- Lena, -b- Barbara and -c- Goldhill.

Adaptive dilation analysis for wavelet coding with EMDC

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Archivio istituzionale della ricerca - Università di Brescia

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