1. Definição
A segmentação subdivide uma imagem nas suas regiões ou objectos constituintes. O nível pelo qual essa subdivisão é feita depende do problema a ser resolvido. Isto é, a segmentação deve terminar quando o objecto de interesse numa aplicação se encontra isolado. Não existe qualquer interesse em levar a segmentação além do nível de detalhe necessário à identificação dos elementos em estudo. A segmentação de imagens não triviais consiste numa das mais difíceis operações de processamento de imagem. A eficiência da segmentação determina o eventual sucesso ou insucesso dos posteriores procedimentos de análise computacional da imagem. Devido a tal, deverão ser tomados certos cuidados de forma a evitar uma segmentação rude, que conduza a uma análise errónea.
Os algoritmos de segmentação de imagens monocromáticas geralmente são baseados em
uma de duas propriedades associadas aos valores de intensidade da imagem:
descontinuidade e semelhança. Para a primeira propriedade, a aproximação considerada reside na partição da imagem baseada em variações abruptas de intensidade, tais como zonas limiares na imagem. As principais aproximações consideradas no caso da segunda propriedade são baseadas na partição da imagem em regiões que são semelhantes num critério predefinido [12].
2. Thresholding
Devido às suas propriedades intuitivas e simplicidade de implementação, a limitação da imagem em termos de intensidade goza de uma posição privilegiada no que respeita a aplicações de segmentação de imagem.
Geralmente o valor de “threshold” associado a uma imagem é determinado a partir do histograma de intensidades da respectiva imagem.
Supondo que é conhecido o histograma de intensidades da imagem, f(x,y) que se pretende analisar. Uma alternativa directa para retirar um dado objecto da restante imagem de fundo traduz-se em criar um valor limitador de intensidade, o conhecido valor de “threshold”. Assim, qualquer ponto (x,y) que verifique a condição f(x,y)≥T, designa-se ponto do objecto; em caso contrário o ponto é considerado como ponto de fundo ou seja:
< ≥ = T y x f se T y x f se y x G ) , ( 0 ) , ( 1 ) , ( (A.1)
Existem vários métodos de escolha de valores de “Threshold”, mas todos eles são baseados na representação do histograma de intensidades da imagem inicial.
(a) (b)
(c) (d)
Figura iv. Método de Binarização da imagem (a) Histograma de intensidades da imagem
inicial, (b) imagem binarizada com representação do objecto compacto, (c) Valor “Threshold” utilizado no procedimento de binarização e (d) imagem binarizada com
Bibliografia
[1] S. De Flora, L.R. Fergusson, “Overview of mechanisms of cancer chemopreventive
agents”, Mutation Research, 591, 8-15, 2005
[2] D.M. Livingston, R. Shivdasani, “Toward Mechanism – Based Cancer Care”, JAMA, Vol 285, No. 5, 588-593, 7 February, 2001
[3] S.D. Hunsting, T.J. Slaga, S.M. Fischer, J. DiGiovanni, J.M. Phang, “Mechanisms –
Based Cancer Prevention Approaches: Targets, Examples and the use of Transgenic Mice”, Journal of the National Cancer Institute, Vol 91, No. 93, 215, 3 February, 1999
[4] Alexander Herman, “Towards a General Model for Solid Tumor Growth”, Wesleyan Universit, SFI REU, 2002
[5] W. Hueck, “Patologia Morfológica”, Editorial Labor S.A., Barcelona, 1944
[6] Highanm, R.P. Brady, J.M., “ Mammographic Image Analysis”, Kluwer Academic Publishers, Dordrecht Boston, London, 1999
[7] Andolina, V.F.. Lillé, S.L. Willison, K.M., “Mammographic Imaging: A Practical
Guide”, Lippincott Company, 1992
[8] Highnam, R.P. Brady, J. M. Shepstone, B.J., “Computing the Scatter Component of
Mammographic Images”, IEEE Transactions in Medical Imaging, Vol 13, 301-313, 1994
[9] S. H. Heywang- Köbrunner, “Diagnostic Breast Imaging”, Thieme, 1997
[10] Roelof, T. Van Woundenberg, S. Hendriks, J.H.C.L. Boedicker, A. Evertsz, C.J.G. Karssemeijer, N., “Performance Evaluation of a Digital Reading Station for Screening
Mammography”, Digital Mammography in Computer Science, Springer-Verlag, Berlin
Heidelberg New York, 455-459, 2002
[11] Customer Information, “GE New Digital Detector X-Ray Technology”, GE Medical Systems in Europe, 2004
[12] Rafael C. Gonzalez, “Digital Image Processing using Matlab”, Prentice Hall, 2004
[13] Etta D. Pisano, Martin J. Yaffe, Cherie M. Kuzmiak, “Digital Mammography”, Lippincott Williams & Wilkins, 2004
[14] Lídia Salgueiro, J.G. Ferreira, “Introdução à Biofísica”, Fundação Calouste Gulbenkian, Lisboa, 1991
[15] J Duncan and N Ayache,: “Medical Image Analysis: Progress over two decades and
challenges ahead”. In IEEE trans. Pattern Analysis and Machine Inteligence, Vol 22, p85,
January, 2000.
