Prospective Digital Processing Methods of Multidimensional Signals with the Use of Irregular Meshes
Keywords:
multidimensional digital signal processing, irregular mesh, figurate numbers
Abstract
The article considers sparse representation of signals based on using irregular meshes, which is one of prospective lines in digital processing of multidimensional signals. Application of irregular meshes has been seen for several decades as a promising field of investigations opening the possibility of using high efficiency of representing a signal carrier in combination with well-developed approximation methods used in solving boundary-value problems. However, lack of tools suitable for solving typical digital signal processing problems with the use of irregular meshes (e.g., for computing orthogonal discrete transforms) had resulted in that any noticeable and practically significant results are lacking in this area. Nevertheless, the recent years have seen a growth of interest in using irregular meshes.
The article presents the results of investigations in this field that were carried out at the MPEI Chair for Computers, Systems and Networks. Matters concerned with generation of irregular meshes adapted to the specific features of multidimensional signals are addressed. Algorithms intended for carrying out interpolation, for making a shift from a regular carrier (a uniform regular mesh) to an irregular one, and for computing discrete transformations for a signal with an irregular carrier are presented. Solutions for arranging intellectual signal processing, such as pattern recognition and motion detection, are suggested.
References
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6. Luo F., Lin C., Gu X., Ma X. Synthesized View Comparison Method for No-reference 3D Image Quality Assessment // Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
7. Ranjani R., Priya C. A Survey on Face Recognition Techniques: a Review// Intern. J. Pure and Appl. Math. 2018. V. 118. Pp. 253—274.
8. Wang X., Gao F., Dong J., Qi Q. Change Detection for Synthetic Aperture Radar Images Based on Pattern and Intensity Distinctiveness Analysis // Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
9. Jin Z., Hou Z., Yu W., Wang X., Sun H. Multiple Feature Fusion Via Covariance Matrix for Visual Tracking // Ibid.
10. Chen S. e. a. Using Ranking-CNN for Age Estimation // Proc. 30th IEEE Conf. on Computer Vision and Pattern Recognition. 2009. Pp. 742—751.
11. Li J. e. a. Robust Face Recognition Using the Deep C2D-CNN Model Based on Decision-level Fusion // Sensors. 2018. V. 18 (7). Pp. 2080—2107.
12. Kolar M., Debattista K., Chalmers A. A Subjective Evaluation of Texture Synthesis Methods // Computer Graphics Forum. 2017. V. 36. Pp. 189—198.
13. Muller H., Michoux N., Bandon D., Geissbuhler A. A Review of Content-based Image Retrieval Systems in Medical Application-clinical Benefits and Future Directions // Intern. J. Medical Informatics. 2009. V. 78 (9). Pp. 1—23.
14. Чобану М.К. Многомерные многоскоростные системы обработки сигналов. М.: Техносфера, 2009.
15. Zhong J., Zou Z. The Solution of Data Gradient on Nonuniform Grid in Direct Volume Rendering // ACM Int. Conf. Proc. 2017. Pp. 1—5.
16. Mersereau R.M. The Processing of Hexagonally Sampled Two-dimensional Signals // Proc. IEEE. 1979. V. 67 (6). Pp. 930—949.
17. Zhang D., Zhang X., Li L., Liu H. Face Recognition via Sparse Representation of SIFT Feature on Hexagonal- Sampling Image // Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
18. Guskov I., Sweldens W., Schroder P. Multiresolution Signal Processing For Meshes // Proc. Comput. Graph. Annual Conf. Series. 1999. Pp. 325—334.
19. Daubechies I., Guskov I., Schroder P., Sweldens W. Wavelets on Irregular Point Sets // Phil. Trans. R. Soc. Lon. 1999. No. 1760. Pp. 2397—2413.
