# June 2001, Volume 10, Number 2

**M. Candik, E. Matus, D. Levicky**
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Digital Watermarking in Wavelet Transform Domain

This paper presents a technique for the digital watermarking of still images based on the wavelet transform. The watermark (binary image) is embedded into original image in its wavelet domain. The original unmarked image is required for watermark extraction. The method of embedding of digital watermarks in wavelet transform domain was analyzed and verified on grey scale static images.

- MILLER, M. L., COX, I. J., LINNARTZ, J. P., KALKER, T.:A review of watermarking principles and practices, 1999, http://www.neci.nj.nec.com/
- TAO, B., DICKINSON, B. Adaptive watermarking in the DCT domain., IEEE Int. Conf. ASSP '97, 1997.
- COX, I. J., MILLER, M. L. A review of watermarking and the importance of perceptual modelling. Proc. of Electronic Ima-ging '97, 1997.
- EDWARDS, T. Discrete wavelet transforms: Theory and implementation. http://sinh.stanford.edu/
- JUN, J. Introduction to wavelet transform., 1999, http://ic.hansung.ac.kr/
- LUKAC, R. An Adaptive Control of LUM Smoother. Radio-engineering, vol. 9, no. 1, April 2000, pp.9-12.
- LUKAC, R., MARCHEVSKY, S. Adaptive LUM Smoother Controlled by Adaptive Threshold System. Journal of Electrical Engineering, no. 3-4, vol. 51, 2000, pp.100-104.

**L. Andras, J. Chmurny**
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Image Compression by Gabor Expansion

Transform-based coding methods are popular in data compression. In the paper, an easily implemented method is proposed for the weighting factors of the Gabor decomposition. The method is based on the least-mean- squares error (LMSE) approach. The solution of the LMSE problem shows that the weighting factors can be extracted by simple multiplication between a matrix and the vector of data. If the set Gabor functions are chosen to be independent of the test images, this matrix is constant. Images are reconstructed by multiplying the matrix of Gabor functions and the vector of weighting factors. The choise of Gabor functions in the decomposition allows that the resulting decomposition has a pyramidal structure. In the paper is proposed simple codec system for pyramidal Gabor expansion for image compression.

- GABOR, D.: Theory of Communication. Journal IEE. London, vol. 93, November 1946, pp. 429-457.
- DAUGMAN, J.G.: Complete Discrete 2-D Gabor Transform by Neural Networks for Image Analysis and Compression. IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 36, no. 7, July 1988, pp. 1169-1179.
- WANG, H., YAN, H.: Efficient Implementation of Gabor Transform for Image Compression. Electronics Letters, vol. 28, no. 9, April 1992, pp. 870-871.
- ANDRAS, L., CHMURNY, J.: Gabor Transform and its Applications. Journal of Electrical Engineering, vol. 48, No. 3-4, 1997, pp. 101-104.
- BASTIAANS, M. J.: A Sampling Theorem for the Complex Spectrogram, and Gabor's Expansion of a Signal in Gaussian Elementary Signals. Optical Engineering, vol. 20, no. 4, 1981, pp. 594-598.
- STEWART, D.F.: Minimal Time-Frequency Localization Techniques and their Application to Image Compression. Disserta-tion Thesis, The Ohio State University, 1994.
- PORAT, M., ZEEVI, Y.Y.: The Generalized Gabor Scheme of Image Representation in Biological and Machine Vision. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 4, 1988, pp. 453-468.
- DUNN, D., HIGINNS, W.E., WAKELEY, J.: Texture Segmentation Using 2-D Gabor Elementary Functions. IEEE Transac-tions on Pattern Analysis and Machine Intelligence, vol. 16, no. 2, 1994, pp. 130-149.
- WEXLER, J., RAZ, S.: Discrete Gabor Expansions. Signal Processing, vol. 21, no. 3, November 1990, pp. 207-221.
- ANDRAS, L., SURIANSKY, J.: The Use of Gabor Transform for Image Processing. In Proceedings of the National Scientific Conference ELEKTRO 95, Zilina, 1995 pp. 159-162.