[16] M. Sallam and K. Bowyer, “Registration and Difference Analysis of Corresponding
Mammogram Images”, Medical Image Analysis, Vol 3, No 2, 103-118, 1999
[17] H.P. Chan et al. ‘’ Medical Physics’’, Vol 14, 538-548, 1987
[18] Marius G. Linguraru, “Feature Detection in Mammographic Image Analysis”, University of Oxford, Michaelmas Term, 2002
[19] Duncan University of South Florida Database, MIASwww.wiau.man.ac.uk
[20] J.S. Duncan, N.Ayache, “Medical Image Analysis: Progress over Two Decades and
Challenges Ahead”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol
[21] F. Shtern, M. Vannier and D. Winfield, “Report of the working group on digital
Mammography Computer Aided Diagnosis and 3D Image Analysis and Display”,
Technical Report U.S., Public Health Services´s Office on Women´s Healthand the Nat. Cancer Inst., Cambridge, Mass., Oct., 1998
[22] Lee, L. Stickland, V. Wilson, P. Roebuck, E., “Fundamentals of Mammography”, W.B. Saunders Company,1995
[23] te Brake, G. M. Karssemeijer, N.: “Single and Multi-Scale Detection of Masses in
Digital mammography”. In IEEE Transactions on Medical Imaging, Vol 18(7), 628-639,
1999
[24] Sahiner, B. Chan, H. P. Petrick, N. Wei, D. Helvie, M. A. Adler, D. D. Goodsitt, M. M.: “Classification of mass and Normal Breast Tissue: A convolution Neural Network
Classifier with Spatial Domain and Texture Images.” In IEEE Transactions on Medical
Images, Vol 15(10), 589-610, 1996
[25] Lai, S. M. Li, X. Bischof, W. F. : “On Techniques for Detecting Circumscribed
Masses in Mammograms.” In IEEE Transactions on Medical Imaging, Vol 8, 377-386,
1989
[26] Ng, S. L. Bischof, W. F.: “Automated Detection and Classification of Breast
Tumours”. In Comput. Biomed. Res, Vol 25, 218-237, 1992
[27] Groshong, B. R. Kegelmeyer, W.P. : “Evolution of a Hough Transform Method for
Circumscribed Lesion detection” In Doi, K. Giger, M.L. Nishikawa, R. A. (eds.): Digital
Mammography, Elsevier, Amsterdam, 361-366, 1996
[28] Zwiggelaar, R., Parr, T.C. Schumm, J. E. Hutt, I. W. Taylor, C.J. Astley, S. M. Boggis, C. R. M.: “Model-Based Detection of Spiculated Lesions in Mammography”. In, Medical Image Analysis, Vol 3(1), 39-62, 1999
[29] Zwiggelaar, R., Taylor, C. J. Rubin, C. M. E.: “Detection of the Central Mass of
Spiculated Lesions – Signature Normalisation and Model Data Aspects”. In IPMI’99,
Springer, 406-411, 1999
[30] Miller, L. Ramsay, N.: “The Detection of Malignant Masses by Non-Linear Multiscale
Analysis”. In Doi, K. Giger, M. L. Nishikawa, R. M. Schmidt, R. A. (eds): Digital
Mammography. Elsevier, Amsterdam, 335-340, 1996
[31] Chan, H. P. Sahiner, B. Helvie, M. A. Petrick, N. Roubidoux, M. A. Wilson, T. E. Adler, D. D. Paramagul, C. Newman, J. S. Sanjay-Gopal, S.: “Improvements of
Radiologists – Characterization of Mammographic Masses by Using Computer-aided Diagnosis: A ROC Study”, in Radiology, 817-827, 1999
[32] Petrick, N. Chan, H. P. Sahiner, B. Helvie, M. A. Paquerault, S.: “Preclinical
Evaluation of a CAD Algotithm for Early Detection of Breast Cancer”, in Yaffe, M. J.
