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Bayes Fast Marching.

    tiger(256x179) P(O|X)= 4 P(O|X)= 29
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References

Application Examples

  • [Giak2000] "Digital Restoration of Painting Cracks.", Ioannis Giakoumis and Ioannis Pitas, IEEE on Image Processing February 2000.
  • [Chet2002] "Finding defects in texture using regularity and local orientation.", D. Chetverikov and
  • [Lew2001] "Lifting Detail from Darkness", J.P.Lewis , ACM Siggraph 2001 Technical Sketch.

General Papers

  • Decision Systems.
    • [Scho1994] "Logique floue et régulation PID.", Henk Scholten, Publitronic 1994.
    • [Pedr1993] "Fuzzy Control and Fuzzy Systems.", Witold Pedrycz, Research Studies Press, J. Wiley 1993.
    • [Boni1992] "Attribute Fusion and Situation Assessment with a many-Valued Logic Approach. Multi-Target MultiSensor Tracking. Application Advances.", R.M.Yannone and P.P.Bonissone,Yaakov Bar-Shalom, Artech 1992.
  • Classification.
    • [Ther1989] "Decision, Estimation and Classification.", Charles W. Therrien, Naval Postgraduate School, Wiley 1989.
    • [Datt1994] "Numerical Linear Algebra and Applications.", Biswa Nath Datta, Brools/cole Publishing Company 1994.
  • Evolution and Fast Marching.
    • [Seth1985] "Curvature and the Evolution of Fronts.", Sethian , Report 1985, New York University.
    • [Seth1995] "A fast marching level set method for monotonically advancing fronts.", Sethian , Proceedings 1995, UCLA.
    • [cohe1996] "Global minimum for active contour models: A minimal path approach.", Cohen & Kimmel , Proceedings IEEE 1996, San Francisco.
    • [Adal1997] "The fast construction of extension velocities in level sets methods.", Adalsteinsson & Sethian , report 1997, UCLA.
    • [Kimm2001] "Optimal Algorithm for Shape from Shading and Path Planning.", Ron Kimmel, James A. Sethian, Kluweer Academic Publishers 2001 , Netherlands.

Restoration Papers

    A large number of restoration techniques will be used in this framework. They will help people to recover images of different kind. Also it is wise that people will select themselve the suitable restoration method:

