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Pawel FORCZMANSKI "Dimensionality reduction methods applied to digital image processing and recognition"

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– Subspace concept in computer vision
– One-dimensional linear dimensionality reduction: PCA/KLT, LDA/KLT
– Two-dimensional linear dimensionality reduction: 2DPCA/2DKLT, 2DLDA/2DKLT
– Application to image recognition: Eignefaces approach
– Application to image processing: watermarking, scrambling

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Pawel FORCZMANSKI "Dimensionality reduction methods applied to digital image processing and recognition"

  1. 1. Erasmus+seminar,18/04/2016 1 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Dimensionality reduction methods applied to digital image processing and recognition Paweł Forczmański Chair of Multimedia Systems, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin Vilnius University, Institute of Mathematics and Informatics, 18/04/2016
  2. 2. Erasmus+seminar,18/04/2016 2 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin AgendaAgenda Subspace concept in computer visionSubspace concept in computer vision Application to image recognition: Eignefaces approach Application to image recognition: Eignefaces approach One-dimensional linear dimensionality reduction: PCA/KLT, LDA/KLT One-dimensional linear dimensionality reduction: PCA/KLT, LDA/KLT Two-dimensional linear dimensionality re- duction: 2DPCA/2DKLT, 2DLDA /2DKLT Two-dimensional linear dimensionality re- duction: 2DPCA/2DKLT, 2DLDA /2DKLT Application to image processing: watermarking, scrambling Application to image processing: watermarking, scrambling
  3. 3. AlgorytmyRozpoznawaniaWzorców 3 / 26 1 1 2 2 1 2 ˆ ... where , ,..., isa basein the -dimensionalsub-space(K<N) K K K x bu b u b u u u u K = + + + ˆx x= 1 1 2 2 1 2 ... where , ,..., isa basein theoriginal N-dimensionalspace N N n x a v a v a v v v v = + + + The problem of determining a basis in low-dimensional sub- space: − Approximation of vectors by projecting them into a new, low-dimensional sub- space: (1) Initial representation: (2) Low-dimensional representation: • Remark: if K==N, then Subspace? (1/2)Subspace? (1/2) where is a basis in N-dimensional space is a basis in K-dimensional subspace (K<N)where
  4. 4. AlgorytmyRozpoznawaniaWzorców 4 / 26 Subspace? (2/2)Subspace? (2/2) Example (K==N):
  5. 5. Erasmus+seminar,18/04/2016 5 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin PCAPCA ● Karhunen-Loève Transform ● Principal Component Analysis = Hoteling Transform ● How? Data decorrelation ● Why? Reduce dimensionality ● What for? Many applications...
  6. 6. Erasmus+seminar,18/04/2016 6 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin introductionintroduction 1998 1902 (Pearson) 1936 (Hoteling) 1987 (Kirby, Sirowich) 1991 (Turk, Pentland) One-dimensional Two-dimensional PCA (Principal Component Analysis) 1998 (Tsapatsoulis N., Alexopoulos V. Kollias S.)2000, 2001, 2004 (Kukharev G., Forczmanski P.), Faculty report 2000, PRIP'2001, MG&V 2004
  7. 7. Erasmus+seminar,18/04/2016 7 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin 2DKLT/ PCArc2DKLT/ PCArc On the input we assume L images X in grayscale of M×N pixels. 1. 2. 3. Then we calculate a matrices of eigenvalues and a matrices of eigenvectors on the basis of covariance matrices RM i CN : Transformation is performed as follows, where V(R) and V(C) are submatrices of W(R) and W(C) : Λ(R) ,Λ(C) W(R) ,W(C) Vector or matrix repre- sentation is possible ̄X M ×N = 1 L ∑ k=1 L X M ×N (l) ̂X M ×N (l) =X M×N (l ) − ̄X M×N ∀l=1,2,…, L RM = 1 L ∑ l=1 L ̂X M× N (l ) [ ̂X M ×N (l) ]T ;C N = 1 L ∑ l=1 L [^X M×N (l ) ]T ^X M ×N (k ) ; Y p×q  l  =[V M×p  R ]T X M×N  l  V N ×q C  G. Kukharev, P. Forczmański, Data dimensionality reduction for face recognition, Ma- chine Graphics & Vision, vol. 13, no. 1/2, 2005, s. 99-122
