Difference expansion and prediction for high bit-rate reversible data hiding

Transcription

1 Difference expansion and prediction for high bit-rate reversible data hiding Giulia Boato Marco Carli Federica Battisti Marco Azzoni Karen Egiazarian

2 Journal of Electronic Imaging 1(3), (Jul Sep 01) Difference expansion and prediction for high bit-rate reversible data hiding Giulia Boato University of Trento Department of Information Engineering and Computer Science Trento 3811, Italy Marco Carli Federica Battisti University of Roma TRE Department of Applied Electronics Roma 00146, Italy Marco Azzoni University of Trento Department of Information Engineering and Computer Science Trento 3811, Italy Karen Egiazarian Tampere University of Technology Department of Signal Processing Tampere 3370, Finland Abstract. Reversible data hiding deals with the insertion of auxiliary information into a host data without causing any permanent degradation to the original signal. In this contribution a high capacity reversible data hiding scheme, based on the classical difference expansion insertion algorithm, is presented. The method exploits a prediction stage, followed by prediction errors modification, both in the spatial domain and in the S-transform domain. Such two step embedding allows us to achieve high embedding capacity while preserving a high image quality, as demonstrated in the experimental results. 01 SPIE and IS&T. [DOI: /1.JEI ] 1 Introduction Digital watermarking schemes are usually adopted for protecting rights of both digital data and their corresponding owners. 1, Such methods invisibly embed a watermark into the data to be protected, thus allowing copyright protection and illegal copies or illegal distributors identification via the embedded information recovery. In particular, classical watermarking applications consist of copy control, broadcast monitoring, fingerprinting, authentication, copyright protection, and access control (see for instance Refs. 3 and 4). This technology can be used also for different purposes, such as multimedia indexing, enrichment, quality assessment, error concealment, and others. In general, the imposed Paper 1196 received Nov. 3, 011; revised manuscript received May 7, 01; accepted for publication Jul. 9, 01; published online Aug. 14, /01/$ SPIE and IS&T requirements are 1. robustness: the hidden data should be detectable after classical signal processing,. imperceptibility: the watermarked signal has to be perceptually similar to the original one, and 3. capacity: the number of bits that can be embedded should be as high as possible. In particular application scenarios (e.g., medical or military) another crucial constraint has to be considered 4. integrity of the recovered signal: the watermarking process has to be invertible, allowing the reconstruction of the original data after the watermark extraction. This last requirement is achieved by the so-called reversible watermarking techniques. Many reversible watermarking algorithms have been proposed in the literature. The main difference among existing schemes lies in the particular method adopted for achieving reversibility. A first class of techniques exploits data compression, which was introduced in Ref. 5 by Fridrich et al. by embedding with the watermark also the lossless compressed original data as well as the corresponding location map. Celik et al. follow this idea in Ref. 6 by presenting a generalized-lsb data hiding method. Xuan et al. 7 propose an algorithm based on integer wavelet transform. Another class of methods is based on histogram shifting. The basic idea to embed the watermark through histogram modification was presented by Ni et al. 8 where the pixel values in the range between peak and zero points are modified. This technique is extended in, Ref. 9, where Hwang et al. propose to use two zero points and one peak point of the histogram as triplets to insert the data, and more Journal of Electronic Imaging Jul Sep 01/Vol. 1(3)