20. Li Y., Zhang C., Yu Q. Quadratic Polynomial Interpolation on Triangular Domain // Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
21. Hilsmann A., Schneider D.C., Eisert P. Realistic Cloth Augmentation in Single View Video under Occlusions // Computers & Graphics. 2010. No. 34 (5). Pp. 567—574.
22. Monga V., Bala R., Mo X. Design and Optimization of Color Look-up Tables on a Simplex Topology // IEEE Trans. Image Process. 2011. V. 21. No. 4. Pp. 1981—1996.
23. Lukin V. e. a. Lossy Compression of Images Corrupted by Mixed Poisson and Additive Noise // Proc. LNLA. 2009. Pp. 33—40.
24. Shen J., Jin X., Zhou C., Wang C. Gradient Based Image Completion by Solving the Poisson Equation // Computers and Graphics. 2007. No. 31 (1). Pp. 119—126.
25. Fettweis A. Multidimensional Wave–digital Principles: from Filtering to Numerical Integration // IEEE Trans. Circuits and Syst. 1994. V. 40. No. 4. Pp. 174—182.
26. Basu S., Zerzghi A. Multidimensional Digital Filter Approach for Numerical Solution of a Class of PDEs of the Propagating Wave Type // IEEE Trans. Circuits and Syst. 1999. V. 41. No. 2. Pp. 170—181.
27. Vasilyev O.V., Bowman C. Second-Generation Wavelet Collocation Method for the Solution of Partial Differential Equations // J. Computational Phys. 2000. V. 165. Pp. 660—193.
28. Вишняков С.В. Применение вейвлет-преобразования для оптимизации сеток при расчете электромагнитных полей методом конечных элементов // Известия РАН. Серия «Энергетика». 2010. № 6. С. 40—45.
29. Вишняков С.В. Модификация метода конечных элементов для решения внешних задач теории электромагнитного поля // Известия РАН. Серия «Энергетика». 2014. № 2. С. 157—166.
30. Jagalur-Mohan J., Feijoo G., Oberai A. A Galerkin Least Squares Method for Time Harmonic Maxwell Equations Using Nedelec Elements // J. Computational Phys. 2013. No. 235. Pp. 67—81.
31. Пехтерев В.В., Вишняков С.В., Чобану М.К. Интегральное выделение структурных особенностей изображения // Цифровая обработка сигналов и ее применение: Материалы 17 Междунар. конф. 2015. С. 501—504.
32. Kallinderis Y., Kontzialis C. A Priori Mesh Quality Estimation via Direct Relation Between Truncation Error and Mesh Distortion // J. Computational Phys. 2009. No. 228 (3). Pp. 881—902.
33. Vishnyakov S. Artificial Neural Networks Implementation in Digital Signal Processing Couses // Proc. IV Intern. Conf. Informatization Engineering Education. 2018.
34. Vishnyakov S., Pekhterev V., Sokolova E. A Novel Method of the Image Processing on Irregular Triangular Meshes // Proc. IX Intern. Conf. Graphic and Image Proc. 2017. V. 10615.
---
Для цитирования: Вишняков С.В., Соколова Е.А., Пехтерев В.В. Перспективные методы цифровой обработки многомерных сигналов на основе применения нерегулярных сеток // Вестник МЭИ. 2019. № 3. С. 98—107. DOI: 10.24160/1993-6982-2019-3-98-107.
#
1. Chobanu M.K., Kurguskin O.S. Primenenie Setochnogo Metoda dlya Szhatiya Graficheskoy Informatsii. Osnovnoy Algoritm. Vestnik Komp'yuternykh i Informatsionnykh Tekhnologiy. 2013;4:13—18. (in Russian).
2. Petrov E.P., Medvedeva E.V., Kharina N.L., Tchobanou M.K. Intra Frame Compression and Video Restoration Based on Conditional Markov Processes Theory. Multi-dimensional Systems and Signal Proc. 2016;27; 3:719—742.
