Download presentation

Presentation is loading. Please wait.

Published byKevin Wilcutt Modified about 1 year ago

1

2
Faculty of Computational Mathematics and Cybernetics, Moscow State University NUS, Singapore, August 14, 2003 Andrey S. Krylov

3
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

4
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

5
B) They derivate a full orthonormal in system of functions. The Hermite functions are defined as: A)

6
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)

7
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)

8
Image filtering and deblocking by projection filtering

9
Original lossy JPEG image

10
Enhanced image

11
Difference image (Subtracted high frequency information)

12
Original image Zoomed in: Enhanced image

13
Scanned image Enhanced image

14
Zoomed in: Scanned image Enhanced image

15
Image matching

16
Information parameterization for image database retrieval Algorithm Image normalizing Graphical information parameterization Parameterized image retrieval _

17
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

18
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)

19

20
Image matching results

21

22
Texture matching

23

24
A method of obtaining the texture feature vectors Input function Fourier coefficients 1-D to 2-D expansion

25
A method of obtaining the texture feature vectors 1-D Hermite functions: 1-D to 2-D expanded Hermite functions:

26
Orientations

27
Localization problem Decomposition process is optimal, if localization segments of the input function and filtering functions are equal.

28
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

29
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

30
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

31
Feature vectors

32
abStandard coding Hierarchical coding Hierarchical coding without subtractions a1a b1b c1c a3a b3b c3c a1b b1c

33

34

35
Image segmentation task: Brodatz textures

36
Image segmentation task

37

38

39
Texture parameterization using 2-D Hermite functions

40
Quasiperiod’s waveforms

41
Signal filtering Speaker indexing Speaker recognition using database Source separation Areas of Hermite transform application:

42
MusicSpeaker 1Speaker 22 speakers Audio sample

43
Quasiperiod waveform Hermite histogram

44
Speaker indexing

45
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:

46
Mix detection One speakerMix

47
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 Krylov A.S., Kortchagine D.N., Projection filtering in image processing, Graphicon’2000 Conf. proceedings, p , 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 , Krylov A.S., Kutovoi A.V., Wee Kheng Leow, Texture Parameterization With Hermite Functions, Graphicon’2002 Conf. proceedings, p , Mohsen Najafi, Andrey Krylov, Danil Kortchagine Image Deblocking With 2-D Hermite Transform, Graphicon’2003 Conf. proceedings.

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google