**J. Valsa**
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The Modified Node Voltage Method as Tool for Calculation of Network
Functions and Sensitivities

The paper deals with the well-known modified node voltage method that is generally used for formulation of system equations in universal network simulation programs. It shows very efficient ways if utilizing this type of equation formulation for evaluation of network transfer functions and their sensitivities to variations of element parameters. The described procedures can be used very effectively namely in connection with some matrix oriented mathematical program like for instance MATLAB. Several illustrative examples support the explanation of the methods described in the paper.

- HO, C. W., RUEHLI A. E., BRENNAN P. A. The Modified No-dal Approach to Network Analysis. IEEE Transactions on Circuits and Systems, CAS22, June 1975, pp. 504-509.
- MATLAB, The Language of Technical Computing. Version 5.2, The Math Works, Inc., 1998.
- VLACH, J. Computer Methods for Circuit Analysis and Design. 2nd Edition, Van Nostrand Reinhold, 1994.

**J. Mihalik, I. Gladisova, V. Michalcin**
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Two Layer Vector Quantization of Images

This paper deals with spatial scaleable vector quantization of images by using two layers. At the base layer the small dimensional full search vector quantization of an image of block means is carried out. After subtracting it from the input image at the enhancement layer the difference of full spatial resolution is quantized by large dimensional weighted pyramid vector quantizer in transform domain. Experimental results demonstrate acceptable quality of the downscaled image from the output of base layer at very low bit rate and possibility of next increasing its quality by the upscaled difference image from the output of enhancement layer.

- NASRABADI, N.M., KING, R.A. Image Coding Using Vector Quantization: A Review. IEEE Transactions on Communications, vol. 36, no. 8 ,1988, pp. 957-971.
- MIHALIK, J. Hierarchical Vector Quantization of Images in Transform Domain. Electrical Engineering Journal, vol. 43, no. 3, 1992, pp. 92-94.
- CHMURNY, J., MIHALIK, J. Algorithms for Optimisation of Vector Quantizers. Slaboproudy obzor, vol. 47, no. 9, 1986, pp. 435-440. (In Slovak)
- LINDE, Y., BUZO, A., GRAY, R.M. An algorithm for Vector Quantizer Design. IEEE Transactions on Communication, vol. 28, no. 1, 1980, pp. 84-95.
- GERSHO, A., GRAY, R.M. Vector Quantization and Signal Compression. Kluwer Academic Publishers, Dordrecht, Notherlands, 1992.
- MIHALIK, J. Multistage Vector Quantization of Image by Using Clustering Interpolation in DCT Domain. Radioengineering, vol. 6, no. 4, 1997, pp. 10-13.
- MIHALIK, J., GLADISOVA, I. Weighted Pyramid Vector Quantizer. Electrical Engineering Journal, vol. 46, no. 2, 1995, pp. 46-50.
- MIHALIK, J. Digital Signal Processing. Alfa Bratislava, 1987. (In Slovak)
- MIHALIK, J. Contour Based Scalar-Vector Quantizer. Electrical Engineering Journal, vol. 46, no. 4, 1995, pp. 121-125.
- FISCHER, T.R. A pyramid Vector Quantizers. IEEE Transactions on Information Theory, vol. 32, no. 4, 1986, pp. 568-583.
- GLADISOVA, I., MIHALIK, J. An Algorithm of Pyramid Vector Quantization. In Proceedings of the International Conference "Digital Signal Processing", Kosice, 1993, pp. 236-239. (In Slovak)

**V. Ricny**
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Contactless Opto-electronic Area and Their Attainable Measuring
Accuracy

This paper deals with the problems of the contactless area measurement on the principle of video signal processing. This video signal generates TV camera, which scans the measured object. Basic principle of these meters is explained and attainable measurement accuracy and factors influencing this accuracy are analyzed.

