Vector Self-dual Morphological Filtering Operators
-
摘要: 自对偶形态学算子不依赖形态学腐蚀、膨胀算子的先后次序, 是一种等同处理图像背景和前景的形态学算子. 而将自对偶形态学算子拓展到多通道图像处理是一个难题. 为了解决该问题, 提出了基于极值约束的矢量自对偶形态学滤波算子(EC-VSDMF). 首先根据对称矢量排序算法构建满足对偶性的矢量形态学算子, 然后依据形态学算子中的极值原理优化矢量集合, 从而有效抑制矢量集合中包含单通道极值的矢量作为输出结果, 最终实现了具有约束功能的矢量自对偶形态学滤波算子(VSDMF). 实验结果表明, EC-VSDMF继承了传统自对偶形态学滤波算子的性质, 将其应用于彩色图像滤波可以改善现有矢量形态学滤波算子导致滤波后图像亮度和色度发生偏移的问题. 滤波后的图像在有效抑制噪声的同时较好地保留了图像细节, 滤波性能甚至超过了多种现有的矢量中值滤波算子.Abstract: Self-dual morphological filtering operators do not rely on the order of the sequence of erosion or dilation. They treat the foreground and background of an image identically. However, it is difficult to apply self-dual morphological operators to multi-channel images. To overcome the problem, vector self-dual morphological filtering operators based on extremum constraint (EC-VSDMF) is proposed in this paper. Firstly, a symmetric vector ordering is introduced to construct vector morphological operators with duality. Besides, vector sets are optical according to the extremum principle of morphological theory. And thus vectors including opposite extrema in single channels are suppressed. Finally, EC-VSDMF is constructed and applied to color image filtering. Experimental results show that the proposed EC-VSDMF inherits the properties of classic self-dual morphological operators. The problem that the brightness, saturation and hue of the filtered image turn to larger or smaller compared to the original image is also addressed. Moreover, EC-VSDMF can suppress noises efficiently while maintaining the image detail, even it can provide better results compared with the various vector median filtering operators.
-
[1] Najman L, Talbot H. Mathematical Morphology. New York: John Wiley and Sons, USA, 2013. [2] [2] Aptoula E, Lefvre S. A comparative study on multivariate mathematical morphology. Pattern Recognition, 2007, 40(11): 2914-2929 [3] [3] Velasco-Forero S, Angulo J. Classification of hyperspectral images by tensor modeling and additive morphological decomposition. Pattern Recognition, 2013, 46(2): 566-577 [4] [4] Valle M E, Vicente D M G. Sparsely connected autoassociative lattice memories with an application for the reconstruction of color images. Journal of Mathematical Imaging and Vision, 2012, 44(3): 195-222 [5] [5] Morales S, Naranjo V, Angulo J, Raya M A. Automatic detection of optic disc based on PCA and mathematical morphology. IEEE Transactions on Medical Imaging, 2013, 32(4): 786-796 [6] [6] Velasco-Forero S, Angulo J, Chanussot J. Morphological image distances for hyperspectral dimensionality exploration using Kernel-PCA and ISOMAP. In: Proceedings of the 2009 IEEE International Geoscience and Remote Sensing Symposium. Cape Town: IEEE, 2009. III-109-III-112 [7] [7] Velasco-Forero S, Angulo J. Morphological scale-space for hyperspectral images and dimensionality exploration using tensor modeling. In: Proceedings of the 1st Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing. Grenoble: IEEE, 2009. 1-4 [8] [8] Tsalides P, Vardavoulia M I, Andreadis I. Vector ordering and morphological operations for colour image processing: fundamentals and applications. Pattern Analysis and Applications, 2002, 5(3): 271-287 [9] [9] Louverdis G, Vardavoulia M I, Andreadis I, Tsalides P. A new approach to morphological color image processing. Pattern Recognition, 2002, 35(8): 1733-1741 [10] De Witte V, Schulte S, Nachtegael M, van der Weken D, Kerre E E. Vector morphological operators for colour images. In: Proceedings of the 2nd International Conference on Image Analysis and Recognition, Lecture Notes in Computer Science. Toronto, Canada: Springer, 2005, 3656: 667 -675 [11] Angulo J. Morphological colour operators in totally ordered lattices based on distances: application to image filtering, enhancement and analysis. Computer Vision and Image Understanding, 