### Impacto

Bustince, H. and Pagola, M. and Fernandez, J. and Melo-Pinto, P. and Couto, P. and Tizhoosh, H.R. and Montero de Juan, Francisco Javier
(2010)
*Ignorance functions. An application to the calculation of the threshold in prostate ultrasound images.*
Fuzzy Sets and Systems, 161
(1).
pp. 20-36.
ISSN 0165-0114

PDF
Restringido a Repository staff only hasta 2020. 519kB |

Official URL: http://www.sciencedirect.com/science/article/pii/S0165011409001389

## Abstract

In this paper, we define the concept of an ignorance function and use it to determine the best threshold with which to binarize an image. We introduce a method to construct such functions from t-norms and automorphisms. By means of these new measures, we represent the degree of ignorance of the expert when given one fuzzy set to represent the background and another to represent the object. From this ignorance degree, we assign interval-valued fuzzy sets to the image in such a way that the best threshold is given by the interval-valued fuzzy set with the lowest associated ignorance. We prove that the proposed method provides better thresholds than the fuzzy classical methods when applied to transrectal prostateultrasoundimages. The experimental results on ultrasound and natural images also allow us to determine the best choice of the function to represent the ignorance.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Ignorance function; Interval-valued fuzzy set; Interval-valued fuzzy entropy; Image thresholding; Ultrasoundimages |