  8. 8. Erasmus+seminar,18/04/2016 8 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Exemplary application to faceExemplary application to face recognitionrecognition G. Kukharev, P. Forczmański, Data dimensionality reduction for face recognition, Ma- chine Graphics & Vision, vol. 13, no. 1/2, 2005, s. 99-122 X
  9. 9. Erasmus+seminar,18/04/2016 9 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin General scheme ofGeneral scheme of 2DPCA/2DKLT application2DPCA/2DKLT application input image block decomposition blocks 2DKLT transformed blocks Eigenvectors Quantization Coding Output file/stream inverse 2DKLT blocks composition embedding message message embedding (1) rearrangement P. Forczmański 2DKLT-Based image compression and scrambling, Congress of Young IT Scientists, 2007, s. 86-89 (Polish Journal of Environmental Studies, vol. 16, no. 4a) P. Forczmański Information Embedding in Remotely sensed images by means of two-Two-dimensional Karhunen-Loeve Transform, Advanced Computer Systems: 14th International Conference: ACS’2007, Ol- sztyn: HARD, 2007, s. 275-279 (Polish Journal of Environmental Studies, vol. 16, no. 5B)
  10. 10. Erasmus+seminar,18/04/2016 10 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin ArtifactsArtifacts original 2DKLT JPEG JPEG 2000
  11. 11. Erasmus+seminar,18/04/2016 11 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin DCT vs 2DKLTDCT vs 2DKLT DCT (JPEG) 2DKLT
  12. 12. Erasmus+seminar,18/04/2016 12 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Watermarking / steganographyWatermarking / steganography ➔ embedding watermarks and copyright information in multimedia (Digital Rights Management – DRM), ➔ hiding secret information for the safe transfer, ➔ protection of data against changes. ➔ All methods work either in spatial or spectral domain (FFT, DFT, DCT, Wavelets). ➔ The most popular, yet the least sophisticated method is "Least Significant Bit (LSB) insertion" ➔ The basic problem with the LSB is a low resistance to typical image manipulations
  13. 13. Erasmus+seminar,18/04/2016 13 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Modification in each blockModification in each block ➔ Modification of block after 2DKLT Message 00010101000101010001... Original (carier) Modifier block Bit-wide decomposition key:{4,1,2,3,...}
  14. 14. Erasmus+seminar,18/04/2016 14 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin ExamplesExamples Carrier image +watermark P. Forczmański, M. Węgrzyn, Virtual Steganographic Laboratory for Digital Ima- ges, Information systems architecture and technology, Polska 2008, s. 163- 173 P. Forczmański, M. Węgrzyn, Open Virtual Steganographic Laboratory Elektronika, nr 11, 2009, s. 60-65
  15. 15. Erasmus+seminar,18/04/2016 15 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin ExperimentsExperiments 100 94 88 82 76 70 64 58 52 46 40 34 28 22 16 10 5 10 15 20 25 30 35 40 0% 20% 40% 60% 80% 100% 120% JPEG Compression PSNR [dB] Information [%] Quality PSNR -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 5 10 15 20 25 30 35 40 0% 20% 40% 60% 80% 100% 120% Brightness PSNR [dB] Information [%] Brightness Coefficient PSNR P. Forczmański Information Embedding in Remotely sensed images by means of twodimensional Karhunen-Lo- eve Transform, Advanced Computer Systems: 14th International Conference: ACS’2007, Olsztyn: HARD, 2007, s. 275-279 (Polish Journal of Environmental Studies, vol. 16, no. 5B) 0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0 16,0 18,0 20,0 22,0 24,0 26,0 28,0 30,0 32,0 34,0 36,0 38,0 40,0 42,0 44,0 46,0 48,0 50,0 5 10 15 20 25 30 35 40 0% 20% 40% 60% 80% 100% 120% Additive noise PSNR [dB] Information [%] Noise Amplitude PSNR 0,05 0,25 0,45 0,65 0,85 1,05 1,25 1,45 1,65 1,85 2,05 2,25 2,45 2,65 2,85 3,05 3,25 3,45 3,65 3,85 5 10 15 20 25 30 35 40 0% 20% 40% 60% 80% 100% 120% Contrast PSNR [dB] Information [%] Contrast Coefficient PSNR
  16. 16. Erasmus+seminar,18/04/2016 16 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin ScramblingScrambling original Scrambled image Recovered image #1 Recovered image #2? ?
