A Multiscale Operator For Document Image Binarization

Basically, document image binarization consists on the segmentation of scanned gray level images into text and background, and is a basic preprocessing stage in many image analysis systems. It is essential to threshold the document image reliably in order to extract useful information and make further processing such as character recognition and feature extraction. The main difficulties arise when dealing with poor quality document images, containing nonuniform illumination, shadows and smudge, for example. This paper presents an efficient morphological-based document image binarization technique that is able to cope with these problems. We evaluate the proposed approach for different classes of images, such as historical and machine-printed documents, obtaining promising results.13439(2008), www.flnereader.com, ABBYYBosworth, J., Acton, S., Morphological scale-space in image processing (2003) Digital Signal Processing, 13, pp. 338-367Dorini, L.E.B., Leite, N.J., A scale-space toggle operator for morphological segmentation (2007) 8th International Symposium on Mathematical Morphology, pp. 101-112Dorini, L.E.B., Leite, N.J., Multiscale image representation using scale-space theory (2008) XXXI Congresso National de Matemtica Aplicada e Computational, pp. 130-137Gatos, B., Pratikakis, I., Perantonis, S., Adap-tative degraded image binarization (2006) Pattern Recognition, 39, pp. 317-327Jackway, P.T., Deriche, M., Scale-space properties of the multiscale morphological dilation-erosion (1996) IEEE Transactions on Pattern Analysis and Machine Intelligence, 18, pp. 38-51Maragos, P., Meyer, F., A pde approach to nonlinear image simplification via levelings andrecon-struction filters (2000) International Conference on Image Processing, pp. 938-941Niblack, W., (1986) An Introduction to Digital Image Processing, , Prentice HallOtsu, N., A threshold selection method from grey-level histograms (1979) IEEE Transactions on Systems, Man and Cybernetics, 9 (1), pp. 377-393Parker, J.R., (1996) Algorithms for Image Processing and Computer Vision, , WileySahoo, P., Soltani, S., Wong, A., A survey of thresholding techniques (1988) Comput. Vision, Graphics Image Processing, 41 (2), p. 233260Sauvola, J., Pietikainen, M., Adaptive document image binarization (2000) Pattern Recognition, 33, pp. 225-236Serra, J., Vicent, L., An overview of morphological filtering (1992) Circuits, Systems and Signal Processing, 11 (1), pp. 47-108Sezgin, M., Sankur, B., Survey over image thresholding techniques and quantitative performance evaluation (2004) J. Electron. Imaging, 13, pp. 146-165Trier, O., Jain, A., Goal-directed evaluation of binarization methods (1995) IEEE Trans. Pattern Anal. Mach. Intell, 17, pp. 1191-1201Witkin, A.P., Scale-space filtering: A new approach to multi-scale description (1984) Image Understanding, pp. 79-95. , Able

Multiscale Methods For Image Processing: The Wavelet And The Scale-space Approaches