- RICNY, V. Properties and Applications of the Light-sensitive Sensors CCD (in Czech). Editorship: Technical University of Brno, Brno 1992.
- STANCIK, P. TV Contactless Area Meter. Technical Report (in Czech). FEECS, BUT, Brno 2000

**R. Lukac**
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Impulse Detectors for Noised Sequences

This paper is focused on a problem of impulse detection in the dynamic image environments corrupted by impulse noise. Using a proposed architecture that includes an impulse detector and the median filter, the effective methods can be designed. Thus, the image points are classified into two classes such as a class of noise free samples and a class of noised image points. In the case of impulse detection the estimate is performed by a median filter whereas a noise free sample is passed on the output without the change i.e. system works as an identity filter.

- ABREU, E., LIGHSTONE, M., MITRA, S. K., ARAKAWA, K. A New Efficient Approach for the Removal of Impulse Noise from Highly Corrupted Images. IEEE Transactions on Image Processing, vol. 5, no. 6, June 1996, pp. 1012-1025.
- ARCE, G. R. Mulstistage Order Statistic Filters for Image Sequence Processing. IEEE Transactions on Signal Pro-cessing, vol. 39, no. 5, May 1991, pp. 1146-1163.
- BEGHDADI, A., KHELLAF, A. A Noise-Filtering Method Using a Local Information Measure, IEEE Transactions on Image Processing, vol. 6, no. 6, June 1997, pp. 879-882.
- JAROSLAVSKIJ, L., BAJLA, I. Metody a systemy cislicoveho spracovania obrazov. Alfa - Vydavatezstvo technickej a ekonomickej literatury, Bratislava, 1989.
- KLEIHORST, R. P., LAGENDIJK, R. L., BIEMOND, J. Noise Reduction of Image Sequences Using Motion Compensation and Signal Decomposition. IEEE Transactions on Image Processing, vol. 4, no. 3, March 1995, pp. 274-284.
- LUKAC, R. Impulse Detection by Entropy Detector (H - Detector). Journal of Electrical Engineering, vol. 50, no. 9-10, November 1999, pp. 310-312.
- LUKAC, R., MARCHEVSKY, S. Threshold Impulse Detector Based on LUM Smoother (LUMsm Detector), Journal of Electrical Engineering, vol. 51, no. 1-2, 2000, pp. 44-47.
- LUKAC, R., MACEKOVA, L., MARCHEVSKY, S. Order Sta-tistic Filters in Dynamic Image Sequences Corrupted by Impulse Noise. In: Proceedings of the 4th International Conference DIGITAL SIGNAL PROCESSING '99, Technical University of Kosice (Slovakia), 1999, pp. 50-53.
- LUKAC, R., STUPAK, CS., MARCHEVSKY, S., MACEKOVA, L. Order-Statistic Filters in Dynamic Image Sequences. Radioengineering, vol. 9, no. 3, September 2000, pp. 8-14.
- LUKAC, R, STUPAK, CS., MARCHEVSKY, S. Neural Net-works for Noised Dynamic Image Sequences. Journal of Electrical Engineering, submitted.
- MACEKOVA, L., MARCHEVSKY, S. Noisy Dynamic Image Sequences Filtering Based on Order Statistic Filters. In: Pro-ceedings of DSP '97 3rd International Conference on Digital Signal Processing, Herzany (Slovakia), 1997, pp. 274-278.
- MARCHEVSKY, S., DRUTAROVSKY, M., CHOMAT, O. Iterative Filtering of Noisy Images by Adaptive Neural Network Filter. In: Proceedings of the Conference New trends in signal processing I, Liptovsky Mikulas, 1996, pp. 118-121.
- STUPAK, CS. Digital Image Filtration Based on Local Statis-tics. 3rd International Scientific Conference Elektro '99, Zilina, May 25-26 1999, pp.106-111.
- STUPAK, CS.: Neural Impulse Detector. In: Proceedings of International Conference NEW TRENDS IN DIGITAL SIGNAL PROCESSING V, Liptovsky Mikulas (Slovakia), 2000, pp. 323-326.
- STUPAK, CS., LUKAC, R. Impulse Detection in Grayscale Images. In: Proceedings of the 4th International Conference DIGITAL SIGNAL PROCESSING '99, Technical University of Kosice (Slovakia), 1999, pp. 96-99.
- STUPAK, CS., LUKAC, R., MARCHEVSKY, S. Utilization of the Impulse Detectors in the Grayscale Image Filtering. Jour-nal of Electrical Engineering, vol. 51, no. 7-8, 2000, pp. 173-181.
- VIERO, T., NEUVO, Y. 3-D Median Structures for Image Se-quence Filtering and Coding, Tampere University of Technology, Finland.