  • General papers.
    • [Blak1987] "Visual Reconstruction.", A. Blake and A. Zisserman , The MIT Press, Cambridge, Massachusetts Institute of Technology 1987, London, England.
    • [Marq1999] "Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring an noise removal.", Marquina & S. Osher , Report 1999, UCLA.
    • [Mraz199x] "Nonlinear Diffusion of Image Derivatives.", P. Mrazek , Report 199x, Czech Technical University.
  • Fast Recursive Filters and Implicit Restorations.
    • [Deri1993] "Recursively Implementing the Gaussian and Its Derivatives.", R. Deriche , Report 1893, 1993, INRIA, France.
    • [DeBr1999] "Recursive Digital Filters.",Victor De Brunner , John Wiley Encyclopedia of Electrical and Electronic Engineer 1999, Volume 18.
    • [Kim199x] "Project: Heat transfert with ADI and PCG-ILU.",Dr. Seongjai Kim , Dep of Mathematics, University of Kentucky, Lexington.
    • [Lai993] "An O(N) Iterative Solution to the Poisson Equation in Low-level Vision Problems.", Lai and Vemuri, Technical Report TR-93-035, 1993, Universty of Florida.
    • [Weic1998] "Efficient and Reliable Schemes for Nonlinear Diffusion Filtering.", Joachim Weickert, report 1998, Utrecht University Hospital.
    • [Weic1999] "Fast Parallel Algorithms for a Broad Class of Nonlinear Variational Diffusion Approaches.", Joachim Weickert & all, report 1999, University of Mannheim, Germany.
    • [Weic2000] "Efficient Image Segmentation Using Partial Differential Equations and Morphology.", Joachim Weickert & all, technical report February 2000, University of Mannheim, Germany.
  • Specialized diffusions.
    • [Mala1995] "Level Set methods for curvature flow, Image enhancement and shape recovery in medical imaging.", R. Malladi & J.A. Sethian, proceeding berlin 1995 , UCLA.
    • [Blom1997] "Color TV: Total Variation Methods for Restoration of Vector Valued Images.", Peter Blomgren & Tony Chan, report 1997 , UCLA.
    • [Kimm1998] "Image processing via beltrami operator.", Ron Kimmel, R. Malladi & all, report 1998 , UCLA/Technion.
    • [Korn1998] "Contribution à la restauration d'images et à l'analyse de séquences: Approches Variationnelles et Solutions de Viscosité.", P. Kornprobst & all,Inria 1998.
    • [Chan2000] "Digital TV filter and nonlinear denoising.", Tony Chan , Stanley Osher & Jianhong Shen, report 2000 , UCLA.
    • [Weic1998] "Coherence-Enhancing Diffusion of colour images.", Joachim Weickert, report 1998, Utrecht University Hospital.
    • [Tang1998] "Direction Diffusion.", Bei Tang, report 1999, University of Minnesota.
    • [Weic2000] "A Scheme for Coherence-Enhancing Diffusion Filtering with Optimize Rotation Invariance.", Joachim Weickert & H. Scharr, Computer Vision 2000.
    • [Leve2000] "Level Set Based segmentation with intensity and curvature priors.", Michael E. Leventon, O. Faugeras & all, MIT & Inria 2000.
  • Enhancement.
    • [Coul2000] "Dual Echo MR Image Processing using multi-spectral probabilistic coupled with shock filters.", O. Coulon & all, report 2000, University College of London.
    • [Tchu2001] "Constrained and unconstrained PDE's for vector image restoration.", D. Tchumperlé & Rachid Deriche, Inria 2001.
  • Wavelets, Lifting and Restoration.
    • [Uytt1997] "The Red Black Transform.", G. Uytterhoeven A. Bultheel, Report TW271 1997, Katholieke Universiteit Leuven, Belgium.
    • [Holm1999] "Solving Hyperbolic PDEs using Intrerpolating Wavelets.", Mats HolmStrom, SIAM 1999.
    • [Vasi2001] "Solving Multi-Dimensionnal Evolution Problems with LocalizedStructures Using Second Generation Wavelets.", Oleg V. Vasilyev, Report University Missouri-Columbia 2001.

Inpainting Papers

    • [Masn1998] "Level lines based disocclusion.", Simon Masnou & JM Morel, Report 1998, Ceremade Université de Paris-IX Dauphine, France.
    • [Masn1998] "Image Restoration involving connectedness.", Simon Masnou & JM Morel, Report 1998, Ceremade Université de Paris-IX Dauphine, France.
    • [Cao1998] "A Generalization of Absolutely Minimizing Lipschitz Extension.", Frederic Cao, Report June 1998, Ecole Normale Supérieure de Cachan, France.
    • [Cass1998] "Image Interpolation.", Vicent Caselles & all, Report July 1998, University of Palma de Mallorca, Spain.
    • [Cass1998] "An Axiomatic Appoach to Image Interpolation.", Vicent Caselles & all, Report July 1998, University of Palma de Mallorca, Spain.
    • [Bert2000] "Image Inpainting.", Marcelo Bertalmio & all, Report 2000, University of Pompeu Fabra, Spain.
    • [Oliv2001] "Fast Digital Image Inpainting.", Manuel M.Oliveira & all, Proceedings on the International Conference on Visualization, Marbella 2001, Spain.
    • [Ball2000] "A Variational Model for Filling-In.", C. Ballester, Marcelo Bertalmio & all, Report 2000, University of Pompeu Fabra, Spain.
    • [Ball2001] "Filling-In by Joint Interpolation of Vector Fields and Gray Levels.", C. Ballester, Marcelo Bertalmio & all, Report April 2001, University of Pompeu Fabra, Spain.
    • [Bert2001] "Navier-Stokes, Fluid Dynamics, and Image and Vidéo Inpainting.", Marcelo Bertalmio, Report 2001, University of Pompeu Fabra, Spain.
    • [Bert2001] "Processing of Flat and non-flat image information on arbitrary manifolds using Partial Differential Equations.", Marcelo Bertalmio, Thesis March 2001, University of Minnesota.
    • [Chan1999] "Mathematical Models for Local Non-Texture Inpaintings.", Tony F. Chan & J. Shen, Report UCLA 1999.
    • [Chan2000] "Non-Texture Inpainting by Curvature-Driven Diffusion (CDD).", Tony F. Chan & J. Shen, Report UCLA 2000.
    • [Chan2001] "Euler'sElastica and Curvature Based Inpaintings.", Tony F. Chan & J. Shen, Report UCLA 2001.
    • [Chan2001] "Morphological Invariant PDE Inpaintings.", Tony F. Chan & J. Shen, Report UCLA 2001.
    • [Chan2001] "Digital Inpainting Based On the Mumford-Shah-Euler Image Model.", Tony F. Chan & J. Shen, Report UCLA 2001.
    • [Wei2000] "Fast Texture Synthesis using Tree-structured Vector Quantization.", L-Yi Wei & Marc Levoy, Report Stanford 2000.
    • [Perl199x] "B-spline Wavelet Paint.", Ken Perlin & Luis Velho, Report New York 199x.
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TV Filtering.(Scale 50%)