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Multiscale approaches have been largely considered in several signal processing applications. They play an important role when designing automatic methods to cope with real world measurements where, in most of the cases, there is no prior information about which would be the appropriate scale. The basic idea behind a multiscale analysis is to embed the original signal into a family of derived signals, thus allowing the analysis of different representation levels and, further, the choice of the ones exhibiting the interest features. This paper presents a brief survey of two broadly used multiscale formulations, namely, wavelets and scale-space filtering. We present the basic definitions and some possible applications of these approaches in image processing. © 2009 IEEE.3144Petrobras,CNPq,CAPES,INCTMat,FAPERJConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Lindeberg, T., (1994) Scale-space theory in computer vision, , Kluwer Academic PublishersJackway, P., Morphological scale-space with application to three-dimensional object recognition, (1994), Ph.D. dissertation, Queensland University if TechnologyStrang, G., Nguyen, G., (1996) Wavelets and Filter Banks, , Wellesley Cambridge PressVelho, L., Gomes, J., Goldenstein, S., (1997) Wavelets: Teoria, Software e Aplicações, , IMPADaubechies, I., Ten Lectures on Wavelets (1992) C B M S - N S F Regional Conference Series in Applied Mathematics, , Soc for Industrial & Applied MathWitkin, A.P., Scale-space filtering: A new approach to multiscale description (1984) Image Understanding, pp. 79-95. , AblexBosworth, J., Acton, S., Morphological scale-space in image processing (2003) Digital Signal Processing, 13, pp. 338-367Iijima, T., Basic theory of pattern normalization for the case of a typical one-dimensional pattern (1962) Bull. Electrotech. Lab, pp. 368-388Jackway, P.T., Deriche, M., Scale-space properties of the multiscale morphological dilation-erosion (1996) IEEE Transactions on Pattern Analysis and Machine Intelligence, 18, pp. 38-51Heijmans, H., van den Boomgaard, R., Algebraic framework for linear and morphological scale-spaces (2002) Journal of Visual Communication and Image Representation, 13, pp. 269-301Babaud, J., Baudin, W.A.P.M., Duda, R., Uniqueness of the gaussian kernel for scale-space filtering (1986) IEEE Transactions on Pattern Analysis and Machine Intelligence, 8, pp. 15-25Lindeberg, T., Discrete scale-space theory and the scale-space primal sketch, (1991), Ph.D. dissertation, Computational Vision and Active Perception Laboratory CVAP, Royal Institute of TechnologyLifshitz, L.M., Pizer, S.M., A multiresolution hierarchical approach to image segmentation based on intensity extrema (1990) IEEE Transactions on Pattern Analysis and Machine Intelligence, 12 (4), pp. 529-540Koenderink, J., The structure of images (1984) Biological Cybernetics, 50 (5), pp. 363-370Florack, L., Non-linear scale-spaces isomorphic to the linear case with applications to scalar, vector and multispectral images (2001) International Journal of Computer Vision, 42 (1-2), pp. 39-53Perona, P., Malik, J., Scale-space and edge detection using anisotropic diffusion (1990) IEEE Transactions on Pattern Analysis and Machine Intelligence, 42 (12), pp. 629-639Matheron, G., (1975) Random Sets and Integral Geometry, , John Wiley and SonsSerra, J., (1982) Image Analysis and Mathematical Morphology, , Academic Press(1988) Image Analysis and Mathematical Morphology, volume 2: Theoretical Advances, , Academic PressSoille, P., (2003) Morphological Image Analysis: Principles and Applications, , Springer-VerlagHeijmans, H., (1994) Morphological Image Operators, , Academic PressLeite, N.J., Teixeira, M.D., An idempotent scale-space approach for morphological segmentation (2000) Mathematical Morphology and its Applications to Image and Signal Processing, pp. 291-300. , Kluwer Academic PublishersDorini, L.B., Leite, N.J., A scale-space toggle operator for morphological segmentation (2007) 8th ISMM, pp. 101-112Kramer, H.P., Bruckner, J.B., Iterations of a non-linear transformation for enhancement of digital images (1975) Pattern Recognition, 7, pp. 53-58Bernsen, J., Dynamic thresholding of grey-level images (1986) International Conference on Pattern Recognition, pp. 1251-1255Serra, J., Vicent, L., An overview of morphological filtering (1992) Circuits, Systems and Signal Processing, 11 (1), pp. 47-108Maragos, P., Meyer, F., A pde approach to nonlinear image simplification via levelings andreconstruction filters (2000) International Conference on Image Processing, pp. 938-941S. Beucher and F. Meyer, Mathematical Morphology in Image Processing. Marcel Dekker, 1993, ch. The morphological approach to segmentation: the watershed transformation, pp. 433-451Dorini, L.B., Leite, N.J., A multiscale operator for document image binarization (2009) 4th International Conference on Computer Vision Theory and Applications, pp. 34-39Dorini, L.E.B., Simões, N.C., Leite, N.J., A scale-dependent morphological approach to motion segmentation (2007) IWSSIP, pp. 122-125Salembier, P., Serra, J., Flat zones filtering, connected operators, and filters by reconstruction (1995) IEEE Transactions on Image Processing, pp. 1153-1160Serra, J., Connections for sets and functions (2000) Fundamenta Informaticae, 41, pp. 147-186Meyer, F., Levelings, image simplification filters for segmentation (2004) Journal of Mathematical Imaging and Vision, 20 (1-2), pp. 59-72Vicent, L., Morphological area openings and closings for grayscale images (1992) NATOWorkshopMallat, S., (1998) A wavelet tour of signal processing, , Academic Press Inc, San Diego, CAStarck, J., Murtagh, F., Bijaoui, A., (1997) Image processing and data analysis: The multiscale approach, , IMPAGoswami, J.C., Chan, A.K., (1999) Fundamentals of Wavelets, , John Wiley and SonsA. Cohen, I. Daubechies, and F. J.C., Biorthogonal bases of compactly supported wavelets, in Communications in Pure and Applied Mathematics, 1992, pp. 485-560Holschneider, M., Kronland-Martinet, R., Morlet, J., Grossmann, A., A real-time algorithm for signal analysis with the help of the wavelet transform (1989) Wavelets, Time-Frequency Methods and Phase Space, pp. 286-297. , J. M. Combes, A. Grossmann, and P. Tchamitchian, Eds. Springer-VerlagStollnitz, E.J., DeRose, T.D., Salesin, D.H., Wavelets for computer graphics: A primer, part 1 (1995), 15 (3), pp. 76-84. , MayKuntuu, I., Lepisto, L., Rauhamaa, J., Visa, A., Multiscale fourier descriptors for defect image retrieval (2006) Pattern Recognition Letters, 27, pp. 123-132Garcia, C., Zikos, G., Tziritas, G., A wavelet-based framework for face recognition (1998) ECCV, pp. 84-9