**P. Novak, I. Zuna, L. Pousek, J. Vrba**
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Ultrasonic Approach to Nonivasive Temperature Monitoring During
Microwave Thermotherapy

Microwave thermotherapy (MT) is an oncological treatment. At present the invasive thermometer probes are clinically used for temperature measuring during an MT. Any invasive handling of tumors is of high-risk. A new possible method of noninvasive monitoring of temperature distribution in tissue has been developed. An MT treatment of the experimentally induced pedicle-tumors of the rat was prepared. For 100 rat samples a strong correlation between the mean gray level in the ROIs in the ultrasound pictures and the invasively measured temperature in the range 37-44 °C was found. The correlation coefficient of the mean gray level and the invasively measured temperature is 0.96a0.05. A system for representation of changes of spatial temperature distribution of the whole tumor during MT is presented.

- NOVAK, P., ZUNA, I., POUSEK, L., PESCHKE, P., VRBA, J., SCHREIB, P. Noninvasive Temperature Monitoring in the Microwave Heated Rat Pedicle Tumors Using Ultrasound Tissue Characterization Method. EMBEC99, Medical&Biological En-gineering & Computing, Journal of the International Federation for Medical & Biological Engineering, Vol. 37 Suppl. 2, Vienna, 1999, ISSN 01400118, pp. 1032-1033, 1668
- P.NOVAK, I. ZUNA, L.POUSEK, P.PESCHKE, A. LORENZ, P. SCHREIB, J. VRBA, J. DEBUS: "Bestimmung der Temperaturverteilung im erhitzten Tumorgewebe durch Segmen-tation von Ultraschallbildern", Ultraschall 2000 Wien, Ultraschall in der Medizin, Suppl. 1, 2000, Georg Thieme Verlag Stuttgart, pp. 73-74, 100
- P.NOVAK, L.POUSEK, I.ZUNA, P.PESCHKE, A.LORENZ, J.VRBA, P.SCHREIB: "Nichtinvasive Bestimmung der Temperaturverteilung im Zielbereich der Hyperthermie durch diagnostischen Ultraschall", Ultraschall 99 Berlin, Ultraschall in der Medizin, Suppl.1, 1999, Georg Thieme Verlag Stuttgart, ISSN 0172-4614, pp. 132, 150
- ZUNA, I., NOVAK, P., POUSEK, L., SCHREIB, P., PESCHKE, P., LORENZ, A., DEBUS, J. "Noninvasive Monitoring of Temperature Distribution in the Target Field of Hyperthermia by Ultrasonic Tissue Characterization". Ultrasound in Medicine and Biology, Suppl. 2, 26 (2000) A54.
- RATH, U., SCHLAPS, D., LIMBERG, B., ZUNA, I., LORENZ, A., KAICK, G. VAN, LORENZ, W.J., KOMMERELL, B. "Diagnostic Accuracy of Computerized B-scan Texture Analysis and Conventional Ultrasonography in Diffuse Parenchymal and Malignant Liver Disease". Journal of Clinical Ultrasound, Vol. 13 (1985), pp. 87-99.
- SCHLAPS, D., ZUNA, I., WALZ, M., VOLK, J., RATH, U., LORENZ, A., KAICK, G. VAN, LORENZ, W.J. "Ultrasonic Tissue Characterization by Texture Analysis: Elimination of Tissue-independent Factors". Proceedings of SPIE - The Int. Soc. for Optical Engineering. Vol. 768. LA Ferrari. Washington: SPIE, (1987) pp. 128-134.
- YOUSSEF A.M., SCHLAPS D., ZUNA I., KAICK G. VAN, LORENZ W.J. "Assessing Hyperthermic Treatment Success by Two Dimensional Ultrasound Textural Analysis". Proceedings of SPIE - The Int. Soc. for Optical Engineering. Vol. 768. LA Ferrari. Washington: SPIE, (1987) pp. 135-145.
- ZUNA I. "Computerized Ultrasonic Tissue Characterization: Methods and Clinical Use". Computer Assisted Radiology. HU Lemke et al. Berlin: Springer, (1987) pp. 155-163.
- BORGEFORS, G. "Hierarchical Chamfer Matching: A Parametric Edge Matching Algorithm", IEEE Trans. PAMI, Vol. 10, No. 6, 1988.
- HAHN, E.W., PESCHKE, P., MASON, R.P., BABCOCK, E.E., ANTICH, P.P. Isolated Tumor Growth in a Surgically Formed Skin Pedicle in the Rat: a New Tumor Model for NMR Studies. Magn Reson Imaging, 11, 1993, pp. 1007-1017.
- ISAACS, J.T., COFFEY, D.S. Model Systems for the Study of Prostate Cancer. Clinics in Oncology, Vol 2, Cancer of the prostate, G.P. Murphy (ed.), London: W.B. Saunders Co Ltd. 1983, pp. 479-498.
- LOHR, F., WENZ, F., FLENTJE, M., PESCHKE, P., HAHN E.W. Measurement of the Proliferative Activity of Three Different Sublines of the Dunning Rat Prostate Tumor R3327. Strahlenther Onkol, 169, 1993, pp. 438-445.
- MASON, R.P., CONSTANTINESCU, A., HUNJAN, S., LE, D., HAHN, E.W., ANTICH, P.P., BLUM, C., PESCHKE, P. Regional Tumor Oxygenation and Measurement of Dynamic Changes. Radiat Res, 152, 1999, pp. 239-249.
- AIDA, S., IWAMA, N., OGURA, I. Fundamental Experiment of Temperature Dependence of Ultrasound Parameters. In Proc. 2nd Annual Meeting Japan Soc. Hyperthermic Onc., Shinshara Publishers Inc.,1985
- JACOBI J.H., LARSEN L.E, HAST C.T.: "Water-immersed Microwave Antennas and Their Application in Microwave Inter-rogation of Biological Targets.", IEEE Trans. Microwave Theory Tech., 1979
- NASONI, R.L., BOWEN, T., CONNER, W.G, SHOLES, R.R. In Vivo Temperature Dependence of Ultrasound Speed in Tissue and Its Applications to Noninvasive Temperature Monitoring. Ultrasonic Imaging, 1979