  17. 17. Erasmus+seminar,18/04/2016 17 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Linear Discriminant Analysis (5/6)Linear Discriminant Analysis (5/6) D. Swets, J. Weng, "Using Discriminant Eigenfeatures for Image Retrieval", IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 8, pp. 831-836, 1996 PCA LDA
  18. 18. Erasmus+seminar,18/04/2016 18 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin LDA : Algorithm (1)LDA : Algorithm (1) Let us assume input images X are grayscale, gathered in K classes, each one having L objects. We calculate means for each K class and one common, for all classes: Then, covariance matrices are calculated:
  19. 19. Erasmus+seminar,18/04/2016 19 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin LDA : Algorithm (2)LDA : Algorithm (2) Total covariance matrix is: Which is decomposed using eigen-approach: where Ω – diagonal of eigen values and U – orthogonal matrix having eigenvectors Transform matix is created from U by selecting sub-matrix with s columns related to the highest values in Ω. Ωpxp → F sxs
  20. 20. Erasmus+seminar,18/04/2016 20 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin LDA : Algorithm (3)LDA : Algorithm (3) Dimensionality reduction is applied in two-step process: 1. initial reduction (down-sampling, DCT/DFT, PCA) 2. final LDA transformation LDA:
  21. 21. Erasmus+seminar,18/04/2016 21 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin LDA: classification of texturesLDA: classification of textures K. Okarma, P. Forczmański, 2DLDA-based texture recognition in the aspect of objec- tive image quality assessment Annales Universitatis Mariae Curie-Skłodowska. Sectio AI Informatica, vol. 8, no. 1, 2008, s. 99-110 Distortion Recognition accuracy Nearest element Centers of classes Median 3x3 81.33 % 71.59 % Median 5x5 62.18 % 57.79 % Low-pass 3x3 71.47 % 63.37 % Low-pass 5x5 46.83 % 47.32 % 5% impulse noise 64.29 % 60.88 % 10% impulse noise 47.24 % 47.89 % 15% impulse noise 38.47 % 38.80 % 20% impulse noise 30.03 % 31.33 % JPEG 60% 89.77 % 78.08 % JPEG 40% 90.10 % 77.11 % JPEG 20% 89.95 % 76.82 % JPEG 10% 88.96 % 76.14 %
  22. 22. Erasmus+seminar,18/04/2016 22 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin LDA : limitationsLDA : limitations Classical LDA method requires to carry out a preliminary dimensionality re- duction of input data, eg. by means of sampling (down-sampling) or PCA / PCArc. It is required to meet the condition: where K – no. classes, L- no. Images in class, DIM – dimensionality of fe- ature-space. G. Kukharev, P. Forczmański, Two-Dimensional LDA Approach to Image Compression and Re- cognition, Computing, Multimedia and Intelligent Techniques, vol.2, no. 1, 2006, s.87-98 G. Kukharev, P. Forczmański, Face Recognition by Means of Two-Dimensional Direct Linear, Discriminant Analysis Pattern recognition and information processing: PRIP ’2005: Proceedings of the Eighth International Conference, 18-20 Maj, Mińsk, Białoruś 2005, s.280-283
  23. 23. Erasmus+seminar,18/04/2016 23 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin 2DLDA/LDArc (1)2DLDA/LDArc (1) The solution to this problem is to use 2DLDA (LDArc), which involves the decomposition of the image into a set of rows and columns and calculating 2 sets of covariance matrices:
  24. 24. Erasmus+seminar,18/04/2016 24 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin 2DLDA/LDArc (5)2DLDA/LDArc (5) Transformation is done using the following formula: Exemplary LDA spectra and the reconstruction is presented below:
  25. 25. Erasmus+seminar,18/04/2016 25 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin 2DLDA/LDArc: Facial recognition2DLDA/LDArc: Facial recognition G. Kukharev, P. Forczmański, Facial images dimensionality reduction and recognition by means of 2DKLT, Machine Graphics & Vision, vol. 16, no. 3/4, 2007, s. 401-425
  26. 26. Erasmus+seminar,18/04/2016 26 / 26 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Thank you for your attenttion! Any questions? Paweł Forczmański Chair of Multimedia Systems, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin Vilnius University, Institute of Mathematics and Informatics, 18/04/2016 ? ?

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