Comments on "On Approximating Euclidean Metrics by Weighted t-Cost Distances in Arbitrary Dimension"

Mukherjee (Pattern Recognition Letters, vol. 32, pp. 824-831, 2011) recently introduced a class of distance functions called weighted t-cost distances that generalize m-neighbor, octagonal, and t-cost distances. He proved that weighted t-cost distances form a family of metrics and derived an approximation for the Euclidean norm in $\mathbb{Z}^n$. In this note we compare this approximation to two previously proposed Euclidean norm approximations and demonstrate that the empirical average errors given by Mukherjee are significantly optimistic in $\mathbb{R}^n$. We also propose a simple normalization scheme that improves the accuracy of his approximation substantially with respect to both average and maximum relative errors.Comment: 7 pages, 1 figure, 3 tables. arXiv admin note: substantial text overlap with arXiv:1008.487

On Euclidean Norm Approximations

Euclidean norm calculations arise frequently in scientific and engineering applications. Several approximations for this norm with differing complexity and accuracy have been proposed in the literature. Earlier approaches were based on minimizing the maximum error. Recently, Seol and Cheun proposed an approximation based on minimizing the average error. In this paper, we first examine these approximations in detail, show that they fit into a single mathematical formulation, and compare their average and maximum errors. We then show that the maximum errors given by Seol and Cheun are significantly optimistic.Comment: 9 pages, 1 figure, Pattern Recognitio

Assembled matrix distance metric for 2DPCA-based face and palmprint recognition

Author name used in this publication: David ZhangBiometrics Research Centre, Department of ComputingVersion of RecordPublishe

Computer Vision and Medical Image Processing: a brief survey of application areas

Every day is greater the number of images obtained to characterize the anatomy and functions of the human body, because of this the automation of the medical image processing has become a practice to improve the diagnosis and treatment of certain diseases. In this study the main areas of application of computer vision to the digital processing of medical images are reviewed. It begins with the selection of the three edges with more publications available in Springer, ScienceDirect, Wiley, and IEEE which are: segmentation of organs and lesions, feature extraction in optical images and labelling machine on x-ray images. Over them, latest algorithms, techniques and methods for medical imaging processing are analyzed exposing its main characteristics and ways of use.Sociedad Argentina de Informática e Investigación Operativa (SADIO

Computer Vision and Medical Image Processing: a brief survey of application areas

Every day is greater the number of images obtained to characterize the anatomy and functions of the human body, because of this the automation of the medical image processing has become a practice to improve the diagnosis and treatment of certain diseases. In this study the main areas of application of computer vision to the digital processing of medical images are reviewed. It begins with the selection of the three edges with more publications available in Springer, ScienceDirect, Wiley, and IEEE which are: segmentation of organs and lesions, feature extraction in optical images and labelling machine on x-ray images. Over them, latest algorithms, techniques and methods for medical imaging processing are analyzed exposing its main characteristics and ways of use.Sociedad Argentina de Informática e Investigación Operativa (SADIO

Evolving localised learning for on-line colour image quantisation

Although widely studied for many years, colour image quantisation remains a challenging problem. We propose to use an evolving self-organising map model for the on-line image quantisation tasks. Encouraging results are obtained in experiments and we look forward to implementing the algorithm in real world applications with further improvement.Unpublished[1] D. Chaudhuri, C.A. Murthy and B.B. Chaudhuri:”, A modified metric to compute distance. Pattern Recognition 7(25) (1992), 667-677. [2] A.H. Dekker: Kohonen neural networks for optimal colour quantization, Network: Computation in Neural Systems 5 (1994), 354-367. [3] D. Deng and N. Kasabov: ESOM: An algorithm to evolve self-organizing maps from on-line data streams. Proc. of IJCNN’2000 VI, Como, Italy (June 2000), 3-8. [4] B. Fritzke: A growing neural gas network learns topologies, in Advances in neural information processing Systems, D. Touretzky and T.K. Keen eds., Cambridge MA: MIT Press (1995), 625-632. [5] T. Kohonen: Self-Organizing Maps, second edition, Springer (1997). [6] P. Heckbert: Color image quantization for frame buffer display. Computer Graphics (SIGGRAPH) 16(3) (1982) 297-307. [7] M. Gervautz and W. Purgathofer: A simple method for color quantization: octree quantization. in Graphics Gems, A. Glassner, ed., Academic Press, New York (1990), 287-293. [8] T.M. Martinetz, S.G. Berkovich and K.J. Schulten: “Neural-Gas” network for vector quantization and its application to time-series prediction. IEEE Trans. on Neural Networks 4 (1993), 558-569. [9] J. Puzicha, M. Held, J. Ketterer, et al.: On Spatial Quantization of Color Images. Technical Report IAI-TR-98-1, University of Bonn (1998). [10] O. Verevka and J.W. Buchanan: Local K-means Algorithm for color image quantization. Proc. of GI’95 Quebec, Canada (1995). [11] S.J. Wan, P. Prusinkiewicz and S.K.M. Wong: Variance-based colour image quantization for frame buffer display. COLOUR Research and Application 15(1) (1990), 52-58. [12] X. Wu: Color quantization by dynamic programming and principal analysis. ACM Trans. on Graphics 11(4) (October 1992) 348-372

Evolving localised learning for on-line colour image quantisation

Although widely studied for many years, colour image quantisation remains a challenging problem. We propose to use an evolving self-organising map model for the on-line image quantisation tasks. Encouraging results are obtained in experiments and we look forward to implementing the algorithm in real world applications with further improvement.Unpublished[1] D. Chaudhuri, C.A. Murthy and B.B. Chaudhuri:”, A modified metric to compute distance. Pattern Recognition 7(25) (1992), 667-677. [2] A.H. Dekker: Kohonen neural networks for optimal colour quantization, Network: Computation in Neural Systems 5 (1994), 354-367. [3] D. Deng and N. Kasabov: ESOM: An algorithm to evolve self-organizing maps from on-line data streams. Proc. of IJCNN’2000 VI, Como, Italy (June 2000), 3-8. [4] B. Fritzke: A growing neural gas network learns topologies, in Advances in neural information processing Systems, D. Touretzky and T.K. Keen eds., Cambridge MA: MIT Press (1995), 625-632. [5] T. Kohonen: Self-Organizing Maps, second edition, Springer (1997). [6] P. Heckbert: Color image quantization for frame buffer display. Computer Graphics (SIGGRAPH) 16(3) (1982) 297-307. [7] M. Gervautz and W. Purgathofer: A simple method for color quantization: octree quantization. in Graphics Gems, A. Glassner, ed., Academic Press, New York (1990), 287-293. [8] T.M. Martinetz, S.G. Berkovich and K.J. Schulten: “Neural-Gas” network for vector quantization and its application to time-series prediction. IEEE Trans. on Neural Networks 4 (1993), 558-569. [9] J. Puzicha, M. Held, J. Ketterer, et al.: On Spatial Quantization of Color Images. Technical Report IAI-TR-98-1, University of Bonn (1998). [10] O. Verevka and J.W. Buchanan: Local K-means Algorithm for color image quantization. Proc. of GI’95 Quebec, Canada (1995). [11] S.J. Wan, P. Prusinkiewicz and S.K.M. Wong: Variance-based colour image quantization for frame buffer display. COLOUR Research and Application 15(1) (1990), 52-58. [12] X. Wu: Color quantization by dynamic programming and principal analysis. ACM Trans. on Graphics 11(4) (October 1992) 348-372