Araştırma Makalesi
Yıl 2025,
Cilt: 38 Sayı: 1, 292 - 303, 01.03.2025
Öz
Kaynakça
- [1] Hutchinson, J.E., “Fractals and self similarity”, Indiana University Mathematics Journal, 30(5): 713-747, (1981).
- [2] Barnsley, M.F., “Fractals Everywhere”, Dover Publications, Inc: Mineola, New York, USA, (2012).
- [3] Barnsley, M.F., Sloan, A.D., “A better way to compress images”, Byte 13(1): 215-223, (1988).
- [4] Aslan, İ., Gökçer Ellidokuz, T.Y., “Approximation by N-dimensional max-product and max-min kind discrete operators with applications”, Filomat, 38(5): 1825-1845, (2024).
- [5] Çelik, D., Deniz, A., Özdemir, Y., “Graph-Directed Fractal Image Compression”, Eskişehir Technical University Journal of Science and Technology B- Theoretical Sciences, 10(1): 1-10, (2022).
- [6] Gökçer, T.Y., Aslan, İ., “Approximation by Kantorovich-type max-min operators and its applications”, Applied Mathematics and Computation 423: 127011, (2022).
- [7] Menassel, R., “Optimization of fractal image compression”, Fractal Analysis-Selected Examples. IntechOpen, (2020).
- [8] Nandi, U., “Fractal image compression using a fast affine transform and hierarchical classification scheme”, The Visual Computer, 38(11): 3867-3880, (2022).
- [9] Jacquin, A.E., “Image coding based on a fractal theory of iterated contractive image transformations”, IEEE Transactions on image processing, 1(1): 18-30, (1992).
- [10] Fischer, Y., “Fractal Image Compression Theory and Application”, Springer, New York, (1994).
- [11] Nandi, U., Fractal image compression with adaptive quardtree partitioning and non-linear affine Map, Multimedia Tools and Applications, 79(35): 26345-26368, (2020).
- [12] Nandi, U., Mandal, J. K., Efficiency and capability of fractal image compression with adaptive quadtree partitioning, The International Journal of Multimedia & Its Applications, 5(4): 53, (2013).
- [13] Xu, C., Xie, D., Guo, H., He, J., Chen, M., “Optimization Method for Fractal Image Compression Based on Self-similarity Evaluation and Gradient Bisection Algorithm”, In International Conference on Intelligent Computing (pp. 218-233). Singapore: Springer Nature, Singapore, (2024).
- [14] Aslan, N., Aslan, İ., “Approximation to the classical fractals by using non-affine contraction mappings”, Portugaliae Mathematica, 79: 45–60, (2022).
Yıl 2025,
Cilt: 38 Sayı: 1, 292 - 303, 01.03.2025
Öz
In this study, considering the well-known fractal image compression, we introduce the image decompression method through non-affine contraction mappings. To achieve this, we convert affine contraction mappings into non-affine contraction mappings using Lipschitz continuous functions, subject to certain assumptions. Our expectation is to obtain decompressed images of superior quality compared to the classical fractal image compression method. We also apply our method for audio decompression. At the end, we illustrate the proposed method with some examples.
Anahtar Kelimeler
Fractal image compression Iterated function system Audio compression Non-affine contraction
Kaynakça
- [1] Hutchinson, J.E., “Fractals and self similarity”, Indiana University Mathematics Journal, 30(5): 713-747, (1981).
- [2] Barnsley, M.F., “Fractals Everywhere”, Dover Publications, Inc: Mineola, New York, USA, (2012).
- [3] Barnsley, M.F., Sloan, A.D., “A better way to compress images”, Byte 13(1): 215-223, (1988).
- [4] Aslan, İ., Gökçer Ellidokuz, T.Y., “Approximation by N-dimensional max-product and max-min kind discrete operators with applications”, Filomat, 38(5): 1825-1845, (2024).
- [5] Çelik, D., Deniz, A., Özdemir, Y., “Graph-Directed Fractal Image Compression”, Eskişehir Technical University Journal of Science and Technology B- Theoretical Sciences, 10(1): 1-10, (2022).
- [6] Gökçer, T.Y., Aslan, İ., “Approximation by Kantorovich-type max-min operators and its applications”, Applied Mathematics and Computation 423: 127011, (2022).
- [7] Menassel, R., “Optimization of fractal image compression”, Fractal Analysis-Selected Examples. IntechOpen, (2020).
- [8] Nandi, U., “Fractal image compression using a fast affine transform and hierarchical classification scheme”, The Visual Computer, 38(11): 3867-3880, (2022).
- [9] Jacquin, A.E., “Image coding based on a fractal theory of iterated contractive image transformations”, IEEE Transactions on image processing, 1(1): 18-30, (1992).
- [10] Fischer, Y., “Fractal Image Compression Theory and Application”, Springer, New York, (1994).
- [11] Nandi, U., Fractal image compression with adaptive quardtree partitioning and non-linear affine Map, Multimedia Tools and Applications, 79(35): 26345-26368, (2020).
- [12] Nandi, U., Mandal, J. K., Efficiency and capability of fractal image compression with adaptive quadtree partitioning, The International Journal of Multimedia & Its Applications, 5(4): 53, (2013).
- [13] Xu, C., Xie, D., Guo, H., He, J., Chen, M., “Optimization Method for Fractal Image Compression Based on Self-similarity Evaluation and Gradient Bisection Algorithm”, In International Conference on Intelligent Computing (pp. 218-233). Singapore: Springer Nature, Singapore, (2024).
- [14] Aslan, N., Aslan, İ., “Approximation to the classical fractals by using non-affine contraction mappings”, Portugaliae Mathematica, 79: 45–60, (2022).
Toplam 14 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Görüntü İşleme, Yaklaşım Teorisi ve Asimptotik Yöntemler, Uygulamalı Matematik (Diğer) |
| Bölüm | Mathematics |
| Yazarlar | |
| Erken Görünüm Tarihi | 11 Aralık 2024 |
| Yayımlanma Tarihi | 1 Mart 2025 |
| Gönderilme Tarihi | 25 Ocak 2024 |
| Kabul Tarihi | 8 Kasım 2024 |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 38 Sayı: 1 |