(ed.): Digital Mammography, Medical Physics Publishing, Madison, 328-333, 2000
[33] Sahiner, B. Chan, H. P. Petrick, N. Hadjiiski, L. M. Helvie, M. A. Paquerault, S.:
“Active Contour Models for Segmentation and Characterisation of Mammogramphic Masses”, in Yaffe, M. J. (ed): Digital Mammography, Medical Physics Publishing,
Madison, 357-362, 2000
[34] Sahiner, B. Chan, H. P. Petrick, N. Helvie, M. A.: “Computerized Characterisation of
Masses on Mammograms: The rubber Band Straghtening Transform and Textute Analysis”, in Medical Physics, Vol 25, 516-526, 1998
[35] Chan, H.P. Sahiner, B. Helvie, M.A. Petrick, N. Roubidoux, M.A. Wilson, T.E. Adler, D.D. Paramagul, C. Newman, J.S. Sanjay-Gopal, S., “Improvements of Radiologists
Characterization of Mammographic Masses by using Computer-Aided Diagnosis: A ROC Study”, in Radiology, 817-827, 1999
[36] te Blake, G.M. Karssemeijer, N. Hendricks. J.H.C.L. “An Automatic Method to
Discriminate Malignant Masses from Norml Tissue in Digital Mammograms”, Phys. Med.
Biol., 2843-2857, 2000
[37] Kita, J.K. Park, H.W., “Correspondence between Different View Breast X-Rays using
a Simulation of Breast Deformation”, Computer Vision and Pattern Recognition, 700-707,
1998
[38] Antani, S., L. Long, L. R. and Thoma, G. R.: “Content-Based Image Retrieval for
Large Biomedical Image Archives”, in 11th World Congress on Medical Informatics (MEDINFO), San Francisco, CA, USA, 829-833, 2004
[39] Sclaroff, S. and Pentland, A. P.: “On Modal Modeling for Medical Images:
Underconstraindes Shape Description and Data Compression”. in IEEE workshop on
Biomedical Image Analysis (BIA’1994), Seatle, WA, USA, 70-79, 1994
[40] Korn, P., Sidiropoulos, N. el al.: “Fast and Effective Retrieval of Medical Tumor
Shapes”, in IEEE Transations on Knoledge Data Engineering, Vol 10, No 6, 889-904, 1998
[41] Alvarenga, A. V., Infantosi, A F. C. et al.: “Aplicação de Operadores Morfológicos
na Segmentação e Determinação do Contorno de Tumores de Mama em Imagens por Ultra-Som”, in Revista Brasileira de Engenharia Biomédica, Vol 19, No2, 91-101, Agosto
2003
[42] J.C. Felipe, J. B. Olioti, A. J. M. Traina: “Discriminação de Aspectos Malignos em
Massas Tumorais de Mamografias usando Características de Forma das Imagens”, in V
Workshop de Informática Médica 2005, Porto-Alegre – RS Anais do V Workshop de Informática Médica, 2005
[43] Highnam, R.P. Brady, J.M., “Mammographic Image Analysis”, Kluwer Academic Publisher, Dordrecht Boston London, 1999
[44] Tech, C. H. and Chin, R. T.: “On Image Analysis by Methods of Moments” in IEEE Transaction on Pattern Analysis and Machine Intelligence, Vol 10, No 4, 496-513, 1998
[45] Twa, M. D., Parthasarathy, S. et al,: “Decision Tree Classification of Spatial Data
Patterns From Videokeratography using Zernike Polynomials”, in SIAM International
Conference on Data Mining, San Francisco, CA, USA, 2003.