3. Zemlyachenko A.N. i dr. Protsedury Avtomaticheskogo Szhatiya Izobrazheniy DZ Zemli pri Signal'nozavisimykh Pomekhakh v Okrestnosti Optimal'noy Rabochey Tochki i ikh Effektivnost'. Issledovaniya Zemli iz Kosmosa. 2013;3:73—90. (in Russian).
4. Dvorkovich V.P., Chobanu M.K. Problemy i Perspektivy Razvitiya Sistem Kodirovaniya Dinamicheskikh Izobrazheniy. Media Vision. 2011;2:55—64. (in Russian).
5. Arlyapov C.A., Priorov A.L., Khryashchev B.B. Modifitsirovannyy Kriteriy Otsenki Kachestva Vosstanovlennykh Izobrazheniy. Tsifrovaya Obrabotka Signalov. 2006;2:27—33. (in Russian).
6. Luo F., Lin C., Gu X., Ma X. Synthesized View Comparison Method for No-reference 3D Image Quality Assessment. Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
7. Ranjani R., Priya C. A Survey on Face Recognition Techniques: a Review// Intern. J. Pure and Appl. Math. 2018;118:253—274.
8. Wang X., Gao F., Dong J., Qi Q. Change Detection for Synthetic Aperture Radar Images Based on Pattern and Intensity Distinctiveness Analysis. Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
9. Jin Z., Hou Z., Yu W., Wang X., Sun H. Multiple Feature Fusion Via Covariance Matrix for Visual Tracking. Ibid.
10. Chen S. e. a. Using Ranking-CNN for Age Estimation. Proc. 30th IEEE Conf. on Computer Vision and Pattern Recognition. 2009:742—751.
11. Li J. e. a. Robust Face Recognition Using the Deep C2D-CNN Model Based on Decision-level Fusion. Sensors. 2018;18 (7):2080—2107.
12. Kolar M., Debattista K., Chalmers A. A Subjective Evaluation of Texture Synthesis Methods. Computer Graphics Forum. 2017;36:189—198.
13. Muller H., Michoux N., Bandon D., Geissbuhler A. A Review of Content-based Image Retrieval Systems in Medical Application-clinical Benefits and Future Directions. Intern. J. Medical Informatics. 2009;78 (9):1—23.
14. Chobanu M.K. Mnogomernye Mnogoskorostnye Sistemy Obrabotki Signalov. M.: Tekhnosfera, 2009. (in Russian).
15. Zhong J., Zou Z. The Solution of Data Gradient on Nonuniform Grid in Direct Volume Rendering. ACM Int. Conf. Proc. 2017:1—5.
16. Mersereau R.M. The Processing of Hexagonally Sampled Two-dimensional Signals. Proc. IEEE. 1979;67 (6): 930—949.
17. Zhang D., Zhang X., Li L., Liu H. Face Recognition via Sparse Representation of SIFT Feature on Hexagonal- Sampling Image. Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
18. Guskov I., Sweldens W., Schroder P. Multiresolution Signal Processing For Meshes. Proc. Comput. Graph. Annual Conf. Series. 1999:325—334.
19. Daubechies I., Guskov I., Schroder P., Sweldens W. Wavelets on Irregular Point Sets. Phil. Trans. R. Soc. Lon. 1999;1760:2397—2413.
20. Li Y., Zhang C., Yu Q. Quadratic Polynomial Interpolation on Triangular Domain. Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
21. Hilsmann A., Schneider D.C., Eisert P. Realistic Cloth Augmentation in Single View Video under Occlusions. Computers & Graphics. 2010;34 (5):567—574.
22. Monga V., Bala R., Mo X. Design and Optimization of Color Look-up Tables on a Simplex Topology. IEEE Trans. Image Process. 2011;21;4:1981—1996.
23. Lukin V. e. a. Lossy Compression of Images Corrupted by Mixed Poisson and Additive Noise. Proc. LNLA. 2009:33—40.
24. Shen J., Jin X., Zhou C., Wang C. Gradient Based Image Completion by Solving the Poisson Equation. Computers and Graphics. 2007;31 (1):119—126.