    Original image(512x350) Beltrami, time= 58 s Geodesic Beltrami, 100 iter, time= 58 s
    Kimmel ROF, 100 iter, time= 78 s Mean Curvature, 100 iter, time= 53 s TV Beltrami, 100 iter, time= 126 s
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Blurring and soft images.(Scale 50%)

    Original image(512x350) IRR sigma=3, time= 1.7 s IRR sigma=10, time= 1.7 s
    Mean Curvature, 100 iter, time= 53 s Sethian/ROF, 100 iter, time= 53 s Sethian/Beltrami, 100 iter, time= 65 s
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TV Filtering.(Scale 50%)

    Original image(512x350) Color Shock, iter= 50, time= 65 s
    ColorShapiro, 100 iter, time= 145 s Selective Deriche, 100 iter, time= 145 s Combined Deriche, 100 iter, time= 233 s
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Contrast and Enhancement.(Scale 50%)

    Original image(512x350) Morphologic contrast, time= 4.2 s
    Simple Shock, 50 iterations, time= 36 s Selective Simple Shock, 50 iter, time= 56 s Color Shock, 50 iterations, time= 65 s
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Calcite(Zwitzerland)

    Calcite Crystal(512x350) Mean Curvature, 100 iter, time= 53 s
    Beltrami, 100 iter, time= 58 s Rudin/Osher/Fathemi-Sethian, 100 iter, time= 75s
    Color Shock(more contrast), 50 iter, time= 65 s Combined deriche (anisotropic diffusion+shock), 100 iter, time= 233 s
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TV Filtering.(Scale 50%)

    Original image(512x350) TV, lambda=0.1, time= 82 s TV, lambda dynamic, time= 116 s
    TV gauss-jacobi, 100 iter, time= 117 s TV 4th Lysaker, 100 iter, time= 130 s
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Cinamon

    Cinamon of Yunnan(512x350)
    Color Shock(more contrast) 30 iter Color Shock(more contrast) followed by beltrami, 50 iter
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Information.

Java Active documentation in Portable Applets

The project features new active documentation of C++ classes in pure Java, running in a browser, with no additional installations.

This permits people wanting a fly overview, like deciders and consultants, to make rapid presentations, avoiding implementation deep analysis. Leaving potential client or coworkers with a first good impression of capabilities, before deciding deeper project investments.

In case o developpers, I write the Java code very near the C++ developped, to reduce study time, and increase understanding. I hope.The new Applets will also benefit of more information, parameter info, reading, ...

Java 1.1x is used to reduce all portable problems related to higher releases, giving most people their chances. We know more can be featured with higher releases, but this is not our aim here.

C++ Restoration & Inpainting Class Library (needs an update)

Crack detection

    One of the best crack detector is the top hat transform, which is not sensitive to light variation. We were able to restore old painting of the XVIs, by detecting cracks, inpainting and fast restorations.