A Scaled Morphological Toggle Operator For Image Transformations

Scale dependent signal representations have proved to be useful in several image processing applications. In this paper, we define a toggle operator for binarization/segmentation purposes based on scaled versions of an image transformed by morphological operations. The toggle decision rule, determining the new value of a pixel, considers local spatial information, in contrast to other multiscale approaches that takes into account mainly global information (e.g., the scale signal under study). We show that the proposed operator can identify significant image extrema information in such a way that when it is used in a binarization process yields very good segmentation and filtering results. Our algorithm is validated against known threshold-based segmentation methods using images of different classes and subjected to different lighting conditions. © 2006 IEEE.323330Haralick, R., Stenberg, S., Zhuang, X., Image analysis using mathematical morphology (1987) IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-9 (4), pp. 532-550Jackway, P., Gradient watershed in morphological scale-space (1996) IEEE Transactions on Image Processing, 15, pp. 913-921Jackway, P., Deriche, M., Scale-space proprieties of the multiscale morphological dilation-erosion (1996) IEEE Transactions on Pattern Analysis and Machine Intelligence, 18, pp. 38-51Jang, B., Chin, R., Morphological scale-space for 2d shape smoothing (1998) Computer Vision and Image Understanding, 70 (2), pp. 121-141Kapur, J., Sahoo, P., Wong, A., A new method for graylevel picture thresholding using the entropy of the histogram (1985) Computer Vision, Graphics, and Image Processing, 29, pp. 273-285Kramer, H.P., Bruckner, J.B., Iterations of a non-linear transformation for enhancement of digital images (1975) Pattern Recognition, 7, pp. 53-58Leite, N.J., Teixeira, M.D., Morphological scale-space theory for segmentation problems (1999) IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, pp. 364-368Leite, N.J., Teixeira, M.D., An idempotent scale-space approach for morphological segmentation (2000) Mathematical Morphology and its Applications to Image and Signal Processing, pp. 291-300. , Kluwer Academic PublishersLifshitz, L., Pizer, S., A multiresolution hierarchical approach to image segmentation based on intensity extrema (1990) IEEE Transactions on Pattern Analysis and Machine Intelligence, 12 (4), pp. 529-540Marsden, J., Hoffman, M., (1993) Elementary Classical Analysis, , FreemanMatheron, G., (1975) Random Sets and Integral Geometry, , John Wiley and SonsOtsu, N., A threshold selection method from grey-level histograms (1979) IEEE Transactions on Systems, Man and Cybernetics, 9 (1), pp. 377-393Park, K., Lee, C., Scale-space using mathematical morphology (1996) IEEE Transactions on Pattern Analysis and Machine Intelligence, 18 (11), pp. 1121-1126Parker, J., (1996) Algorithms for Image Processing and Computer Vision, , WileyRidler, T., Calvard, S., Picture thresholding using a iterative selection method (1978) IEEE Transactions on Systems, Man and Cybernetics, SMC-8 (8), pp. 233-260Rosenfeld, A., Kak, A., (1982) Digital Picture Processing, , Academic PressSchavemaker, J.G.M., Reinders, M.J.T., Gerbrands, J., Backer, E., Image sharpening by morphological filtering (1999) Pattern Recognition, 33, pp. 997-1012Serra, J., (1982) Image Analysis and Mathematical Morphology, , Academic PressSerra, J., Image Analysis and Mathematical Morphology (1988) Theoretical Advances, 2. , Academic PressSerra, J., Vicent, L., An overview of morphological filtering (1992) Circuits, Systems and Signal Processing, 11 (1), pp. 47-108Soille, P., (2003) Morphological Image Analysis: Principles and Applications, , Springer-VerlagWellner, P., Adaptive thresholding for the digital desk Technical Report EPC1993-110, Xerox, 1993Witkin, A.P., Scale-space filtering: A new approach to multiscale description (1984) Image Understanding, pp. 79-95. , Able