3 recently by Tai et al. 10 Bo et al. 11 and Yoo et al. 1 to extend histogram shifting using small blocks of the image to embed data. A third class of algorithms uses difference expansion to achieve reversibility. The first proposal is due to Tian 13 and embeds the watermark by modifying the difference between a pair of pixels, thus exploiting the redundancy among neighboring pixel values. Following Tian s intuition, many extensions were proposed, which extend this approach to triplets, 14 quads, 15 three-pixel blocks, 16 or n-pixel blocks, 17,18 therefore allowing a reduction of the location map and an increase in both efficiency and capacity. Further modifications are presented in Ref. 19 by Thodi et al. 0 by Kamstra et al. 1 by Hu et al. while novel techniques based on other integer transforms are proposed by Coltuc et al. and by Chen et al. 3 Finally, a new idea based on pixel prediction is elaborated in a set of recent contributions. The median edge detector predictor is used by Thodi et al. 4 by Hong et al. 5 and by Yang et al. 6 while the gradient adjusted prediction is exploited by Fallahpour et al. 7 Kuribayashi et al. 8 apply difference expansion and prediction, while Tsai et al. 9 and Pan et al. 30 apply predictive coding and histogram shifting in the specific domain of medical imaging. In Ref. 31, prediction and histogram shifting are dynamically applied depending on human visual system characteristic while in Refs. 3 to 34, interpolation is used as prediction to calculate the error band. Xuan et al. 35 and Kuo et al. 36 apply error control and histogram shifting to embed data keeping good stego-image quality. Tseng et al. 37 study various predictors, while Hu et al. 38 improve the location map compressibility, Sachnev et al. 39 reduce its size, and Fujiyoshi et al. 40 avoid any image-dependent parameter or location map. In Ref. 41, Yang et al. propose a data hiding technique in both the spatial and frequency domain which seems to be robust against JPEG and JPEG000. In this context, the authors proposed in Ref. 4 to exploit both local dependency and non-local similarity for prediction, by employing block-matching techniques, while in Ref. 43 histogram shifting was combined with a particular prediction exploiting directional differences. In this work a double embedding scheme is proposed, where a prediction stage, followed by prediction errors modification, is applied both 1. in the spatial domain and in. the S-transform domain. The adoption of this multilayer approach allow us to achieve very high capacity while preserving good image quality. A preliminary study on multiresolution approaches was presented in Ref. 44 Recently, high capacity was achieved by in Refs. 45 and 46, which we compare the performances with in the experimental section. The rest of the work is organized as follows: details on the proposed algorithm are given in Sec., while the experimental results are reported in Sec. 4, and finally in Sec. 5 some conclusions are drawn. Embedding As depicted in Fig. 1 the proposed scheme works as follows: the spatial prediction is first applied to the original image and a first embedding is performed exploiting the obtained prediction error. Then, an integer transform is applied to the resulting image, and a novel prediction scheme is applied to the low-and high-frequency subbands. Thus, a second embedding is performed on the prediction errors. Let us detail all steps of the scheme: 1. Prediction is applied to the original image X ¼fx i;j gi, j ¼ 1; :::;n in the spatial domain, thus obtaining ^X as described in Sec..1 and correspondingly the spatial prediction error E sp ¼ X ^X: (1). Embedding via difference expansion into prediction error E sp as detailed in Sec..4: Definition of positions used for embedding and of the corresponding location map (required at the detector side to perform watermark extraction and original image reconstruction). Watermark and overhead information embedding thus defining a new watermarked prediction error E 0 sp. The watermarked image X 0 is defined as follows X 0 ¼ ^X þ E 0 sp: () 3. S-transform is applied to the watermarked image X 0, thus obtaining low-and high-frequency bands L and H, respectively (see details in Sec..). Starting from L, prediction is applied to get ^H and the transform prediction error is calculated as follows E tr ¼ H ^H; (3) as described in Sec Embedding via difference expansion into prediction error E tr defining a new watermarked prediction error Etr, 0 as in step. The watermarked highfrequency band H 0 is defined as follows Fig. 1 Proposed scheme for watermark embedding. Journal of Electronic Imaging Jul Sep 01/Vol. 1(3)

