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Erschienen in: Pattern Analysis and Applications 1/2017

31.01.2015 | Theoretical Advances

Improving a firefly meta-heuristic for multilevel image segmentation using Tsallis entropy

verfasst von: Paulo S. Rodrigues, Guilherme A. Wachs-Lopes, Horst R. Erdmann, Monael P. Ribeiro, Gilson A. Giraldi

Erschienen in: Pattern Analysis and Applications | Ausgabe 1/2017

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Abstract

In this paper we show that the non-extensive Tsallis entropy, when used as kernel in the bio-inspired firefly algorithm for multi-thresholding in image segmentation, is more efficient than using the traditional cross-entropy presented in the literature. The firefly algorithm is a swarm-based meta-heuristic, inspired by fireflies-seeking behavior following their luminescence. We show that the use of more convex kernels, as those based on non-extensive entropy, is more effective at \(5\,\%\) of significance level than the cross-entropy counterpart when applied in synthetic spaces for searching thresholds in global minimum.

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Fußnoten
1
We define the composed distribution, also called direct product of \(P=(p_{1},\ldots ,p_{n})\) and \(Q=(q_{1},\ldots ,q_{m})\), as \(P*Q=\{p_{i}q_{j}\}_{i,j}\), with \(1\le i\le n\) and \(1\le j\le m\)
 
