On the importance of metrics in practical applications
DOI:
https://doi.org/10.4995/msel.2011.3066Palabras clave:
Colour image filter, Fuzzy metric, Impulse noiseResumen
Students motivation for learning mathematical concepts can be increased when showing the usefulness of these concepts in practical problems. One important mathematical concept is the concept of metric space and, more related to the applications, the concept of metric function. In this work we aim to illustrate how important is to appropriately choose the metric when dealing with a practical problem. In particular, we focus on the problem of detection of noisy pixels in colour images. In this context, it is very important to appropriately measure the distances and similarities between the image pixels, which is done by means of an appropriate metric. We study the performance of different metrics, including recent fuzzy metrics, within a specific filter to show that it is indeed a critical choice to appropriately solve the task.Descargas
Citas
J. Astola, P. Haavisto, Y. Neuvo, Vector Median Filters, Proc. IEEE , vol. 78 num. 4, pp. 678-689, 1990. http://dx.doi.org/10.1109/5.54807
K.N. Plataniotis, A.N. Venetsanopoulos, Color Image Processing and Applications, Springer-Verlag , Berlin, 2000. http://dx.doi.org/10.1007/978-3-662-04186-4
R. Lukac, B. Smolka, K. Martin, K.N. Plataniotis, A.N. Venetsanopoulos, Vector Filter- ing for Color Imaging, IEEE Signal Processing Magazine, Special Issue on Color Image Processing , vol. 22 num. 1, pp. 74-86, 2005.
R. Lukac, K.N. Plataniotis, A taxonomy of color image filtering and enhancement solutions, in Advances in Imaging and Electron Physics, (eds.) P.W. Hawkes, Elsevier, 140, 187-264, 2006.
B. Smolka, A. Chydzinski, Fast detection and impulsive noise removal in color images, Real-Time Imaging, vol. 11 num. 5-6, pp. 389-402, 2005. http://dx.doi.org/10.1016/j.rti.2005.07.003
J.G. Camarena, V. Gregori, S. Morillas, A. Sapena, Fast detection and removal of impulsive noise using peer groups and fuzzy metrics, Journal of Visual Communication and Image Representation 19 (2008) 20-29. http://dx.doi.org/10.1016/j.jvcir.2007.04.003
J.G. Camarena, V. Gregori, S. Morillas, A. Sapena, Some improvements for image filtering using peer group techniques, Image and Vision Computing /, in press.
J.G. Camarena, V. Gregori, S. Morillas, A. Sapena, Two-step fuzzy logic-based method for impulse noise detection in colour images, Pattern Recognition Letters,In Press Corrected Proof http://dx.doi.org/10.1016/j.patrec.2010.01.008
B. Smolka, K.N. Plataniotis, A. Chydzinski, M. Szczepanski, A.N. Venetsanopoulos, K. Wojciechowski, Self-adaptive algorithm of impulsive noise reduction in color images, Pat- tern Recognition, 35 8 (2002) 1771-1784. http://dx.doi.org/10.1016/S0031-3203(01)00169-8
S. Schulte, S. Morillas, V. Gregori, E.E. Kerre, A New Fuzzy Color Correlated Impulsive Noise Reduction Method, IEEE Transactions on Image Processing 16 10 (2007) 2565-2575. http://dx.doi.org/10.1109/TIP.2007.904960
Chung-Chia Kang, Wen-June Wang, Fuzzy reasoning-based directional median filter de- sign, Signal Processing 89 (2009) 344-351. http://dx.doi.org/10.1016/j.sigpro.2008.09.003
S. Morillas, V. Gregori, G. Peris-Fajarnés, P. Latorre, A fast impulsive noise color image filter using fuzzy metrics, Real-Time Imaging, 11 5-6 (2005) 417-428.
S. Morillas, V. Gregori, G. Peris-Fajarnés, Isolating impulsive noise pixels in color images by peer group techniques, Computer Vision and Image Understanding, 110 1 (2008) 102-116. http://dx.doi.org/10.1016/j.cviu.2007.05.001
S. Morillas, V. Gregori, G. Peris-Fajarnés, A. Sapena, New Adaptive Vector Filter Using Fuzzy Metrics, Journal of Electronic Imaging 16 3 (2007) 1-15. http://dx.doi.org/10.1117/1.2767335
S. Morillas, V. Gregori, G. Peris-Fajarnes, A. Sapena, Local Self-Adaptive Fuzzy Filter for Impulsive Noise Removal in Color Images, Signal Processing , 88 (2008) 390-398. http://dx.doi.org/10.1016/j.sigpro.2007.05.019
A. Sapena, A contribution to the study of fuzzy metric spaces, Appl. Gen. Topology 2 1 (2001) 63-76.
V. Gregori, S. Romaguera, Characterizing completable fuzzy metric spaces, Fuzzy Sets and Systems 144 (2004), 411-420. http://dx.doi.org/10.1016/S0165-0114(03)00161-1
A. George, P.V. Veeramani, On some results in fuzzy metric spaces, em Fuzzy Sets and Systems 64 (1994), 395-399. http://dx.doi.org/10.1016/0165-0114(94)90162-7
V. Gregori, S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Systems 115 (2000), 485-489. http://dx.doi.org/10.1016/S0165-0114(98)00281-4
Descargas
Publicado
Número
Sección
Licencia
Esta revista publica bajo una Creative Commons Attribution-NonCommercial 4.0 International License