4 H 0 ¼ ^H þ E 0 tr: (4) 5. Finally, the inverse S-transform is applied to L and H 0 to obtain the watermarked image X 0. Let us notice that the watermark and the required overhead information are embedded into two steps ( and 4) and will be denoted as W ¼ðW sp ;W tr Þ..1 Prediction in Spatial Domain The gradient adjust predictor (GAP) 7 considers seven neighbors of the to-be-predicted pixel ^x i;j as follows: d v ¼jx i 1;j x i 1;j 1 jþjx i;j 1 x i;j j þjx iþ1;j 1 x iþ1;j j d h ¼jx i 1;j x i ;j jþjx i;j 1 x i 1;j 1 jþjx i;j 1 x iþ1;j 1 j D ¼ d v d h 8 >< ^x i;j ¼ >: x i;j ¼ x i 1;j þ x i;j 1 if D < 80 x i;j 1 x i;j þx i;j 1 if 80 D < 3 3 x i;j þx i;j 1 4 if 3 D < 8 x i;j if 8 D < 8 3 x i;j þx i 1;j 4 if 8 D < 3 x i;j þx i 1;j if 3 D < 80 x i 1;j if D 80 þ x iþ1;j 1 þ x i 1;j 1 4 This defines ^X ¼f^x i;j gi, j ¼ 1; :::;nand the spatial prediction error E sp ¼ X ^X that will be used for watermark embedding via difference expansion.. S-Transform The S-transform 47 is an invertible time-frequency spectral localization technique often called also integer Haar wavelet transform. Let us consider the image X 0 of size n n. The low-frequency L and the high-frequency H sub-band decomposition of X can be computed as follows: x 0 iþ1;j þ x 0 iþ;j l iþ1;j ¼ : (5) h iþ1;j ¼ x 0 iþ1;j x 0 iþ;j ; (6) where i ¼ 0; :::; n 1, j ¼ 1; :::;nand L ¼fl iþ1;jg while H ¼fh iþ1;j g. The corresponding inverse transformation is given by xiþ1;j 0 ¼ l hiþ1;j þ 1 iþ1;j þ xiþ;j 0 ¼ x0 iþ1;j h iþ1;j: (7) Notice that in this case we are applying the S-transform in the vertical direction. Horizontal decomposition can be performed just by defining L ¼fl j;iþ1 g and H ¼fh j;iþ1 g..3 Prediction in Transform Domain To guarantee the reversibility of the watermarking method, the proposed prediction scheme aims at predicting highfrequency sub-band starting from the low frequency one in a way all required information will be available also at the detection side. The prediction scheme can be summarized as follows. Given the low frequency coefficients we define relative differences Δl iþ1;j ¼ l i;j l iþ1;j ; (8) where i ¼ 1; :::; n 1. Notice that differences can be calculated starting from the second row, thus we impose Δl 1;j ¼ 0. The predicted high-frequency sub-band ^H is estimated as following: ^h iþ1;j ¼ 1 4 l i;j þ 1 8 l iþ1;j 1 l iþ;j þ 1 8 l iþ3;j; (9) where i ¼ 1; :::; n 3 represent the range of coefficients used in the prediction. Notice that this prediction differs from the one presented in Ref. 44 since a new combination of weights is used exploring also second order differences. The prediction error is finally given by e iþ1;j ¼ h iþ1;j ^h iþ1;j þ 1 ; (10) where i ¼ 1; :::; n 3, j ¼ 1; :::;n. This defines the transform prediction error E tr ¼fe iþ1;j g that will be used for watermark embedding via difference expansion..4 Embedding Via Difference Expansion The main idea of difference expansion is to hide information into a set of values, in two slightly different ways according to their characteristics. Once E sp and E tr are defined, the watermark W ¼ðW sp ;W tr Þ insertion is performed by applying Tian s method 13 to E sp and E tr, thus defining the watermarked prediction error Esp 0 and Etr, 0 used in Eqs. () and (4), respectively. For simplicity and coherence with the original Tian s method we describe the process in the transform domain but the same procedure is applied in the spatial domain. In particular, following Eq. (4) Etr 0 is used to define the watermarked values of H 0 (similarly Esp 0 allows to define the watermarked values of X 0 ), which have to satisfy following rules in order to avoid overflow and underflow problems. Indeed, X, X 0, and X 00 values should be bounded in the range ½0; 55Š h 0 iþ1;j þ 1 0 l iþ1;j þ h 0 0 l iþ1;j iþ1;j Since both l and h 0 are integer values jh 0 iþ1;j j ð55 l iþ1;jþ ¼a; jh 0 iþ1;j j l iþ1;j þ 1 ¼ b: 55 55: (11) (1) Now we can define two different types of values in E tr (similarly in E sp ): Journal of Electronic Imaging Jul Sep 01/Vol. 1(3)

