Morphological hat-transform scale spaces and their use in pattern classification

In this paper we present a multi-scale method based on mathematical morphology which can successfully be used in pattern classification tasks. A connected operator similar to the morphological hat-transform is defined, and two scale-space representations are built. The most important features are extracted from the scale spaces by unsupervised cluster analysis, and the resulting pattern vectors provide the input of a decision tree classifier. We report classification results obtained using contour features, texture features, and a combination of these. The method has been tested on two large sets, a database of diatom images and a set of images from the Brodatz texture database. For the diatom images, the method is applied twice, once on the curvature of the outline (contour), and once on the grey-scale image itself.

[1]  H. Heijmans.  Morphological image operators , 1994 .

[2]  Jitendra Malik,et al.  Blobworld: A System for Region-Based Image Indexing and Retrieval , 1999, VISUAL.

[3]  I. Jolliffe.  Principal Component Analysis , 2002 .

[4]  Michael H. F. Wilkinson,et al.  A Comparison of Algorithms for Connected Set Openings and Closings , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Guido Gerig,et al.  Multiscale detection of curvilinear structures in 2-D and 3-D image data , 1995, Proceedings of IEEE International Conference on Computer Vision.

[6]  J. Andrew Bangham,et al.  Scale-space from nonlinear filters , 1995, Proceedings of IEEE International Conference on Computer Vision.

[7]  Luc Vincent,et al.  Morphological grayscale reconstruction in image analysis: applications and efficient algorithms , 1993, IEEE Trans. Image Process..

[8]  Peter J. van Otterloo,et al.  A contour-oriented approach to shape analysis , 1991 .

[9]  Josef Kittler,et al.  Robust and Efficient Shape Indexing through Curvature Scale Space , 1996, BMVC.

[10]  J. Andrew Bangham,et al.  Scale-Space From Nonlinear Filters , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Henk J. A. M. Heijmans,et al.  Nonlinear multiresolution signal decomposition schemes. I. Morphological pyramids , 2000, IEEE Trans. Image Process..

[12]  Larry D. Hostetler,et al.  The estimation of the gradient of a density function, with applications in pattern recognition , 1975, IEEE Trans. Inf. Theory.

[13]  Ronald Jones,et al.  Connected Filtering and Segmentation Using Component Trees , 1999, Comput. Vis. Image Underst..

[14]  Peter F. M. Nacken.  Chamfer metrics, the medial axis and mathematical morphology , 2004, Journal of Mathematical Imaging and Vision.

[15]  Philippe Salembier,et al.  Antiextensive connected operators for image and sequence processing , 1998, IEEE Trans. Image Process..

[16]  H. Heijmans,et al.  Multiresolution signal decomposition schemes , 1998 .

[17]  Ulrich Eckhardt,et al.  Shape descriptors for non-rigid shapes with a single closed contour , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[18]  D Marr,et al.  Bandpass channels, zero-crossings, and early visual information processing. , 1979, Journal of the Optical Society of America.

[19]  Paul L. Rosin.  Measuring shape: ellipticity, rectangularity, and triangularity , 2003, Machine Vision and Applications.

[20]  Henk J. A. M. Heijmans.  Connected Morphological Operators for Binary Images , 1999, Comput. Vis. Image Underst..

[21]  Peter J. Burt,et al.  Smart sensing within a pyramid vision machine , 1988, Proc. IEEE.

[22]  Tony Lindeberg,et al.  Scale-space theory , 2001 .

[23]  Michael Werman,et al.  Computing 2-D Min, Median, and Max Filters , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Erkki Oja,et al.  Reduced Multidimensional Co-Occurrence Histograms in Texture Classification , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  John Goutsias,et al.  Centrum Voor Wiskunde En Informatica Reportrapport Multiresolution Signal Decomposition Schemes. Part 1: Linear and Morphological Pyramids Multiresolution Signal Decomposition Schemes. Part 1: Linear and Morphological Pyramids , 2022 .

[26]  Philippe Salembier,et al.  Flat zones filtering, connected operators, and filters by reconstruction , 1995, IEEE Trans. Image Process..

[27]  Refractor.  Vision , 2000, The Lancet.

[28]  Arnold W. M. Smeulders,et al.  Image Databases and Multi-Media Search , 1998, Image Databases and Multi-Media Search.

[29]  Miroslaw Bober,et al.  MPEG-7 visual shape descriptors , 2001, IEEE Trans. Circuits Syst. Video Technol..

[30]  Ming-Kuei Hu,et al.  Visual pattern recognition by moment invariants , 1962, IRE Trans. Inf. Theory.

[31]  Joachim Weickert,et al.  Anisotropic diffusion in image processing , 1996 .

[32]  VincentL..  Morphological grayscale reconstruction in image analysis , 1993 .

[33]  Farzin Mokhtarian,et al.  A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[34]  Josef Kittler,et al.  Efficient and Robust Retrieval by Shape Content through Curvature Scale Space , 1998, Image Databases and Multi-Media Search.

[35]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .

[36]  M. Docarmo.  Differential geometry of curves and surfaces , 1976 .

[37]  Ron Kohavi,et al.  A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection , 1995, IJCAI.

[38]  Farzin Mokhtarian,et al.  Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[39]  Chung-Nim Lee,et al.  Scale-Space Using Mathematical Morphology , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[40]  Jos B. T. M. Roerdink,et al.  Identification by mathematical morphology , 2002 .

[41]  Tony Lindeberg,et al.  Shape from texture from a multi-scale perspective , 1993, 1993 (4th) International Conference on Computer Vision.

[42]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[43]  Jitendra Malik,et al.  Blobworld: Image Segmentation Using Expectation-Maximization and Its Application to Image Querying , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[44]  Mohamed A. Deriche,et al.  Scale-Space Properties of the Multiscale Morphological Dilation-Erosion , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[45]  H. D. Buf,et al.  Automatic diatom identification , 2002 .

[46]  T. Lindeberg,et al.  Scale-Space Theory : A Basic Tool for Analysing Structures at Different Scales , 1994 .

[47]  Ronald Jones,et al.  Attribute Openings, Thinnings, and Granulometries , 1996, Comput. Vis. Image Underst..

[48]  M.-H. Chen,et al.  A Multiscanning Approach Based on Morphological Filtering , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[49]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[50]  Tony Lindeberg,et al.  Direct computation of shape cues using scale-adapted spatial derivative operators , 1996, International Journal of Computer Vision.

[51]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[52]  J. Andrew Bangham,et al.  Morphological scale-space preserving transforms in many dimensions , 1996, J. Electronic Imaging.

[53]  J. Ross Quinlan,et al.  C4.5: Programs for Machine Learning , 1992 .

[54]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[55]  Jan Flusser,et al.  Pattern recognition by affine moment invariants , 1993, Pattern Recognit..