A General Self-dual Adaptative Filtering Toggle Operator

In the mathematical morphology context, a filter is an operator that is increasing and idempotent. We propose an alternative way to build self-dual morphological filters, extending some results obtained for morphological centers to a different class of toggle operators whose decision rule is based on which primitive value is closer to the original one. With this new approach, a wider range of primitives can be considered without causing oscillations, a common problem in toggle mappings. We also explore the use of non-flat structuring elements which are shown to produce sharper filtered images. To evaluate the proposed approach, we carry out tests on images with different kinds of noise using different pairs of primitives. Experimental tests on Synthetic Aperture Radar (SAR) images show promising results, outperforming some well-known filters related to this type of pictures. © 2008 IEEE.189195Frost, V., Stiles, J.A., Shanmugan, K.S., Holtzman, J.C., A model for radar image and its application to adaptive digital filtering of multiplicative noise (1982) IEEE Transactions on Pattern Analysis and Machine Intelligence, 4, pp. 157-166Heijmans, H., Morphological filters (1995) Summer School on Morphological Image and Signal ProcessingHeijmans, H., Self-dual morphological operators and filters (1996) J. Math. Imaging Vision, 6, pp. 15-36Heijmans, H., Composing morphological filters (1997) IEEE Transactions on Image Processing, 6, pp. 713-723Lee, J., Digital image enhancement and noise filtering by use of local statistics (1980) IEEE Transactions on Pattern Analysis and Machine Intelligence, 2, pp. 165-168Lee, J., A simple speckle smoothing algorithm for synthetic aperture radar images (1983) IEEE Transactions on System, Man and Cybernetics, 13, pp. 85-89McDonald, D., Speckle reduction in synthetic aperture radar images (1988), Technical Report SRL-0010-TM, Departament of Defense, Surveillance Research LaboratoryOliver, C., Quegan, S., (2004) Understanding Synthetic Aperture Radar Images, , SciTech PublishingSchavemaker, J.G.M., Reinders, M.J.T., Gerbrands, J., Backer, E., Image sharpening by morphological filtering (1999) Pattern Recognition, 33, pp. 997-1012Serra, J., Vincent, L., An overview of morphological filtering (1992) Circuits, Systems, and Signal Processing, 11, pp. 47-108Soille, P., (2003) Morphological Image Analysis: Principles and Applications, , Springer-Verla