5 The error is expandable if for both the watermark entries w m ¼ 0 and w m ¼ 1 jhiþ1;j 0 j¼j^h iþ1;j þ eiþ1;j 0 j minða; bþ: (13) In this case we can perform the embedding of the bit w m of the watermark W by expanding the error and define the watermarked value as follows: e 0 iþ1;j ¼ e iþ1;j þ w m : (14) The error is changeable if for both the watermark entries w m ¼ 0 and w m ¼ 1 jhiþ1;j ^h 0 j¼ eiþ1;j iþ1;j þ þ w m minða; bþ: (15) In this case embedding is performed just by substituting the least significant bit (LSB) of e iþ1;j with the bit w m of the watermark W. Notice that an expandable value is also changeable, as depicted in Fig. (a). Therefore, it can be used in both ways. This property will be exploited in the following subsets definition. Indeed, before embedding error values are partitioned into four sets: E1 which contains all expandable differences with e iþ1;j ¼ 0 or e iþ1;j ¼ 1. E which contains all expandable differences that do not belong to E1 and are used as expandable. E3 which contains all expandable differences that do not belong to E1 and are used as changeable. C which contains all changeable differences that do not belong to E1 or E or E3. NC which contains all non-changeable differences. Embedding is now performed in E1 E and E3 C following the two different rules, expansion and LSB substitution, respectively..5 Overhead Information In order to design a reversible method some information must be sent to the detector: such extra information is composed by original LSB of every error value changed through LSB substitution, and the so-called location map that is used to identify the positions of the bits that have been modified and the particular embedding adopted. The location map is a binary matrix of same size of the original image with value 1 in the position corresponding to differences belonging to E1 E and with value 0 in the position belonging to E3 C NC [see Fig. (a)]. It is worth noticing that a changeable value remains changeable also after embedding, thus it is always distinguishable from a value in NC. This way, during the detection stage it is possible to distinguish places where a bit of mark was introduced, and where not [see Fig. (b)]. The location map is lossless compressed defining the overhead information LM which has to be sent to the detector together with the mark. The compression ratio depends on the applied technique and affects the capacity of the algorithm. For each value of e iþ1;j in E3 and C, LSB values have to be collected since bit insertion change them. Such values are stored into a bit-stream called LSB. Therefore, the complete stream W ¼fW sp ;W tr g which is embedded consists of LM LSB watermark for both W sp and W tr. Thus, the watermark payload size is defined depending on the size of E and on the compression rate of the location map. 3 Detection Let us now describe in detail all phases of the detection process, illustrated also in Fig. 3: 1. The S-transform is applied to the watermarked image X 00, resulting in L and H 0 decomposition.. Starting from L, prediction is applied thus recovering ^H. The modified prediction error is calculated as E 0 tr ¼ H 0 ^H: (16) Since the L sub-band coefficients used for predicting ^H have not been modified (bitwise equal), the predicted ^H is exactly the same as in the embedding phase. Thus, information extracted from Etr 0 is bitwise identical to the one inserted (thanks to the reversibility of the difference expansion method, see for instance Ref. 13). 3. Bit-stream W tr is extracted from Etr 0 from all changeable values. Now from the recovered LM it is possible to differentiate among differences used as expandable E1 E, changeable E3 C, and non-changeable NC. From LSB it is then possible to recover all original LSB values of changeable differences. Finally, the watermark can be extracted and all original values of E tr can be restored. The original highfrequency sub-band H can be recovered by calculating Fig. (a) Distinction between values used as expandable and non-expandable positions within the location map; and (b) distinction between changeable positions and non-changeable positions recognizable at the detector side without any side information. Journal of Electronic Imaging Jul Sep 01/Vol. 1(3)

6 Fig. 3 Proposed scheme for watermark extraction and original image recovery. H ¼ ^H þ E tr : (17) 4. The image X 0 can be restored by computing the inverse S-transform of L and H. 5. Starting from X 0, prediction is applied thus recovering ^X. The modified prediction error is calculated as E 0 sp ¼ X 0 ^X: (18) Sec..3. In Figs. 4 to 7 results are reported for six different well known spatial predictors: GAP, median edge detector (MED), DARK, PAETH, simple average (SA), and previous pixel (DIFF). In all cases (we report here results for four images) GAP gives the best results and this motivates our choice in the algorithm design. Results reported in Figs. 8 to 11 present the detailed performances achieved by the proposed method for four images Also in this case, prediction is defined in order to be reversible: starting from the same input, the predicted set of coefficients will be exactly the same, independently from coefficients modified by the watermak (inserted only into high frequencies), see for instance Ref Bit-stream W sp is extracted from E 0 sp as in step 3 and all original values of E sp can be restored. Finally, the original image X can be recovered by calculating X ¼ ^X þ E sp : (19) Since both extraction steps (3 and 5) are reversible, the whole process can be inverted and the original image bitwise perfectly recovered. 4 Experimental Results To evaluate the effectiveness of the proposed schemes several experimental tests have been performed. The achieved results are reported by considering both capacity (payload of the watermark inserted without considering the overhead information: location map bit-stream LM and LSB of differences used as changeable, as described in Sec..5), measured in bit per pixel (bpp) and quality of the watermarked image measured with different perceptual metrics: PSNR, PSNR-HVS, and PNSR-HVS-M. 48 All tests have been computed on a set of 3 images taken from the GrayScale Set image repository of the University of Waterloo ( and the Tampere Image Database 008 ( info/tid008.htm), considering the gray-scaled version of original images only. Although the reversibility of the exploited techniques is already proved in the literature (see for instance Ref. 7), first of all we have verified that both the original image and the embedded data can be perfectly recovered from the watermarked one, after the hidden information extraction procedure. As far as the spatial prediction is concerned, different types of prediction have been tested and combined with the prediction in the transform domain described in Fig. 4 Spatial predictors performances in terms of PSNR for the Lena image. Fig. 5 Spatial predictors performances in terms of PSNR for the Barbara image. Journal of Electronic Imaging Jul Sep 01/Vol. 1(3)