[46] Kan, C. and Srinath, M. D.: “Combined Features of Cubic B-Spline Wavelet Moments
and Zernike Moments for Invariant Character Recognition”, in IEEE, International
Conference on Information Technology; Coding and Computing (ITCC’01), Las Vegas, NV, USA, 2001
[47] T. McInerney, D. Tersopoulos: “Deformable Models is Medical Image Analysis: A
survey”, in Medical Image Analysis, Vol 1(2), 91-108, 1996
[48] L.H. Staib and J. S. Duncan: “Boundary Finding with Parametrically Deformable
Models”, in IEEE Trans. On Pattern Analysis and Machine Intelligence Vol 14(11), 1061-
1075, 1992
[49] P.J. Besl, “Geometric modelling and Computer Vision”, in Proc IEEE, Vol 76(8), 936-958, 1998
[50] A.P. Pentland, “Automatic extration of deformable part models”, in Int J. Computer Vision, Vol 4,107-126, 1990
[51] F. Solina and R. Bajcsy, “Recovery of parametric image operators: Their use in
location for superquadratics with global deformations”, in IEEE trans. Pattern Anal.
Machine Intell., Vol 12(2), 131-147, February, 1990
[52] D.H. Ballard and C. M. Brown, “Computer Vision”, in Prentice-Hall, Englewood Cliffs, 1982
[53] R.B. Schudy, “Harmonic surfaces and parametric image operators: Their use in
locating the moving endocardial surface from three-simensional cardiac ultrasound data”,
in Computer Science Tech. Rpt. 112, University of Rochester, Rochester, New York, March, 1982
[54] K. Rao and R. Nevastia, “Computing volume descriptions from sparse 3D data”, in Int J. Computer Vision, Vol 2(1), 33-50, 1988
[55] Sund and Eilersten, “An Algorithm for fast adaptive image binarization with
applications in radiotherapy imaging”, in IEEE Transaction in Medical Imaging, 22, 2003
[56] Nora Székely, Norbert Tóth, Bela Pataki, “A Hybrid System for Detecting Masses in
Mammographic Images”, IMTC 2004 – Instrumentation and Measurement Technology
Conference, Italy, 18-20 May 2004
[57] Rafael C. Gonzalez, “Digital Image Processing using Matlab”, Prentice Hall, 2004
[58] Cheryl L. B., “Fractal Analysis of DNA Sequence Data”, in Dissertation of Doctor Philosophy, Unervisity of Utah, Chapter 2, March, 1993
[59] S S Cross, “Fractals in Pathology”, in Journal of Pathology, 182, 1-8 (1997)
[60] Radu Dobrescu, Florin Talos, Catalin Vasilescu, “Using Fractal dimensions for
Cancer Diagnosis” in VI PromCom-2002, 4th EURASIP – IEEE Region 8, International Symposium on Video/Image Processing and Multimedia Communications, Zadar, Croatia,16-19 June, 2002
[61] Claridge E., Hall PN, Keefe M, et al., “Shape Analysis for classification of malignant
melanoma”, in J. Biomed Eng, 14, 229-234, 1992
[62] Matsubara, T.; Fujita, H.; Kasai, S.; Goto, M.; Tani, Y.; Hara, T.; Endo, T.,
“Development of new schemes for detection and analysis of mammographic masses” in
[63] James W. Baish, Rakesh K. Jain, “Fractals and Cancer”, Cancer Research 60, 3683- 3688, July 15, 2000
[64] Jens Feder, “Fractals”, Plenum Publishing Corporation, Plenum Press, 1988
[65] W. Bauer and C. D. Mackenzie, “Cancer Detection on a Cell-by-Cell Basis Using a
Fractal Dimension Analysis”, in Heavy Ion Physics, Vol 14, 39-46, 2001
[66] J.R. Castregón Pita, A. Sarmiento Galán and R. Castrejon Garcia, “Fractal Dimension
and Self-Similarity in Asparagus Plumosus”, in Fractals, Vol 10, No 4, 429-434, 2002
[67] B.B. Mandelbrot, “The Fractal Geometry of Nature”, in W.H. Freeman and Company, New York, 1982
[68] O. Zmeškal, M. Veselý, M. N dal, M. Buchni ek, “Fractal Analysis of Image
Structures” in Harmonic and Fractal Image Analysis, 3-5, 2001
[69] Theiler, J., “Estimating Fractal Dimension”, in Journal of the Optical Society of America, 1055-1073, 1990
[70] Sugihara, G. and May R., “Applications of Fractals in Ecology”, in TREE, 5, 79-86, 1990
[71] C. Faloutsos and V. Gaede, “Analysis of n-dimensional quadtrees using the Hausdorff
Fractal Dimension”, in VLDB, 40-50, 1996
[72] Oana Craciunescu, Shiva K. Das and Mark W. Dewhirst, “Three-Dimensional
Microvascular Network Fractal Structure: Potencial for Tissue Characterization?”, Dep.