Literatur
1.
Zurück zum Zitat Abutaleb AS (1989) A new method for gray-level picture thresholding using the entropy of the histogram. Comput Graph Image Process 47:22–32CrossRef Abutaleb AS (1989) A new method for gray-level picture thresholding using the entropy of the histogram. Comput Graph Image Process 47:22–32CrossRef
2.
Zurück zum Zitat Albuquerque MP, Albuquerque MP, Esquef IA, Mello ARG (2004) Image thresholding using Tsallis entropy. Pattern Recogn Lett 25:1059–1065CrossRef Albuquerque MP, Albuquerque MP, Esquef IA, Mello ARG (2004) Image thresholding using Tsallis entropy. Pattern Recogn Lett 25:1059–1065CrossRef
3.
Zurück zum Zitat Chang C-I, Du Y, Wang J, Guo S-M, Thouin PD (2006) Survey and comparative analysis of entropy and relative entropy thresholding techniques. IEEE Proc Vis Image Signal Process 153(6):837–850CrossRef Chang C-I, Du Y, Wang J, Guo S-M, Thouin PD (2006) Survey and comparative analysis of entropy and relative entropy thresholding techniques. IEEE Proc Vis Image Signal Process 153(6):837–850CrossRef
4.
Zurück zum Zitat Cardoso JS, Corte-Real L (2005) Toward a generic evaluation of image segmentation. IEEE Trans Image Process 14(11):1773–1782CrossRef Cardoso JS, Corte-Real L (2005) Toward a generic evaluation of image segmentation. IEEE Trans Image Process 14(11):1773–1782CrossRef
5.
Zurück zum Zitat Cheng HD, Shan J, Ju W, Guo Y, Zhang L (2010) Automated breast cancer detection and classification using ultrasound images: a survey. Pattern Recogn 43:299–317CrossRefMATH Cheng HD, Shan J, Ju W, Guo Y, Zhang L (2010) Automated breast cancer detection and classification using ultrasound images: a survey. Pattern Recogn 43:299–317CrossRefMATH
6.
Zurück zum Zitat Dorigo M (1992) Optimization, learning, and natural algorithms. Ph.D. Thesis, “Dipartimento di Elettronica e Informazione, Politecnico di Milano,” Italy Dorigo M (1992) Optimization, learning, and natural algorithms. Ph.D. Thesis, “Dipartimento di Elettronica e Informazione, Politecnico di Milano,” Italy
8.
Zurück zum Zitat Goldberg DE (1997) Genetic algorithms in search, optimization, and machine learning. Addison Wesley, Boston, USA Goldberg DE (1997) Genetic algorithms in search, optimization, and machine learning. Addison Wesley, Boston, USA
9.
Zurück zum Zitat Gonzalez RC, Woods RE (1992) Digital image processing. Addison Wesley, Boston, USA Gonzalez RC, Woods RE (1992) Digital image processing. Addison Wesley, Boston, USA
10.
Zurück zum Zitat Hassanzadeh T, Vojodi H, Eftekhari AM (2011) An image segmentation approach based on maximum variance intra-cluster method and FireFly algorithm. In: IEEE (ed) Seventh international conference on natural computation, Shanghai, China, pp 1844–1848 Hassanzadeh T, Vojodi H, Eftekhari AM (2011) An image segmentation approach based on maximum variance intra-cluster method and FireFly algorithm. In: IEEE (ed) Seventh international conference on natural computation, Shanghai, China, pp 1844–1848
11.
Zurück zum Zitat Horng MH, Liou RJ (2011) Multilevel minimum cross entropy threshold selection based on fire-fly algorithm. Exp Syst Appl 38:14805–14811CrossRef Horng MH, Liou RJ (2011) Multilevel minimum cross entropy threshold selection based on fire-fly algorithm. Exp Syst Appl 38:14805–14811CrossRef
12.
Zurück zum Zitat Kapur JN, Sahoo PK, Wong AKC (1985) A new method for gray-level picture thresholding using the entropy of the histogram. Comput Graph Image Process 29:273–285CrossRef Kapur JN, Sahoo PK, Wong AKC (1985) A new method for gray-level picture thresholding using the entropy of the histogram. Comput Graph Image Process 29:273–285CrossRef
13.
Zurück zum Zitat Kennedy J, Goldberg RC (1997) Particle swarm optimization. Proc IEEE Int Conf Neural Netw 4:1942–1948CrossRef Kennedy J, Goldberg RC (1997) Particle swarm optimization. Proc IEEE Int Conf Neural Netw 4:1942–1948CrossRef
15.
Zurück zum Zitat Kullback S (1968) Information theory statistics. Dover, New YorkMATH Kullback S (1968) Information theory statistics. Dover, New YorkMATH
16.
Zurück zum Zitat Li CH, Lee CK (1993) Minimum cross entropy thresholding. Pattern Recogn 26:617–625CrossRef Li CH, Lee CK (1993) Minimum cross entropy thresholding. Pattern Recogn 26:617–625CrossRef
17.
Zurück zum Zitat Lukasik S, Zak S (2009) Fire y algorithm for continuous constrained optimization tasks. In: 1st international conference on computational collective intelligence and semantic web, pp 5–7 Lukasik S, Zak S (2009) Fire y algorithm for continuous constrained optimization tasks. In: 1st international conference on computational collective intelligence and semantic web, pp 5–7
18.
Zurück zum Zitat Pal NR (1996) On minimum cross entropy thresholding. Pattern Recogn 26:575–580CrossRef Pal NR (1996) On minimum cross entropy thresholding. Pattern Recogn 26:575–580CrossRef
19.
Zurück zum Zitat Pun T (1981) Entropic thresholding: a new approach. Comput Graph Image Process 16:210–239CrossRef Pun T (1981) Entropic thresholding: a new approach. Comput Graph Image Process 16:210–239CrossRef
20.
Zurück zum Zitat Rodrigues PS, Giraldi GA (2009) Computing the q-index for Tsallis nonex- tensive image segmentation. In: IEEE Society (ed) Proceedings of the XXII international Simposium on Computer Graphics and Image Processing. Rio de Janeiro, pp 232–237 Rodrigues PS, Giraldi GA (2009) Computing the q-index for Tsallis nonex- tensive image segmentation. In: IEEE Society (ed) Proceedings of the XXII international Simposium on Computer Graphics and Image Processing. Rio de Janeiro, pp 232–237