7 Fig. 6 Spatial predictors performances in terms of PSNR for the Boat image. Fig. 9 Performances of the proposed approach in terms of different perceptual metrics for the Barbara image. Fig. 7 Spatial predictors performances in terms of PSNR for the Goldhill image. Fig. 10 Performances of the proposed approach in terms of different perceptual metrics for the Boat image. Fig. 8 Performances of the proposed approach in terms of different perceptual metrics for the Lena image. Fig. 11 Performances of the proposed approach in terms of different perceptual metrics for the Goldhill image. Journal of Electronic Imaging Jul Sep 01/Vol. 1(3)

8 Table 1 Maximum capacity and corresponding quality of watermarked images for the whole dataset. Image Max payload (bpp) PSNR (db) PSNR-HVS-M (db) PSNR-HVS (db) Zelda Washsat Peppers Mandrill Lena Goldhill Frog France Boat Barb I I I I I I I I I I I I I I I I I I I I I I (due to lack of space) in terms of different quality metrics: PSNR, PSNR-HVS, and PNSR-HVS-M. This way, we do not only have the information about classical PSNR measure of quality but also about state-of-art perceptual quality metrics which allow to better understand the real user evaluation of distortion introduced with the watermark. It is worth noticing that the proposed method allows us to achieve high capacity by keeping the quality of the watermarked images pretty high. With respect to Ref. 45, we achieve better results: for example, for Lena 45 reports 1,70 bpp with 19,60 db of PSNR while we reach a lower maximum capacity (1,47 bpp) but with much higher quality (7,54 db); for Barbara for capacity 1 bpp. 45 gets a PSNR of 18,8 db while we have 6,37 db; for Boat 45 reports 1,56 bpp with 19,5 db while we reach a 1,46 bpp with 7,01 db. As far as Ref. 46 is concerned, the proposed technique achieves very similar results for high-capacity ranges (see for example Lena and Barbara images). Comparison with high-capacity techniques cannot be done in terms of perceptual quality metrics due to the fact that results are usually reported just in terms of PSNR. The maximum capacity achieved and the corresponding perceptual quality of the watermarked image in terms of the three metrics are shown in Table 1 for all 3 tested images. It is evident that the proposed technique allows us to embed a high number of bits for the watermark without impacting too much on the quality of the data. In particular, capacity higher that 1 bpp can be achieved for Mandrill whereas Refs. 45 and 46 present maximum capacity lower than 1 bpp. 5 Conclusions In this work a reversible data hiding method has been presented. It is based on the combination of prediction and difference expansion insertion algorithms and on the use of such combination both in the spatial and in the transform domain. The adoption of a multilayer technique results in high capacity and good image quality as demonstrated in the performed simulations. References 1. I. Cox et al., Digital Watermarking and Steganography, Morgan Kaufmann, Burlington, MA (007).. F. Perez-Gonzales and S. Voloshynovskiy, Fundamentals of Digital Image Watermarking, John Wiley & Sons Inc., Hoboken, NJ (009). 3. B. Furht and D. Kirovski, Multimedia Watermaking Techniques and Application, Taylor & Francis Group, New York, NY (006). 4. G. Boato, F. G. B. De Natale, and C. Fontanari, An improved asymmetric watermarking scheme suitable for copy protection, IEEE Trans. Signal Process. 54(7), (006). 5. J. Fridrich, M. Goljan, and R. Du, Lossless data embedding: new paradigm in digital watermarking, EURASIP J. Appl. Signal Process. 00(), (00). 6. M. U. Celik et al., Lossless generalized LSB data embedding, IEEE Trans. Image Process. 14(), (005). 7. G. Xuan et al., Distortionless data hiding based on integer wavelet trans-form, Electron. Lett. 38(5), (00). 8. Z. Ni et al., Reversible data hiding, IEEE Trans. Circuits Syst. Video Technol. 16(3), (006). 9. J. Hwang, J. Kim, and J. Choi, A reversible watermark-ing based on histogram shifting, in Proc. of International Workshop on Digital Watermarking 006, LNCS, Vol. 483, pp (006). 10. W.-L.- Tai, Reversible data hiding based on histogram modification of pixel differences, IEEE Trans. Circuits Syst. Video Technol. 19(6), (009). 11. X. Bo, Y. Lizhi, and H. Yongfeng, Reversible data hiding using histogram shifting in small blocks, in IEEE International Conference in Communication (ICC), IEEE Content Engineering Publishing Technology, Piscataway, NJ (010). 1. H.-M. Yoo, S.-K. Lee, and J.-W. Suh, High capacity reversible data hiding using the histogram modification of block image, in LNCS Journal of Electronic Imaging Jul Sep 01/Vol. 1(3)