Unscented Klt: Nonlinear Feature And Uncertainty Tracking

Accurate feature tracking is the foundation of several high level tasks, such as 3D reconstruction and motion analysis. Although there are many feature tracking algorithms, most of them do not maintain information about the error of the data being tracked. In this paper, we propose a new generic framework that uses the Scaled Unscented Transform (SUT) to augment arbitrary feature tracking algorithms, by introducing Gaussian Random Variables (GRV) for the representation of features' locations uncertainties. Here, we apply the framework to the wellunderstood Kanade-Lucas-Tomasi (KLT) feature tracker, giving birth to what we call Unscented KLT (UKLT). It tracks probabilistic confidences and better rejects errors, all on-line, and leads to more robust computer vision applications. We also validade the experiments with a bundle adjustment procedure, using real and synthetic sequences. © 2006 IEEE.187193Chowdhury, A.K.R., (2002) Statistical Analysis of 3D Modeling from Monocular Video Streams, , PhD thesis, University of MarylandFischler, M., Bolles, R., Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography (1981) Communications of the ACM, 24 (6), pp. 381-395Fusiello, A., Trucco, E., Tommasini, T., Roberto, V., Improving feature tracking with robust statistics (1999) Pattern Analysis and Applications, 2, pp. 312-320Goldenstein, S., A gentle introduction to predictive filters (2004) Revista de Informatica Teórica e Aplicada (RITA), 11 (1), pp. 61-89. , OctHager, G., Belhumeur, P., Efficient region tracking with parametric models of geometry and illumination (1998) PAMI, 20, pp. 1025-1039Jin, H., Favaro, P., Soatto, S., Real-time feature tracking and outlier rejection with changes in illumination (2001) ICCV, pp. 684-689Julier, S., Uhlmann, J., A new extension of the kalman filter to nonlinear systems (1997) In SPIEKanazawa, Y., Kanatani, K., Do we really have to consider covariance matrices for image features? (2001) ICCV, pp. 301-306Lowe, D., Distinctive image features from scale-invariant keypoints (2004) IJCV, 60 (2), pp. 91-110Lucas, B., Kanade, T., An iterative image registration technique with an application to stereo vision (1981) IJCAI81, pp. 674-679Ma, Y., Soatto, S., Kosecka, J., Sastry, S., (2004) An Invitation to 3D Vision - From Images to Geometric Models, , SpringerShi, J., Tomasi, C., Good features to track (1994) CVPR, pp. 593-600Simoncelli, E., (1999) Handbook of Computer Vision and Applications, 2, pp. 397-422. , chapter Bayesian Multi-scale Differential Optical Flow, Academic PressSteele, P.M., Jaynes, C., Feature uncertainty arising from covariant image noise (2005) CVPR, 1, pp. 1063-1070Tomasi, C., Kanade, T., Detection and tracking of point features (1991), Technical Report CMU-CS-91-132, Carnegie Mellon University, AprilTorr, P., Zisserman, A., S., M., Robust detection of degeneracy (1995) ICCV, pp. 1037-1044Triggs, B., McLauchlan, P., Hartley, R., Fitzgibbon, A., Bundle adjustment - a modern synthesis (1999) Proceedings of the International Workshop on Vision Algorithms: Theory and Practice, pp. 298-372van der Merwe, R., Doucet, A., de Freitas, N., Wan, E., The unscented particle filter (2000), Technical Report CUED/FINFENG/TR380, Cambridge University, AugustWan, E., van der Merwe, R., (2001) Kalman Filtering and Neural Networks, , Wiley PublishingZhang, Z., Determining the epipolar geometry and its uncertainty: A review (1998) IJCV, 27 (2), pp. 161-198Zhu, J., Schwartz, S., Liu, B., Object tracking: Feature selection and confidence propagation (2004) CRV, pp. 18-2

White Blood Cell Segmentation Using Morphological Operators And Scale-space Analysis

Cell segmentation is a challenging problem due to both the complex nature of the cells and the uncertainty present in video microscopy. Manual methods for this purpose are onerous, imprecise and highly subjective, thus requiring automated methods that perform this task in an objective and efficient way. In this paper, we propose a novel method to segment nucleus and cytoplasm of white blood cells (WBC). WBC composition of the blood provides important information to doctors and plays an important role in the diagnosis of different diseases. We use simple morphological operators and explore the scale-space properties of a toggle operator to improve the segmentation accuracy. The proposed scheme has been successfully applied to a large number of images, showing promising results for varying cell appearance and image quality, encouraging future works. © 2007 IEEE.294301Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., Walter, P., (2002) Molecular Biology of the Cell, , Garland ScienceBeucher, S., Meyer, F., The morphological approach to segmentation: The watershed transformation (1993) Mathematical Morphology in Image Processing, pp. 433-1993Dougherty, E.R., Lotufo, R.A., (2003) Hands-on Morphological Image Processing, , SPIE-International Society for Optical Engine, ISBN: 081944720XFalcão, A.X., Stolfi, J., Lotufo, R.A., The image foresting transform: Theory, algorithms, and applications (2004) IEEE Trans. on Pattern Analysis and Machine Intelligence, 26 (1), pp. 19-29. , JanGonzalez, R.C., Woods, R.E., (2001) Digital Image Processing, , Prentice Hall Upper Saddle River, ISBN: 0-20118-075-8Jackway, P.T., Deriche, M., Scale-space properties of the multiscale morphological dilation-erosion (1996) IEEE Transactions on Pattern Analysis and Machine Intelligence, 18, pp. 38-51Jiang, K., Liao, Q., Dai, S., A novel white blood cell segmentation scheme using scale-space filtering and watershed clustering (2003) 2nd International conference on machine learning and cybernetics, pp. 2820-2825Kumar, B., Sreenivas, T., Teager energy based blood cell segmentation (2002) International conference of digital signal processing, 2, pp. 619-622Leite, N.J., Dorini, L.E.B., A scaled morphological toggle operator for image transformations (2006) XIX Brazilian Symposium on Computer Graphics and Image Processing, pp. 323-330. , IEEE PressQ. Liao and D. Y.Y. An accurate segmentation method for white blood cell images. In IEEE International symposium on biomedical imaging, pages 245-248, 2002Lotufo, R.A., Falcão, A.X., Zampirolli, F., IFT-Watershed from gray-scale marker (2002) Proc. of XV Brazilian Symp. on Computer Graphics and Image Process ing, pp. 146-152. , IEEE, OctMatheron, G., (1975) Random Sets and Integral Geometry, , John Wiley and SonsMiranda, P., Bergo, F., Rocha, L., Falcão, A., Tree-pruning: A new algorithm and its comparative analysis with the watershed transform for automatic image segmentation (2006) XIX Brazilian Symposium on Computer Graphics and Image Processing, pp. 231-239. , IEEE PressRuberto, C., Dempster, A., Khan, S., Jarra, B., Segmentation of blood images using morphological operators (2000) International conference on pattern recognition, pp. 3401-3405Schavemaker, J.G.M., Reinders, M.J.T., Gerbrands, J., Backer, E., Image sharpening by morphological filtering (1999) Pattern Recognition, 33, pp. 997-1012Serra, J., (1982) Image Analysis and Mathematical Morphology, , Academic PressSerra, J., Image Analysis and Mathematical Morphology (1988) Theoretical Advances, 2. , Academic PressSerra, J., Vicent, L., An overview of morphological filtering (1992) Circuits, Systems and Signal Processing, 11 (1), pp. 47-108Soille, P., (2003) Morphological Image Analysis: Principles and Applications, , Springer-VerlagTheera-Umpon, N., White blood cell segmentation and classification in microscopic bone marrow images (2005) Lecture Notes on Computer Science, 3614, pp. 787-79

