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Automatic colourization of grayscale images based on tensor decomposition

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Abstract

In this paper a colourizing technique based on some tensor properties is proposed. Toward this goal, it is clarified that tensor decomposition possesses the ability of extracting and gathering overall colour information. The methodology considers a grayscale pixel as a balanced vector in RGB colour space. Any deviation to unbalance the colour coordinates means adding colour information to the initial pixel. For finding the appropriate direction of deviation, the proposed technique uses tensor decomposition to extract colour information from a block divided exemplar colour image called reference. Then apply this direction to the best matched block of the grayscale image based on a similarity criterion while its basic structure is preserved. Finally by retrieving from tensor space into spatial domain the conversion is fulfilled. The similarity criteria for block matching and the plausibility of the system output are the most challenging problems. Both images blocks are considered as 3D tensors and Tucker3 with its unique properties is utilized for transferring the colour information. The novelty, simplicity, accuracy, and the conversion speed are some parameters which are introduced and developed by the proposed algorithm. This approach proves that in comparison with spatial or frequency domain, transforming the colour information into tensor space make it more clear and give us better ability of rendering. The results show that the proposed algorithm is able to present the average structural similarity up to 94%.

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References

  1. Bader BW, Kolda TG et al (2016) MATLAB Tensor Toolbox Version 2.6, Available online. URL: http://www.sandia.gov/~tgkolda/TensorToolbox/

  2. Bugeau A, Ta V-T, Papadakis N (2014) Variational exemplar-based image colorization. IEEE Trans Image Process 23(1):298–307

    Article  MathSciNet  MATH  Google Scholar 

  3. Burger W, Burge MJ (2009) Principal of Digital Signal Processing. British Library Cataloguing in Publication Data, Springer-Verlag London Limited

  4. Casaca W, Gomez-Nieto E, Ferreira COL, Tavares G, Pagliosa P, Paulovich F, Nonato LG, Paiva A (2012) Colorization by multidimensional projection. In: XXV SIBGRAPI Conference on Graphics, Patterns and Images

  5. Charpiat G, Hofmann M, Schölkopf B (2008) Automatic image colorization via multimodal predictions. In: ECCV 2008: 10th European Conference on Computer Vision–ECCV, Marseille, france, 2008 procedding, Part III - Springer, pp 126-139

  6. Chatzichristofis SA, Boutalis YS (2008) Fcth: Fuzzy color and texture histogram-a low level feature for accurate image retrieval. Image Analysis for Multimedia Interactive Services. WIAMIS'08. Ninth International Workshop on. IEEE

  7. Cheng Z, Cheng Z, Sheng B (2015) Deep Colorization. In:The IEEE International Conference on Computer Vision (ICCV), 2015 I.E. International Conference on, pp. 415-423

  8. Chia AY-S, Zhuo S, Gupta RK, Tai Y-W, Cho S-Y, Tan P, Lin S (2011) Semantic colorization with internet images. In: Proceedings of the 2011 SIGGRAPH Asia Conference Volume 30 Issue 6, December 2011

  9. Cichocki A, Mandic D, Phan A-H, Caiafa C, Zhou G, Zhao Q, De Lathauwer L (2014) Tensor Decompositions for Signal Processing Applications. In: IEEE Singnal Processing Magazine, pp 1053–5888

  10. Dang-Nguyen D-T, Pasquini C, Conotter V, Boato G (2015) RAISE–A raw images dataset for digital image forensics. In: ACM Multimedia Systems, Portland, Oregon

  11. De Lathauwer L, De Moor B, Vandewalle J (2000) A multilinear singular value decomposition. SIAM J Matrix Anal Appl 21(4):1253–1278

    Article  MathSciNet  MATH  Google Scholar 

  12. Deshpande A, Rock J, Forsyth D (2015) Learning large-scale automatic image colorization. In Proceedings of the IEEE International Conference on Computer Vision, pp 567–575

  13. Doulamis AD, Doulamis ND, Kollias SD (2000) A fuzzy video content representation for video summarization and content-based retrieval. Signal Process 80(6):1049–1067

    Article  MATH  Google Scholar 

  14. Drew MS, Finlayson GD (2008) Realistic colorization via the structure tensor. In: ICIP, 978–1–4244-1764-3/08, IEEE

  15. Dunlavy DM, Kolda TG, Kegelmeyer WP (2006) Multilinear algebra for analyzing data with multiple linkages. Tech. Rep. SAND2006–2079, Sandia National Laboratories, Albuquerque, NM and Livermore, CA

  16. Gupta RK, Chia AY-S, Rajan D, Ng ES, Zhiyong H (2012) Image colorization using similar images. In: Proceedings of the 20th ACM international conference on Multimedia, pp 369–378

  17. Hu M, Ou B, Xiao Y (2016) Efficient Image Colorization Based on Seed Pixel Selection. In: Multimed Tools Appl (2017) 76:23567. https://doi.org/10.1007/s11042-016-4112-9, Springer

