پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 610 |
| تعداد مقالات | 9,026 |
| تعداد مشاهده مقاله | 67,082,746 |
| تعداد دریافت فایل اصل مقاله | 7,656,162 |
Edge-preserving smoothing of Perona-Malik nonlinear diffusion in two-dimensions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 10، دوره 16، شماره 1، فروردین 2025، صفحه 113-122 اصل مقاله (417.6 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.21467.2261 | ||
| نویسندگان | ||
| Anas Tiarimti-Alaoui* ؛ Mostafa Jourhmane | ||
| TIAD Laboratory, Department of Mathematics, Faculty of Sciences and Technics, Sultan Moulay Slimane University, Beni Mellal 23000, Morocco | ||
| تاریخ دریافت: 08 مهر 1399، تاریخ پذیرش: 02 دی 1402 | ||
| چکیده | ||
| It has been thirty years since Perona and Malik (PM) introduced the nonlinear diffusion equation in image processing and analysis. The problem's complexity was to find a suitable and adaptive diffusion function that smooths away noise or textures while preserving sharp edges of a sufficiently smooth intensity. This paper provides a new two-dimensional analysis of the PM diffusion equation to examine its behavior during scales and an explicit formula to select the right diffusion function adequately. In this context, we study the PM equation at the zero crossings of the first and second directional derivatives of a sufficiently smooth function in the gradient direction. | ||
| کلیدواژه‌ها | ||
| Nonlinear PDE؛ Diffusion Function؛ Scale-Space؛ Edge-Detection؛ Image Processing | ||
| مراجع | ||
|
[1] G. Aubert and P. Kornprobst, Image restoration, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, Springer, New York, NY, 2006, pp. 65–147. [2] J. Babaud, A.P Witkin, M. Baudin, and R.O Duda, Uniqueness of the Gaussian kernel for scale-space filtering, IEEE Trans. Pattern Anal. Mach. Intell. PAMI 8 (1986), no. 1, 26–33. [3] T. Barbu, Robust anisotropic diffusion scheme for image noise removal, Procedia Comput. Sci. 35 (2014), 522–530. [4] J. Canny, A computational approach to edge detection, IEEE Trans. Pattern Anal. Mach. Intell. PAMI 8 (1986), no. 6, 679–698. [5] P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, Deterministic edge-preserving regularization in computed imaging, IEEE Trans. Image Process. 6 (1997), no. 2, 298–311. [6] J.J. Clark, Authenticating edges produced by zero-crossing algorithms, IEEE Trans. Pattern Anal. Mach. Intell. 11 (1989), no. 1, 43–57. [7] R.M. Haralick, Digital step edges from zero crossing of second directional derivatives, IEEE Trans. Pattern Anal. Mach. Intell. PAMI 6 (1984), no. 1, 58–68. [8] R.A. Hummel, Representations based on zero-crossings in scale-space, In Readings in Computer Vision, Morgan Kaufmann, San Francisco, CA, 1987. [9] J.J. Koenderink, The structure of images, Biol. Cybern. 50 (1984), no. 5, 363–370. [10] T. Lindeberg, Feature detection in scale-space, Scale-Space Theory in Computer Vision, Springer US, Boston, MA, 1994, pp. 149–162. [11] B.J. Maiseli, On the convexification of the perona–malik diffusion model, Signal Image Video Process. 14 (2020), 1283–1291. [12] B.J. Maiseli and H. Gao, Robust edge detector based on anisotropic diffusion-driven process, Inf. Process. Lett. 116 (2016), no. 5, 373–378. [13] P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell. 12 (1990), no. 7, 629–639. [14] H.K. Rafsanjani, M.H. Sedaaghi, and S. Saryazdi, Efficient diffusion coefficient for image denoising, Comput. Math. Appl. 72 (2016), no. 4, 893–903. [15] B.M. ter Haar Romeny, Differential structure of images, Front-End Vision and Multi-Scale Image Analysis: Multi-Scale Computer Vision Theory and Applications, written in Mathematics, Springer Netherlands, Dordrecht, 2003, pp. 91–136. [16] J. Weickert, Anisotropic Diffusion in Image Processing, Treubner Verlag, Stuttgart, 1998. [17] A. Witkin, Scale-space filtering: A new approach to multi-scale description, ICASSP ’84. IEEE Int. Conf. Acoustics, Speech, and Signal Process., 9 (1984), 150–153. [18] A.L. Yuille and T.A. Poggio, Scaling theorems for zero crossings, IEEE Trans. Pattern Anal. Mach. Intell. PAMI 8 (1986), no. 1, 15–25. | ||
|
آمار تعداد مشاهده مقاله: 450 تعداد دریافت فایل اصل مقاله: 187 |
||