25. Fettweis A. Multidimensional Wave–digital Principles: from Filtering to Numerical Integration. IEEE Trans. Circuits and Syst. 1994;40;4:174—182.
26. Basu S., Zerzghi A. Multidimensional Digital Filter Approach for Numerical Solution of a Class of PDEs of the Propagating Wave Type. IEEE Trans. Circuits and Syst. 1999;41;2:170—181.
27. Vasilyev O.V., Bowman C. Second-Generation Wavelet Collocation Method for the Solution of Partial Differential Equations. J. Computational Phys. 2000;165: 660—193.
28. Vishnyakov S.V. Primenenie Veyvlet-preobrazovaniya dlya Optimizatsii Setok pri Raschete Elektromagnitnykh Poley Metodom Konechnykh Elementov. Izvestiya RAN. Seriya «Energetika». 2010;6:40—45. (in Russian).
29. Vishnyakov S.V. Modifikatsiya Metoda Konechnykh Elementov dlya Resheniya Vneshnikh Zadach Teorii Elektromagnitnogo Polya. Izvestiya RAN. Seriya «Energetika». 2014;2:157—166. (in Russian).
30. Jagalur-Mohan J., Feijoo G., Oberai A. A Galerkin Least Squares Method for Time Harmonic Maxwell Equations Using Nedelec Elements. J. Computational Phys. 2013;235:67—81.
31. Pekhterev V.V., Vishnyakov S.V., Chobanu M.K. Integral'noe Vydelenie Strukturnykh Osobennostey Izobrazheniya. Tsifrovaya Obrabotka Signalov i ee Primenenie: Materialy 17 Mezhdunar. Konf. 2015:501—504. (in Russian).
32. Kallinderis Y., Kontzialis C. A Priori Mesh Quality Estimation via Direct Relation Between Truncation Error and Mesh Distortion. J. Computational Phys. 2009;228 (3): 881—902.
33. Vishnyakov S. Artificial Neural Networks Implementation in Digital Signal Processing Couses. Proc. IV Intern. Conf. Informatization Engineering Education. 2018.
34. Vishnyakov S., Pekhterev V., Sokolova E. A Novel Method of the Image Processing on Irregular Triangular Meshes. Proc. IX Intern. Conf. Graphic and Image Proc. 2017;10615.
---
For citation: Vishnyakov S.V., Sokolova E.A., Pekhterev V.V. Prospective Digital Processing Methods of Multidimensional Signals with the Use of Irregular Meshes. Bulletin of MPEI. 2019;3:98—107. (in Russian). DOI: 10.24160/1993-6982-2019-3-98-107
2. Petrov E.P., Medvedeva E.V., Kharina N.L., Tchobanou M.K. Intra Frame Compression and Video Restoration Based on Conditional Markov Processes Theory // Multidimensional Systems and Signal Proc. 2016. V. 27. No. 3. Pp. 719—742.
3. Земляченко А.Н. и др. Процедуры автоматического сжатия изображений ДЗ Земли при сигнально-зависимых помехах в окрестности оптимальной рабочей точки и их эффективность // Исследования Земли из космоса. 2013. Вып. 3. C. 73—90.
4. Дворкович В.П., Чобану М.К. Проблемы и перспективы развития систем кодирования динамических изображений // Media Vision. 2011. № 2. С. 55—64.
5. Арляпов C.A., Приоров A.Л., Хрящев B.B. Модифицированный критерий оценки качества восстановленных изображений // Цифровая обработка сигналов. 2006. № 2. С. 27—33.
6. Luo F., Lin C., Gu X., Ma X. Synthesized View Comparison Method for No-reference 3D Image Quality Assessment // Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
7. Ranjani R., Priya C. A Survey on Face Recognition Techniques: a Review// Intern. J. Pure and Appl. Math. 2018. V. 118. Pp. 253—274.