of Radiation Oncology, Duke University Medical Center, 2000.
[73] A.L. Barclay, P.J. Sweeney, L.A. Dissado and G.C. Stevens, “Stochastic modelling of
electrical treeing: fractal and statistical characteristics”, in J. Phys. D: Appl. Phys. 23,
[74] Correspondence re: J.W. Baish and R.K. Jain, “Fractals and Cancer”, in Cancer Res., 60, 3683-3688, 2000
[75] Backe A.R., Bruno O.M., “Técnicas de Estimativa da Dimensão Fractal: Um estudo Comparativo”, Universidade de S. Paulo, 2005
[76] Sabo E., Boltenko A., Yanina S., Stein A., Kleinhaus S., Resnick M. B., “Microscopic
analysis and significance of vascular architectural complexity in ernal cell carcinoma.”, in
Clin. Cancer Res., 7: 533-537, 2001
[77] Tricot C., “Curves and Fractal Dimension”, New York, Springer-Verlag, 1995
[78] G Landini and J P Rigaut “A method for estimating the dimension of asymptotic fractal sets”, Bioimaging 5, 65-70, 1997
[79] J P Rigaut, et. Al , “Asynptotic fractal sets in the context of grey-sacle images”, in J. of Microscopy, Vol 189, 57-63, 1998
[80] Tel, Tamas, Agnes Fulop and Tamas Vicsek, “Determination of Fractal Dimensions
for geometrical multifractals”, in Physica A 159, 155-166, 1989
[81] S.S. Chen and J.M. Keller, “On the calculation of fractal features from images”, in IEEE transactions on machine intelligence, Vol 15, No 10, 1087-1090, 1987
[82] R.F. Voss, “Random Fractals: Characterization and Measurement in Scaling
Phenomena in disordered Systems”, in Physica Scripta, Vol 33, 27-32, 1986
[83] R.F. Voss, “The Science of Fractal Images”, Springer-Verlag, New York Inc, 1988
[84] J.G. Moreira et. al, “On the Fractal dimensions of self-affine profiles”, in J. Phys. A:Math. Gen. 27, 8079-89, 1994
[85] António Brú, Juan M. Pastor, Isabel Fernaud, Isabel Brú, Sónia Melle, Carolina Berenguer, “Super-Rough Dynamics on Tumor Growth”, Physics Review Letters, Vol 81, No 18, 4008-4011, 2 November, 1998
[86] Adriana N. Dos Reis, José C.M. Mombach, Marcelo Walter, “Role of Decreased Cell
Adhesion in Tumor Morphology: A simulation study.”, UNISINOS, 2001
[87] Irini S. Reljin, Branimir D. Reljin, “Fractal geometry and multifractal in analysing
and processing medical data and images”, ONCOnet, Institute of Oncology, Sremska
Kamenica, Yugoslavia, 2002
[88] C.C. Chen, J.S. DaPonte, M.D. Fox, “Fractal feature analysis and classification in
medical imaging”, in IEEE transactions on medical imaging, Vol 8, No 2, 133, 1989
[89] W Bauer e C.D Mackenzie, “Cancer determination via determination of fractal cell
dimension”, in Heavy Ion Physics 14 (1-4), 43-50, 2001
[90] L. Bocchi, G. Coppini, J. Nori, G. Valli, “Detection of single and clustered
microcalcifications in mammograms using fractals models and neural networks”, in