  18. Huang H, Li X, Zhao H, Nie G, Hu Z, Xiao L (2014) Manifold-preserving image colorization with nonlocalestimation. In: Mult imed Tools Appl. Springer(2015) 74: 7555. https://doi.org/10.1007/s11042-014-1991-5

  19. Irony R, Cohen-Or D, Lischinski D (2005) Colorization by example. In: Proceeding of the 16th Eurographics conference on rendering techniques (EGSR 2005) Switzerland (2005)

  20. Kolda T, Bader B (2009) Tensor decompositions and applications. SIAM Rev 51(3):455–500

    Article  MathSciNet  MATH  Google Scholar 

  21. Larsson G, Maire M, Shakhnarovich G (2016) Learning Representations for Automatic Colorization. In: Leibe B et al (eds) ECCV 2016, Part IV, LNCS 9908. Springer International Publishing AG 2016, pp 577–593

  22. Levin A, Lischinski D, Weiss Y (2004) Colorization using optimization. ACM Trans Graphics 23:689–694

    Article  Google Scholar 

  23. Li B, Zhao F, Su Z, Liang X, Lai Y-K, Rosin PL (2017) Example-based image colorization using locality consistent sparse representation. IEEE Trans Image Process 26(11):5188–5202

    Article  MathSciNet  Google Scholar 

  24. Lu H, Plataniotis KN, Venetsanopoulos AN (2011) A survey of mul-tilinear subspace learning for tensor data. Pattern Recognit 44(7):1540–1551

    Article  MATH  Google Scholar 

  25. Lu H, Plataniotis KN, Venetsanopoulos AN (2014) Multilinear Subspace Learning. In: Machine Learning & Pattern Recognition Series, 1th ed. CRC Press Taylor & Francis, Boca Raton

    Google Scholar 

  26. Morten Morup (2011) Applications of tensor (multiway array) factorizations and decompositions in data mining, vol 1. Wiley, New York

  27. Peter P, Kaufhold L, Weickert J (2016) Turning diffusion-based image colorization into efficient color compression. IEEE Trans Image Process. 2016 Nov 10. Published in: IEEE Transactions on Image Processing (Volume: 26, Issue: 2, Feb. 2017) pp 860-869

  28. Pierre F, Aujol J-F, Bugeau A, Papadakis N, Ta V-T (2014) Exemplar-based colorization in RGB color space. In: Internationnal Conference on Image Processing, Oct, Paris, France. pp 1–5. <hal-01019627>

  29. Pierre F, Aujol JF, Bugeau A, Papadakis N, Ta VT (2015) Luminance-chrominance model for image colorization. SIAM Journal on Imaging Sciences 8(1):536–563

    Article  MathSciNet  MATH  Google Scholar 

  30. Saravanan C (2010) Color Image to Grayscale Image Conversion. In: Computer Engineering and Applications (ICCEA), 2010 Second International Conference on

  31. Sivalingam R, Sivalingam R, Boley D, Morellas V, Papanikolopoulos N (2014) Tensor sparse coding for positive definite matrices. IEEE Trans Pattern Anal Mach Intell 36(3):592–605

    Article  Google Scholar 

  32. Vertan C, Boujemaa N (2000). Using fuzzy histograms and distances for color image retrieval. Challenge of image retrieval, Brighton

  33. Vervliet N, Debals O, Sorber L, Van Barel M, De Lathauwer L (2017) Tensorlab 3.0, Available online. URL: http://www.tensorlab.net

  34. Wan Y, Xie Q (2016) A Novel Framework for Optimal RGB to Grayscale Image Conversion. In: Intelligent Human-Machine Systems and Cybernetics (IHMSC), 2016 8th International Conference on

  35. Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. In: IEEE Transactions on Image Processing (Volume: 13, Issue: 4, April 2004) pp 600-612

  36. Welsh T, Ashikhmin M, Mueller K (2002) Transferring color to greyscale images. ACM Trans Graph 21(3):277–280

    Article  Google Scholar 

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Author notes

  1. Hassan Rahmanian Koushkaki & Ebrahim Abiri

    Present address: Electrical and Electronics Engineering Department, Shiraz University of Technology, Shiraz, Iran

Authors and Affiliations

  1. Electrical and Electronics Engineering Department, Shiraz University of Technology, Shiraz, Iran

    Mohammad Reza Salehi

  2. Regional Information Center for Science & Technology (RICeST), Jam-e-Jam Ave, Shiraz, Iran

    Mohammad Reza Salehi

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  1. Hassan Rahmanian Koushkaki
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  2. Mohammad Reza Salehi
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  3. Ebrahim Abiri
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Correspondence to Mohammad Reza Salehi.

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Rahmanian Koushkaki, H., Salehi, M.R. & Abiri, E. Automatic colourization of grayscale images based on tensor decomposition. Multimed Tools Appl 77, 20043–20063 (2018). https://doi.org/10.1007/s11042-017-5419-x

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  • DOI: https://doi.org/10.1007/s11042-017-5419-x

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