8. Wang X., Gao F., Dong J., Qi Q. Change Detection for Synthetic Aperture Radar Images Based on Pattern and Intensity Distinctiveness Analysis // Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
9. Jin Z., Hou Z., Yu W., Wang X., Sun H. Multiple Feature Fusion Via Covariance Matrix for Visual Tracking // Ibid.
10. Chen S. e. a. Using Ranking-CNN for Age Estimation // Proc. 30th IEEE Conf. on Computer Vision and Pattern Recognition. 2009. Pp. 742—751.
11. Li J. e. a. Robust Face Recognition Using the Deep C2D-CNN Model Based on Decision-level Fusion // Sensors. 2018. V. 18 (7). Pp. 2080—2107.
12. Kolar M., Debattista K., Chalmers A. A Subjective Evaluation of Texture Synthesis Methods // Computer Graphics Forum. 2017. V. 36. Pp. 189—198.
13. Muller H., Michoux N., Bandon D., Geissbuhler A. A Review of Content-based Image Retrieval Systems in Medical Application-clinical Benefits and Future Directions // Intern. J. Medical Informatics. 2009. V. 78 (9). Pp. 1—23.
14. Чобану М.К. Многомерные многоскоростные системы обработки сигналов. М.: Техносфера, 2009.
15. Zhong J., Zou Z. The Solution of Data Gradient on Nonuniform Grid in Direct Volume Rendering // ACM Int. Conf. Proc. 2017. Pp. 1—5.
16. Mersereau R.M. The Processing of Hexagonally Sampled Two-dimensional Signals // Proc. IEEE. 1979. V. 67 (6). Pp. 930—949.
17. Zhang D., Zhang X., Li L., Liu H. Face Recognition via Sparse Representation of SIFT Feature on Hexagonal- Sampling Image // Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
18. Guskov I., Sweldens W., Schroder P. Multiresolution Signal Processing For Meshes // Proc. Comput. Graph. Annual Conf. Series. 1999. Pp. 325—334.
19. Daubechies I., Guskov I., Schroder P., Sweldens W. Wavelets on Irregular Point Sets // Phil. Trans. R. Soc. Lon. 1999. No. 1760. Pp. 2397—2413.
20. Li Y., Zhang C., Yu Q. Quadratic Polynomial Interpolation on Triangular Domain // Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
21. Hilsmann A., Schneider D.C., Eisert P. Realistic Cloth Augmentation in Single View Video under Occlusions // Computers & Graphics. 2010. No. 34 (5). Pp. 567—574.
22. Monga V., Bala R., Mo X. Design and Optimization of Color Look-up Tables on a Simplex Topology // IEEE Trans. Image Process. 2011. V. 21. No. 4. Pp. 1981—1996.
23. Lukin V. e. a. Lossy Compression of Images Corrupted by Mixed Poisson and Additive Noise // Proc. LNLA. 2009. Pp. 33—40.
24. Shen J., Jin X., Zhou C., Wang C. Gradient Based Image Completion by Solving the Poisson Equation // Computers and Graphics. 2007. No. 31 (1). Pp. 119—126.
25. Fettweis A. Multidimensional Wave–digital Principles: from Filtering to Numerical Integration // IEEE Trans. Circuits and Syst. 1994. V. 40. No. 4. Pp. 174—182.
26. Basu S., Zerzghi A. Multidimensional Digital Filter Approach for Numerical Solution of a Class of PDEs of the Propagating Wave Type // IEEE Trans. Circuits and Syst. 1999. V. 41. No. 2. Pp. 170—181.
27. Vasilyev O.V., Bowman C. Second-Generation Wavelet Collocation Method for the Solution of Partial Differential Equations // J. Computational Phys. 2000. V. 165. Pp. 660—193.