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Giulia Boato received the MSc degree in mathematics in 00, and the PhD degree in information and communication technologies in 005, both from the University of Trento, Italy. In 006, she was a visiting researcher at the University of Vigo, Spain, and in 009 and 010 she was a visiting researcher at the Tampere University of Technology, Finland. Currently, she is an assistant professor of telecommunications at the University of Trento, working within the Multimedia Signal Processing and Understanding Laboratory. Her research interests are focused on image and signal processing, with particular attention to multimedia data protection, data hiding, and digital forensics. Marco Carli received the Laurea degree in telecommunication engineering from the University of Rome, La Sapienza, Rome, Italy, in He joined Datamat Systems Engineering Company until Since 1997, he is involved in the European Union international programs in Distance Education. Since 000, he is a visiting researcher with the Image Processing Laboratory directed by S.Mitra, UCSB, University of California, Santa Barbara, California, USA. He currently holds an assistant professor position at the University of Rome, Roma TRE. His research interests are in the area of digital signal and image processing, in multimedia communications, and in security of telecommunication systems. He is an IEEE senior member and a SPIE member; he is a reviewer for many conferences and for IEEE Transactions. Federica Battisti received the MSc degree in electronic engineering in 006, and the PhD degree in telecommunication engineering in 010, from the Università degli Studi Roma TRE, Italy. In 008, she was a visiting researcher in the Groupe Multimedia at Telecom ParisTech, France. In 009, she was a visiting researcher in the signal processing in communications group at the University of Vigo, Spain. Currently, she is an assistant professor in the telecommunication group at Università degli Studi Roma TRE, Italy. Her research interests Journal of Electronic Imaging Jul Sep 01/Vol. 1(3)

10 are focused on image and video processing, with particular attention to data hiding and multimedia quality assessment. Marco Azzoni received the Bachelor degree in telecommunication engineering in 006 and the MSc degree in telecommunication engineering in 010 both from the University of Trento, Italy. From November 010 to December 010 he was a visiting researcher in the signal processing group in the Tampere University of Technology. Karen Egiazarian received the PhD degree from Moscow M. V. Lomonosov State University, Russia, in 1986, and Doctor of Technology degree from Tampere University of Technology (TUT), Finland, in He is a professor of signal processing leading the computational imaging and transforms group at TUT. He has published over 500 refereed journal and conference articles, books, and patents. His main interests are in the field of image and video denoising and compression, transforms, efficient algorithms, and digital logic. He is an associate editor of several journals, including the SPIE Journal of Electronic Imaging and Research Letters in Signal Processing. He is a member of the DSP Technical Committee of the IEEE Circuits and Systems Society and a senior member of the IEEE. Journal of Electronic Imaging Jul Sep 01/Vol. 1(3)