Subjects: | Sciences > Mathematics > Logic, Symbolic and mathematical |

ID Code: | 16020 |

References: | American Cancer Society: Cancer Facts and Figures 2007 P. Burillo, H. Bustince Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets Fuzzy Sets and Systems, 78 (1996), pp. 305–3016 P. Burillo, H. Bustince Construction theorems for intuitionistic fuzzy sets Fuzzy Sets and Systems, 84 (1996), pp. 271–281 H. Bustince Construction of intuitionistic fuzzy relations with predetermined properties Fuzzy Sets and Systems, 109 (2000), pp. 379–403 H. Bustince, E. Barrenechea, M. Pagola Restricted equivalence functions Fuzzy Sets and Systems, 157 (2006), pp. 2333–2346 H. Bustince, E. Barrenechea, M. Pagola Image thresholding using restricted equivalence functions and maximizing the measures of similarity Fuzzy Sets and Systems, 158 (2007), pp. 496–516 H. Bustince, M. Pagola, E. Barrenechea Construction of fuzzy indices form DI-subsethood measures: application to the global comparison of images Information Sciences, 177 (2007), pp. 906–929 H. Bustince, J. Montero, E. Barrenechea, M. Pagola Semiautoduality in a restricted family of aggregation operators Fuzzy Sets and Systems, 158 (12) (2007), pp. 1360–1377 H. Bustince, M. Pagola, E. Barrenechea, R. Orduna, Representation of uncertainty associated with the fuzzification of an image by means of interval type 2 fuzzy sets. Application to threshold computing, in: B. De Baets, L. Martinez, L.G. Perez (Eds.), Proc. EUROFUSE Workshop: New Trends in Preference Modelling, EUROFUSE, Jaén, Spain, 2007, pp. 73–78. H. Bustince, E. Barrenechea, M. Pagola Relationship between restricted dissimilarity functions, restricted equivalence functions and EN normal functions: image thresholding invariant Pattern Recognition Letters, 29 (2008), pp. 525–536 H. Bustince, M. Pagola, P. Melo-Pinto, E. Barrenechea, P. Couto, Use of Atanassov's intuitionistic fuzzy sets for modelling the uncertainty of the thresholds associated to an image, in: Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. Intelligent Systems from Decision Making to Data Mining, Web Intelligence and Computer Vision, Springer, Berlin, 2008. H. Bustince, E. Barrenechea, M. Pagola Generation of interval-valued fuzzy and Atanassov's intuitionistic fuzzy connectives from fuzzy connectives and from Kα operators. Laws for conjunctions and disjunctions. Amplitude International Journal of Intelligent systems, 23 (2008), pp. 680–714 O. Castillo, P. Melin, Fuzzy logic for plant monitoring and diagnostics, in: Proc. 2004 IEEE Internat. Conf. Fuzzy Systems, Vol. 1, 2004, pp. 25–29. T. Chaira, A.K. Ray Segmentation using fuzzy divergence Pattern Recognition Letters, 24 (2003), pp. 1837–1844 T. Chaira, A.K. Ray Region extraction using fuzzy similarity measures Journal of Fuzzy Mathematics, 11 (2003), pp. 601–607 T. Chaira, A.K. Ray A new measure using intuitionistic fuzzy set theory and its application to edge detection Applied Soft Computing, 8 (2) (2008), pp. 919–927 P. Couto, M. Pagola, H. Bustince, E. Barrenechea, P. Melo-Pinto, Image segmentation using A-IFS, in: 12th Conf. Information Processing and Management of Uncertainty in Knowledge-Based Systems, Malaga, Spain, 2008, pp. 1620–1627. D. Dubois, On degrees of truth, partial ignorance and contradiction, in: L. Magdalena, M. Ojeda-Aciago, J.L. Verdegay (Eds.), Proc. Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU, Málaga, Spain, 2008, pp. 31–38. I. Glockner, Towards an operational interpretation of membership grades. On H-valued fuzzy sets and their use for fuzzy quantification, in: Symp. Foundation of Computational Intelligence FOCI’07, EEUU, 2007. N. Hu, D.B. Downey, A. Fenster, H.M. Ladak Prostate boundary segmentation from 3D ultrasoundimages Medical Physics, 30 (7) (2003), pp. 1648–1659 L.K. Huang, M.J. Wang Image thresholding by minimizing the measure of fuzziness Pattern Recognition, 28 (1) (1995), pp. 41–51 C. Knoll, M. Alcaniz, V. Grau, C. Monserrat, M.C. Juan Outlining of the prostate using snakes with shape restrictions based on the wavelet transform Pattern Recognition, 32 (1999), pp. 1767–1781 H.M. Ladak, F. Mao, Y. Wang, D.B. Downey, D.A. Steinman, A. Fenster Prostate boundary segmentation from 2D ultrasoundimages Medical Physics, 27 (2000), pp. 1777–1788 N. Otsu A threshold selection method from gray level histograms IEEE Transactions on Systems, Man and Cybernetics, 9 (1979), pp. 62–66 F. Sahba, H.R. Tizhoosh, M.M. Salama A coarse-to-fine approach to prostate boundary segmentation in ultrasoundimages Biomedical Engineering Online, 4 (2005), p. 58 R. Sambuc, Function Φ-Flous, Application a l’aide au Diagnostic en Pathologie Thyroidienne, These de Doctorat en Medicine, University of Marseille, 1975. E. Szmidt, J. Kacprzyk Entropy for intuitionistic fuzzy sets Fuzzy Sets and Systems, 118 (3) (2001), pp. 467–477 H.R. Tizhoosh Image thresholding using type-2 fuzzy sets Pettern Recognition, 38 (2005), pp. 2363–2372 E. Trillas, Sobre funciones de negación en la teoría de conjuntos difusos, in: S. Barro et al. (Eds.), Stochastica, III-1, 47–59 (1979) (in Spanish). English version in Advances of Fuzzy Logic, Universidad de Santiago de Compostela, 1998, pp. 31–43. I.K. Vlachos, G.D. Sergiadis Intuitionistic fuzzy information—applications to pattern recognition Pattern Recognition Letters, 28 (2007), pp. 197–206 L.A. Zadeh Fuzzy sets Information Control, 8 (1965), pp. 338–353 |

Deposited On: | 20 Jul 2012 10:33 |

Last Modified: | 06 Feb 2014 10:36 |

Repository Staff Only: item control page