Illumination and Color Enhancement

    Improving the image brightness without changing color uses simple technology like the histogram equalisation, gamma correction. The result is a greyish image loosing colors. One of the reason is that illumination in the image is non uniform.

    The Retinex Theory shows that the image can be separated in two parts the illuminance and the reflectance. Knowing the illuminance allows to do more appropriate gamma correction.

    In Homomorphic filters the illuminance is approximated by a luminance blurring. Kimmel's Variational Retinex allows to compute more accurate illuminance, taking into account visual properties and illuminance constraints. The result is a better color rendering during gamma modification. Finally, selecting an appropriate color space, can improve even more the results, avoiding chrominance losses.

Restoration

    Accurate restoration which maintains image details is important. We use sophisticated techniques based on the Alvarez-Lions-Morlet restoration model, to recover as much as possible the original image.

    Such techniques use, for example, complex differential equations which will reduce noise through diffusion, and enhance images through shocks.

    Some of these techniques may require a large amount of time(1 to 6 minutes, PIII/500Mhz). This is do to the difficulty of the restoration problem. We will progressively speedup these techniques when possible. We will also add alternative fast restorations.

    Fast AOS restoration reduces the time to 0.4 to 15 seconds(PIII/500Mhz) (divided be 2.5 with SSE1)

Inpainting

    Inpainting is an advanced interpolation scheme. It can be derived from differential equations and Sethian Level Sets...

    In short, the image is an hot area of pixels, and the cracks in the image,or unknown lost parts, are cold pixels. By maintaining the temperature of the pixels of the image, we will warm up the crack image areas on the basis of a border modulated conductivity factor which can locally change on a "material" basis.(e.g.: a metal becomes faster hot than wood,...). In our case the material is the image pixels, edges, curvature,...

    One of the simplest and fastest inpainting scheme, comes from Oliveira, it uses simple diffusion masks, well suited for removing thin areas.

    Faster techniques may exist, in practical condition, a weighted variant of the fast marching does a good and very fast job on thin objects.

    Inpainting on large areas is still a challenging difficult job. Mutiresolution facilitates inpainting. It permits to look images from far, and move to the image. Details are first small, and steadily will grow in size. This will happen to the inpainting areas too.
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Restoration Examples

Inpainting Examples

Segmentation Examples (reduced size)

Tools

If your images are to dark, your monitor has a low gamma. We provide a gamma corrector in the software. On PC(24 bits displays are lighter than 32 bits)
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Mean Shift versus Fast Restoration.

The Mean Shift competes very well against Fast Restorations, in very noisy situations.
Fast Restorations take less time, and are more effective when we do not want to flatten the images.
    Original image(1024x518). : The Titanic taken from an original picture in a Belgium newspaper, December 1912.
    AOS Perona Fast Restoration(RGB): 4 iterations, tau=5, sigma=1, contrast=1, time=36s, with SSE1 9.28s
    Mean Shift with space sigma=8, range sigma=8, time=109s
    Mean Shift with space sigma=16, range sigma=16, time=443s
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Color Bayes Classification Bi-Object/Multi-Class.

    Fountain Object Pass Filter
    Pont d'Avignon Object Pass Filter foreground
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Color Bayes Classification Bi-Objects (background/foreground).

    Calcite Crystal ObjectFilter Foreground Label
    Blende (Spain) ObjectFilter Foreground Label
    Benitoite/Joachinite(San Benito, US) ObjectFilter Foreground Label
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Color Bayes Classification Bi-Object/Multi-Class.

    Benitoite(blue) and Joachinite(orange) (San Benito)
    ObjectFilter Multi ObjectFilter
    Foreground Label Multi Labels
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Restoration of Calcite Crystals.

Performance table

Example Restorations (images are of reduced size)
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Test of Top Hat Transform and Cracks on Old Paintings Test Samples.

    Painting sample with cracks
    Crack detection using Black Top Hat (radial, closing size=8)
    Crack detection (thresholds: 32 and 92)
    Cracks
    Restored Painting using Fast Inpaintings
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