Image Processing - Variational and PDE Methods · 2018. 10. 8. · Image Processing - Variational...
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Image Processing - Variational and PDE Methods Carola-Bibiane Sch ¨ onlieb DAMTP University of Cambridge Cambridge - January, 17th 2013 Sch ¨ onlieb (Cambridge) Image Processing Cambridge-17. January 2013 1 / 11
Transcript of Image Processing - Variational and PDE Methods · 2018. 10. 8. · Image Processing - Variational...
Image Processing - Variational and PDE Methods
Carola-Bibiane Schonlieb
DAMTPUniversity of Cambridge
Cambridge - January, 17th 2013
Schonlieb (Cambridge) Image Processing Cambridge-17. January 2013 1 / 11
Outline
Outline
1 Digital Image ProcessingWhat is a Digital Image and how do we Process it?Examples
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Digital Image Processing
Outline
1 Digital Image ProcessingWhat is a Digital Image and how do we Process it?Examples
Schonlieb (Cambridge) Image Processing Cambridge-17. January 2013 3 / 11
Digital Image Processing What is a Digital Image and how do we Process it?
Digital images
A digital image is obtained from an analogue image (representing thecontinuous world) by sampling and quantization . . .
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Digital Image Processing What is a Digital Image and how do we Process it?
Digital images
A digital image is obtained from an analogue image (representing thecontinuous world) by sampling and quantization . . .
Schonlieb (Cambridge) Image Processing Cambridge-17. January 2013 4 / 11
Digital Image Processing What is a Digital Image and how do we Process it?
Digital images (cont.)
. . . it consists of pixels (grid element, matrix positions) which areassigned with the mean grayscale or colour information within thiselement . . .
grayscale imageu : Ω = 1, 2, . . . ,m × 1, 2, . . . , n → I = 0, 1, . . . , 255colour image u : Ω→ I3, where u(x, y) = (r, g, b) = (red, green,blue).
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Digital Image Processing What is a Digital Image and how do we Process it?
Digital images (cont.)
. . . it consists of pixels (grid element, matrix positions) which areassigned with the mean grayscale or colour information within thiselement . . .
grayscale imageu : Ω = 1, 2, . . . ,m × 1, 2, . . . , n → I = 0, 1, . . . , 255colour image u : Ω→ I3, where u(x, y) = (r, g, b) = (red, green,blue).
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Digital Image Processing Examples
Imaging tasks (cont.)
Image Denoising Link
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Image Deblurring
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Digital Image Processing Examples
Imaging tasks (cont.)
Image Segmentation
Image Inpainting
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Digital Image Processing Examples
Imaging tasks (cont.)
Image Reconstruction
⇓
Image Registration
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Digital Image Processing Examples
Books & online resources
Course page http://www.damtp.cam.ac.uk/user/cbs31/Teaching.html
Image Processing Online http://www.ipol.im
CAM preprints http://www.math.ucla.edu/applied/cam/Aubert & Kornprobst. Mathematical Problems in ImageProcessing. Applied Mathematical Sciences Vol. 147, Springer2002.Chan & Shen. Image Processing and Analysis. Variational, PDE,Wavelet, and Stochastic Methods, SIAM 2005.Scherzer, Grasmair, Grossauer, Haltmeier & Lenzen. VariationalMethods in Imaging. Applied Mathematical Sciences 2009.Bredies & Lorenz. Mathematische Bildverarbeitung. Einfuhrung inGrundlagen und moderne Theorie, Vieweg & Teuber 2011.
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Digital Image Processing Examples
Imaging tasks
Image Denoising – Acquisition under bad lighting conditions
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Digital Image Processing Examples
Imaging tasks (cont.)
Image Denoising – Acquisition under bad lighting conditions
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