A Scale-dependent Morphological Approach To Motion Segmentation

Accurate motion segmentation is the foundation of several high-level applications, such as surveillance and traffic monitoring systems. Here, we use a simple toggle operator, defined on a scaled morphological framework, to process the image frames in such a way that moving objects can be easily detected. The operator is able to cope with cast shadows and illumination changes, it is robust to false positives and sufficiently fast enough to be used in real-time applications. Experimental results show that the proposed approach outperforms existing methods besides having low computational cost.122125Ferryman, M., Maybank, S.J., Worral, A.D., Visual surveillance for moving vehicles (1998) IEEE Workshop on Visual Surveillance, pp. 73-80Wang, L., Hu, W., Tan, T., Recent developments in human motion analysis (2003) Pattern Recognition, 36, pp. 585-601Haritaoglu, I., Harwood, D., Davis, L.S., W4: Who? when? where? what? a real time system for detecting and tracking people (1998) International Conference on Automatic Face and Gesture Recognition, pp. 222-227Lara, A.C., Hirata, R., Motion segmentation using mathematical morphology (2006) XIX Brazilian Symposium on Computer Graphics and Image Processing, pp. 315-322. , IEEE Presshttp://homepages.inf.ed.ac.uk/rbf/caviar, Caviar project, February 2007Matheron, G., (1975) Random Sets and Integral Geometry, , John Wiley and SonsSerra, J., Image Analysis and Mathematical Morphology (1988) Theoretical Advances, 2. , Academic PressSoille, P., (2003) Morphological Image Analysis: Principles and Applications, , Springer-VerlagHaralick, R.M., Stenberg, S.R., Zhuang, X., Image analysis using mathematical morphology (1987) IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-9, pp. 532-550Jackway, P.T., Deriche, M., Scale-space properties of the multiscale morphological dilation-erosion (1996) IEEE Transactions on Pattern Analysis and Machine Intelligence, 18, pp. 38-51Kramer, H.P., Bruckner, J.B., Iterations of a non-linear transformation for enhancement of digital images (1975) Pattern Recognition, 7, pp. 53-58Schavemaker, J.G.M., Reinders, M.J.T., Gerbrands, J.J., Backer, E., Image sharpening by morphological filtering (1999) Pattern Recognition, 33, pp. 997-1012Serra, J., Vicent, L., An overview of morphological filtering (1992) Circuits, Systems and Signal Processing, 11 (1), pp. 47-108Leite, N.J., Dorini, L.E.B., A scaled morphological toggle operator for image transformations (2006) XIX Brazilian Symposium on Computer Graphics and Image Processing, pp. 323-330. , IEEE PressWitkin, A.P., Scale-space filtering: A new approach to multi-scale description (1984) Image Understanding, pp. 79-9