28. Вишняков С.В. Применение вейвлет-преобразования для оптимизации сеток при расчете электромагнитных полей методом конечных элементов // Известия РАН. Серия «Энергетика». 2010. № 6. С. 40—45.
29. Вишняков С.В. Модификация метода конечных элементов для решения внешних задач теории электромагнитного поля // Известия РАН. Серия «Энергетика». 2014. № 2. С. 157—166.
30. Jagalur-Mohan J., Feijoo G., Oberai A. A Galerkin Least Squares Method for Time Harmonic Maxwell Equations Using Nedelec Elements // J. Computational Phys. 2013. No. 235. Pp. 67—81.
31. Пехтерев В.В., Вишняков С.В., Чобану М.К. Интегральное выделение структурных особенностей изображения // Цифровая обработка сигналов и ее применение: Материалы 17 Междунар. конф. 2015. С. 501—504.
32. Kallinderis Y., Kontzialis C. A Priori Mesh Quality Estimation via Direct Relation Between Truncation Error and Mesh Distortion // J. Computational Phys. 2009. No. 228 (3). Pp. 881—902.
33. Vishnyakov S. Artificial Neural Networks Implementation in Digital Signal Processing Couses // Proc. IV Intern. Conf. Informatization Engineering Education. 2018.
34. Vishnyakov S., Pekhterev V., Sokolova E. A Novel Method of the Image Processing on Irregular Triangular Meshes // Proc. IX Intern. Conf. Graphic and Image Proc. 2017. V. 10615.
---
Для цитирования: Вишняков С.В., Соколова Е.А., Пехтерев В.В. Перспективные методы цифровой обработки многомерных сигналов на основе применения нерегулярных сеток // Вестник МЭИ. 2019. № 3. С. 98—107. DOI: 10.24160/1993-6982-2019-3-98-107.
#
1. Chobanu M.K., Kurguskin O.S. Primenenie Setochnogo Metoda dlya Szhatiya Graficheskoy Informatsii. Osnovnoy Algoritm. Vestnik Komp'yuternykh i Informatsionnykh Tekhnologiy. 2013;4:13—18. (in Russian).
2. Petrov E.P., Medvedeva E.V., Kharina N.L., Tchobanou M.K. Intra Frame Compression and Video Restoration Based on Conditional Markov Processes Theory. Multi-dimensional Systems and Signal Proc. 2016;27; 3:719—742.
3. Zemlyachenko A.N. i dr. Protsedury Avtomaticheskogo Szhatiya Izobrazheniy DZ Zemli pri Signal'nozavisimykh Pomekhakh v Okrestnosti Optimal'noy Rabochey Tochki i ikh Effektivnost'. Issledovaniya Zemli iz Kosmosa. 2013;3:73—90. (in Russian).
4. Dvorkovich V.P., Chobanu M.K. Problemy i Perspektivy Razvitiya Sistem Kodirovaniya Dinamicheskikh Izobrazheniy. Media Vision. 2011;2:55—64. (in Russian).
5. Arlyapov C.A., Priorov A.L., Khryashchev B.B. Modifitsirovannyy Kriteriy Otsenki Kachestva Vosstanovlennykh Izobrazheniy. Tsifrovaya Obrabotka Signalov. 2006;2:27—33. (in Russian).
6. Luo F., Lin C., Gu X., Ma X. Synthesized View Comparison Method for No-reference 3D Image Quality Assessment. Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
7. Ranjani R., Priya C. A Survey on Face Recognition Techniques: a Review// Intern. J. Pure and Appl. Math. 2018;118:253—274.
8. Wang X., Gao F., Dong J., Qi Q. Change Detection for Synthetic Aperture Radar Images Based on Pattern and Intensity Distinctiveness Analysis. Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
9. Jin Z., Hou Z., Yu W., Wang X., Sun H. Multiple Feature Fusion Via Covariance Matrix for Visual Tracking. Ibid.
10. Chen S. e. a. Using Ranking-CNN for Age Estimation. Proc. 30th IEEE Conf. on Computer Vision and Pattern Recognition. 2009:742—751.