**P. Kvarda**
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Identifying the Deterministic Chaos by Using the Lyapunov Exponents

This paper presents an investigation of deterministic chaos. The modified Colpitts oscillator is used as an example of deterministic chaos in electronic circuits. The most known quality of deterministic chaotic systems the positive Lyapunov exponent is used for investigation the chaotic Colpitts oscillator.

- KENNEDY, P., Chaos in the Colpitts Oscillator. IEEE Trans. Circuits Syst., vol. 41, no. 11, p. 771-774, 1994
- KVARDA, P., Identifying the Deterministic Chaos by Using the Lorenz Maps. Radioengineering, vol. 9, no. 4, p. 32-33, 2000
- MIKHAILOV, A. S., LOSKUTOV A. Y., Foundation of Synergetics II: Complex Patterns. Berlin: Springer, 1991
- LORENZ, E. N., J. Atmos. Sci., vol. 20, p. 130, 1963
- WEBSTER, J., Wiley Encyclopedia of Electrical and Electronics Engineering Online, John Wiley & Sons, (http://www.inter-science.wiley.com). 1999
- SHIMADA I., NAGASHIMA T., A Numerical Approach to Ergodic Problem of Dissipative Dymamical Systems. Progress of Theoretical Physics, vol. 61, no. 6, June 1979
- WOLF A., SWIFT B., Determining Lyapunov Exponents from a Time Series. Physica, vol. 16D, p. 285-317, 1985