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Faculty of Computational Mathematics and Cybernetics, Moscow State University NUS, Singapore, August 14, 2003 Andrey S. Krylov

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Outline: Projection Method (Hermite series approach)Projection Method (Hermite series approach) ApplicationsApplications 1. 1.Image filtering and deblocking by projection filtering 2. 2.Image matching 3. 3.Texture matching 4. 4.Low-level methods for audio signal processing

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The proposed methods is based on the features of Hermite functions. An expansion of signal information into a series of these functions enables one to perform information analysis of the signal and its Fourier transform at the same time. Hermite transform

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B) They derivate a full orthonormal in system of functions. The Hermite functions are defined as: A)

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Original image 2D decoded image by 45 Hermite functions at the first pass and 30 Hermite functions at the second pass Difference image (+50% intensity)

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Original image 2D decoded image by 90 Hermite functions at the first pass and 60 Hermite functions at the second pass Difference image (+50% intensity)

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Image filtering and deblocking by projection filtering

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Original lossy JPEG image

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Enhanced image

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Difference image (Subtracted high frequency information)

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Original image Zoomed in: Enhanced image

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Scanned image Enhanced image

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Zoomed in: Scanned image Enhanced image

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Image matching

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Information parameterization for image database retrieval Algorithm Image normalizing Graphical information parameterization Parameterized image retrieval _

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Information parameterization for image database retrieval Algorithm Image normalizing Graphical information parameterization Parameterized image retrieval =+ HF componentLF component Normalized image Recovered image with the recovered image plane

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Information parameterization for image database retrieval Algorithm Image normalizing Graphical information parameterization Parameterized image retrieval Database size Initial images format Normalized images format Number of parameterization coefficients Error rate Search time – 768 images (4.12Gb) – 1600x1200x24bit (5.5Mb) – 512x512x24bit (0.75Mb) – 32x32x3 – <0.14% – 4 sec. (for K7-750)

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Image matching results

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Texture matching

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A method of obtaining the texture feature vectors Input function Fourier coefficients 1-D to 2-D expansion

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A method of obtaining the texture feature vectors 1-D Hermite functions: 1-D to 2-D expanded Hermite functions:

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Orientations

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Localization problem Decomposition process is optimal, if localization segments of the input function and filtering functions are equal.

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Feature vectors In this approach to get the feature vectors we consider the functions n (x,y) where n1=0..64, and 6 energy coefficients are calculated as: E 1 = ( 0 ) 2 + ( 1 ) 2, E 2 = ( 2 ) 2 +( 3 ) 2 + ( 4 ) 2, E 3 = ( 5 ) 2 +( 6 ) 2 +( 7 ) 2 +( 8 ) 2, … E 6 = ( 33 ) 2 +( 34 ) 2 + … + ( 63 ) 2 +( 64 ) 2, f(x,y) is the source image. Standard coding

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Feature vectors E 1 = ( 0 (1) ) 2 + ( 1 (1) ) 2, E 2 = ( 0 (2) ) 2 +( 1 (2) ) 2 + ( 2 (2) ) 2 +( 3 (2) ) 2, … E 6 = ( 0 (6) ) 2 +( 1 (6) ) 2 + … + ( 62 (6) ) 2 +( 63 (6) ) 2, f(x,y) is the source image. Hierarchical coding

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Feature vectors E 1 = ( 0 (1) ) 2 + ( 1 (1) ) 2, E 2 = ( 0 (2) ) 2 +( 1 (2) ) 2 + ( 2 (2) ) 2 +( 3 (2) ) 2, … E 6 = ( 0 (6) ) 2 +( 1 (6) ) 2 + … + ( 62 (6) ) 2 +( 63 (6) ) 2, f(x,y) is the source image. Hierarchical coding without subtractions

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Feature vectors

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abStandard coding Hierarchical coding Hierarchical coding without subtractions a1a20.0045050.0053490.003739 b1b20.0099050.0081600.007742 c1c20.0177780.0118480.009946 a3a40.0088070.0060470.002422 b3b40.0200750.0106670.006275 c3c40.1283220.1015910.080176 a1b10.4884200.4922380.491653 b1c10.3156440.3045970.305442

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Image segmentation task: Brodatz textures

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Image segmentation task

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Texture parameterization using 2-D Hermite functions

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Quasiperiod’s waveforms

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Signal filtering Speaker indexing Speaker recognition using database Source separation Areas of Hermite transform application:

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MusicSpeaker 1Speaker 22 speakers Audio sample

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Quasiperiod waveform Hermite histogram

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Speaker indexing

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Speech/music separation Analysis of signal dynamics (distribution of amplitudes in time) Analysis of base tone distribution in time Currently implemented criterions: Result of speech/music separation:

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Mix detection One speakerMix

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References 1.Krylov A.S., Liakishev A.N., Numerical Projection Method For Inverse Fourier Transform and its Application, Numerical Functional Analysis and optimization, vol. 21 (2000) p. 205-216. 2.Krylov A.S., Kortchagine D.N., Projection filtering in image processing, Graphicon’2000 Conf. proceedings, p. 42-45, 2000. 3.Krylov A.S., Kortchagine D.N., Lukin A.S., Streaming Waveform Data Processing by Hermite Expansion for Text-Independent Speaker Indexing from Continuous Speech, Graphicon’2002 Conf. proceedings, p. 91-98, 2002. 4.Krylov A.S., Kutovoi A.V., Wee Kheng Leow, Texture Parameterization With Hermite Functions, Graphicon’2002 Conf. proceedings, p. 190-194, 2002. 5.Mohsen Najafi, Andrey Krylov, Danil Kortchagine Image Deblocking With 2-D Hermite Transform, Graphicon’2003 Conf. proceedings.

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