21.
Zurück zum Zitat Rodrigues PS, Giraldi GA (2011) Improving the non-extensive medical image segmentation based on Tsallis entropy. Pattern Anal Appl 14(4):369–379MathSciNetCrossRef Rodrigues PS, Giraldi GA (2011) Improving the non-extensive medical image segmentation based on Tsallis entropy. Pattern Anal Appl 14(4):369–379MathSciNetCrossRef
22.
Zurück zum Zitat Rodrigues PS, Giraldi GA, Chang RF, Suri J (2008) Automatic classification of breast lesions in 3D ultrasound images. In: Advances in diagnostic and therapeutic ultrasound imaging, Chapter 8. Artech House, Boston and London, pp 189–2232 Rodrigues PS, Giraldi GA, Chang RF, Suri J (2008) Automatic classification of breast lesions in 3D ultrasound images. In: Advances in diagnostic and therapeutic ultrasound imaging, Chapter 8. Artech House, Boston and London, pp 189–2232
23.
Zurück zum Zitat Rodrigues PS, Giraldi GA, Suri J, Chang RF (2006) Non-extensive entropy for cad systems for breast cancer images. In: IEEE Computer Society (ed) International symposium on computer graphics and image processing, SIBIGRAPI’06, Manaus, 8–11 October 2006, pp 121–128 Rodrigues PS, Giraldi GA, Suri J, Chang RF (2006) Non-extensive entropy for cad systems for breast cancer images. In: IEEE Computer Society (ed) International symposium on computer graphics and image processing, SIBIGRAPI’06, Manaus, 8–11 October 2006, pp 121–128
24.
Zurück zum Zitat Sahoo P, Soltani S, Wong A, Chen Y (1988) A survey of thresholding techniques. Comput Vis Graph Image Process 41(1):233–260CrossRef Sahoo P, Soltani S, Wong A, Chen Y (1988) A survey of thresholding techniques. Comput Vis Graph Image Process 41(1):233–260CrossRef
25.
Zurück zum Zitat Sezgin M, Sankur B (2004) Survey over image thresholding techniques and quantitative performance evaluation. J of Electr Imaging 13(1):146–165CrossRef Sezgin M, Sankur B (2004) Survey over image thresholding techniques and quantitative performance evaluation. J of Electr Imaging 13(1):146–165CrossRef
26.
Zurück zum Zitat Shannon C, Weaver W (1948) The mathematical theory of communication. University of Illinois Press, UrbanaMATH Shannon C, Weaver W (1948) The mathematical theory of communication. University of Illinois Press, UrbanaMATH
27.
Zurück zum Zitat Suri JS, Rangayyan RM (eds) (2006) Recent advances in breast imaging, mammography and computer aided diagnosis of breast cancer. SPIE, Bellingham Suri JS, Rangayyan RM (eds) (2006) Recent advances in breast imaging, mammography and computer aided diagnosis of breast cancer. SPIE, Bellingham
28.
Zurück zum Zitat Tavares AHMP (2003) Aspectos matematicos da entropia. Master thesis, Universidade de Aveiro Tavares AHMP (2003) Aspectos matematicos da entropia. Master thesis, Universidade de Aveiro
29.
Zurück zum Zitat Tsallis C (1999) Nonextensive statistics: theoretical, experimental and computational evidences and connections. Braz J Phys 29:1–35CrossRef Tsallis C (1999) Nonextensive statistics: theoretical, experimental and computational evidences and connections. Braz J Phys 29:1–35CrossRef
30.
Zurück zum Zitat Wu SH, Zhang XJ, Wu YQ (2011) Two-dimensional exponential cross entropy image thresholding based on decomposition. Signal Process 4:546–551 Wu SH, Zhang XJ, Wu YQ (2011) Two-dimensional exponential cross entropy image thresholding based on decomposition. Signal Process 4:546–551
31.
Zurück zum Zitat Wu S, Zhang Y, Wu Y, Song Y (2011) Multilevel thresholding based on exponential cross entropy and niche Chaotic particle swarm optimization. In: Wu Y (ed) Advances in computer, communication, control & automation. LNEE 121. Springer, Berlin, Heidelberg, pp 617–624 Wu S, Zhang Y, Wu Y, Song Y (2011) Multilevel thresholding based on exponential cross entropy and niche Chaotic particle swarm optimization. In: Wu Y (ed) Advances in computer, communication, control & automation. LNEE 121. Springer, Berlin, Heidelberg, pp 617–624
32.
Zurück zum Zitat Yang XS (2009) Firefly algorithms for multimodal optimization. In: Stochastic algorithms: fundation and applications, SAGA 2009. Lecture notes in computer science, vol 5792, pp 169–178 Yang XS (2009) Firefly algorithms for multimodal optimization. In: Stochastic algorithms: fundation and applications, SAGA 2009. Lecture notes in computer science, vol 5792, pp 169–178
33.
Zurück zum Zitat Yin PY (2007) Multilevel minimum cross entropy threshold selection based on particle swarm optimization. Appl Math Comput 184:503–513MathSciNetMATH Yin PY (2007) Multilevel minimum cross entropy threshold selection based on particle swarm optimization. Appl Math Comput 184:503–513MathSciNetMATH
Metadaten
Titel
Improving a firefly meta-heuristic for multilevel image segmentation using Tsallis entropy
verfasst von
Paulo S. Rodrigues
Guilherme A. Wachs-Lopes
Horst R. Erdmann
Monael P. Ribeiro
Gilson A. Giraldi
Publikationsdatum
31.01.2015
Verlag
Springer London
Erschienen in
Pattern Analysis and Applications / Ausgabe 1/2017
Print ISSN: 1433-7541
Elektronische ISSN: 1433-755X
DOI
https://doi.org/10.1007/s10044-015-0450-x

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