11. Li J. e. a. Robust Face Recognition Using the Deep C2D-CNN Model Based on Decision-level Fusion. Sensors. 2018;18 (7):2080—2107.
12. Kolar M., Debattista K., Chalmers A. A Subjective Evaluation of Texture Synthesis Methods. Computer Graphics Forum. 2017;36:189—198.
13. Muller H., Michoux N., Bandon D., Geissbuhler A. A Review of Content-based Image Retrieval Systems in Medical Application-clinical Benefits and Future Directions. Intern. J. Medical Informatics. 2009;78 (9):1—23.
14. Chobanu M.K. Mnogomernye Mnogoskorostnye Sistemy Obrabotki Signalov. M.: Tekhnosfera, 2009. (in Russian).
15. Zhong J., Zou Z. The Solution of Data Gradient on Nonuniform Grid in Direct Volume Rendering. ACM Int. Conf. Proc. 2017:1—5.
16. Mersereau R.M. The Processing of Hexagonally Sampled Two-dimensional Signals. Proc. IEEE. 1979;67 (6): 930—949.
17. Zhang D., Zhang X., Li L., Liu H. Face Recognition via Sparse Representation of SIFT Feature on Hexagonal- Sampling Image. Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
18. Guskov I., Sweldens W., Schroder P. Multiresolution Signal Processing For Meshes. Proc. Comput. Graph. Annual Conf. Series. 1999:325—334.
19. Daubechies I., Guskov I., Schroder P., Sweldens W. Wavelets on Irregular Point Sets. Phil. Trans. R. Soc. Lon. 1999;1760:2397—2413.
20. Li Y., Zhang C., Yu Q. Quadratic Polynomial Interpolation on Triangular Domain. Proc. IX Intern. Conf. Graphic and Image Proc. 2017.
21. Hilsmann A., Schneider D.C., Eisert P. Realistic Cloth Augmentation in Single View Video under Occlusions. Computers & Graphics. 2010;34 (5):567—574.
22. Monga V., Bala R., Mo X. Design and Optimization of Color Look-up Tables on a Simplex Topology. IEEE Trans. Image Process. 2011;21;4:1981—1996.
23. Lukin V. e. a. Lossy Compression of Images Corrupted by Mixed Poisson and Additive Noise. Proc. LNLA. 2009:33—40.
24. Shen J., Jin X., Zhou C., Wang C. Gradient Based Image Completion by Solving the Poisson Equation. Computers and Graphics. 2007;31 (1):119—126.
25. Fettweis A. Multidimensional Wave–digital Principles: from Filtering to Numerical Integration. IEEE Trans. Circuits and Syst. 1994;40;4:174—182.
26. Basu S., Zerzghi A. Multidimensional Digital Filter Approach for Numerical Solution of a Class of PDEs of the Propagating Wave Type. IEEE Trans. Circuits and Syst. 1999;41;2:170—181.
27. Vasilyev O.V., Bowman C. Second-Generation Wavelet Collocation Method for the Solution of Partial Differential Equations. J. Computational Phys. 2000;165: 660—193.
28. Vishnyakov S.V. Primenenie Veyvlet-preobrazovaniya dlya Optimizatsii Setok pri Raschete Elektromagnitnykh Poley Metodom Konechnykh Elementov. Izvestiya RAN. Seriya «Energetika». 2010;6:40—45. (in Russian).
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For citation: Vishnyakov S.V., Sokolova E.A., Pekhterev V.V. Prospective Digital Processing Methods of Multidimensional Signals with the Use of Irregular Meshes. Bulletin of MPEI. 2019;3:98—107. (in Russian). DOI: 10.24160/1993-6982-2019-3-98-107
Published
2018-08-03
Issue
Section
System Analysis, Management and Information Processing (05.13.01)