2007, 107(1-2): 56-73 [12] Aptoula E, Lefvre S. On lexicographical ordering in multivariate mathematical morphology. Pattern Recognition Letters, 2008, 29(2): 109-118 [13] Aptoula E, Lefvre S. -Trimmed lexicographical extrema for pseudo-morphological image analysis. Journal of Visual Communication and Image Representation, 2008, 19(3): 165-174 [14] Lei T, Wang Y, Fan Y Y, Zhao J. Vector morphological operators in HSV color space. Science China Information Sciences, 2013, 56(1): 1-12 [15] Angulo J. Geometric algebra colour image representations and derived total orderings for morphological operators Part I: colour quaternions. Journal of Visual Communication and Image Representation, 2010, 21(1): 33-48 [16] Angulo J. Hypercomplex mathematical morphology. Journal of Mathematical Imaging and Vision, 2011, 41(1-2): 86-108 [17] Lei T, Fan Y Y, Zhang C R, Wang X P. Vector mathematical morphological operators based on fuzzy extremum estimation. In: Proceedings of the 20th IEEE International Conference on Image Processing (ICIP). Melbourne, VIC: IEEE, 2013. 3031-3034 [18] Lezoray O, Elmoataz A. Nonlocal and multivariate mathematical morphology. In: Proceedings of the 19th IEEE International Conference on Image Processing (ICIP). Orlando, FL: IEEE, 2012. 129-132 [19] Velasco-Forero S, Angulo J. Random projection depth for multivariate mathematical morphology. IEEE Journal of Selected Topics in Signal Processing, 2012, 6(7): 753-763 [20] Velasco-Forero S, Angulo J. Morphological processing of hyperspectral images using kriging-based supervised ordering. In: Proceedings of the 17th IEEE ICIP on Image Processing. Hong Kong, China: IEEE, 2010. 1409-1412 [21] Velasco-Forero S, Angulo J. Supervised ordering in RP: application to morphological processing of hyperspectral images. IEEE Transactions on Image Processing, 2011, 20(11): 3301-3308 [22] Heijmans H J A M. Self-dual morphological operators and filters. Journal of Mathematical Imaging and Vision, 1996, 6(1): 15-36 [23] Ray N, Acton S T. Inclusion filters: a class of self-dual connected operators. IEEE Transactions on Image Processing, 2005, 14(11): 1736-1746 [24] Bouaynaya N, Charif-Chefchaouni M, Schonfeld D. M-idempotent and self-dual morphological filters. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012, 34(4): 805-813 [25] Lei T, Fan Y Y. Noise gradient reduction based on morphological dual operators. IET Image Processing, 2011, 5(1): 1 -17 [26] Soille P. Beyond self-duality in morphological image analysis. Image and Vision Computing, 2005, 23(2): 249-257 [27] Lei Tao, Fan Yang-Yu, Mao Li. Generalized self-dual morphological filters and the applications in image-denoising. Journal of Optoelectronics Laser, 2011, 21(1): 7215-7218 (雷涛, 樊养余, 毛力. 广义自对偶形态学滤波器及其在图像去噪中的应用. 光电子激光, 2011, 21(1): 7215-7218) [28] Astola J, Haavisto P, Neuvo Y. Vector median filters. Proceedings of the IEEE, 1990, 78(4): 678-689 [29] Lukac R. Adaptive vector median filtering. Pattern Recognition Letters, 2003, 24(12): 1889-1899 [30] Smolka B, Chydzinski A. Fast detection and impulsive noise removal in color images. Real-Time Imaging, 2005, 11(5-6): 389-402 [31] Jin L H, Li D H. A switching vector median filter based on the CIELAB color space for color image restoration. Signal Processing, 2007, 87(6): 1345-1354 [32] Celebi M E, Aslandogan Y A. Robust switching vector median filter for impulsive noise removal. Journal of Electronic Imaging, 2008, 17(4): 043006 (1-9) [33] Camarena J G, Gregori V, Morillas S, Sapena A. Two-step fuzzy logic-based method for impulse noise detection in colour images. Pattern Recognition Letters, 2010, 31(13): 1842-1849 [34] Geng X, Hu X G, Xiao J. Quaternion switching filter for impulse noise reduction in color image. Signal Processing, 2012, 92(1): 150-162
点击查看大图
计量
- 文章访问数: 1510
- HTML全文浏览量: 88
- PDF下载量: 917
- 被引次数: 0