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Computational Photography Si Lu Spring 2018 http://web.cecs.pdx.edu/~lusi/CS510/CS510_Computati onal_Photography.htm 04/10/2018 Last Time o Digital Camera n History of Camera n Controlling Camera o Photography Concepts Today o Filters and its

  1. Computational Photography Si Lu Spring 2018 http://web.cecs.pdx.edu/~lusi/CS510/CS510_Computati onal_Photography.htm 04/10/2018

  2. Last Time o Digital Camera n History of Camera n Controlling Camera o Photography Concepts

  3. Today o Filters and its applications naïve denoising better denoising noisy image Gaussian blur edge-preserving filter Slide credit: Sylvain Paris and Frédo Durand

  4. The raster image (pixel matrix) Slide credit: D. Hoiem

  5. The raster image (pixel matrix) 0.92 0.93 0.94 0.97 0.62 0.37 0.85 0.97 0.93 0.92 0.99 0.95 0.89 0.82 0.89 0.56 0.31 0.75 0.92 0.81 0.95 0.91 0.89 0.72 0.51 0.55 0.51 0.42 0.57 0.41 0.49 0.91 0.92 0.96 0.95 0.88 0.94 0.56 0.46 0.91 0.87 0.90 0.97 0.95 0.71 0.81 0.81 0.87 0.57 0.37 0.80 0.88 0.89 0.79 0.85 0.49 0.62 0.60 0.58 0.50 0.60 0.58 0.50 0.61 0.45 0.33 0.86 0.84 0.74 0.58 0.51 0.39 0.73 0.92 0.91 0.49 0.74 0.96 0.67 0.54 0.85 0.48 0.37 0.88 0.90 0.94 0.82 0.93 0.69 0.49 0.56 0.66 0.43 0.42 0.77 0.73 0.71 0.90 0.99 0.79 0.73 0.90 0.67 0.33 0.61 0.69 0.79 0.73 0.93 0.97 0.91 0.94 0.89 0.49 0.41 0.78 0.78 0.77 0.89 0.99 0.93 Slide credit: D. Hoiem

  6. Perception of Intensity Slide credit: C. Dyer

  7. Perception of Intensity Slide credit: C. Dyer

  8. Color Image R G B Slide credit: D. Hoiem

  9. Image Filtering o Image filtering: compute function of local neighborhood at each pixel position o One type of “Local operator,” “Neighborhood operator,” “Window operator” o Useful for: Enhancing images n o Noise reduction, smooth, resize, increase contrast, etc. Extracting information from images n o Texture, edges, distinctive points, etc. n Detecting patterns o Template matching, e.g., eye template Source: D. Hoiem Slide credit: C. Dyer

  10. Blurring in the Real World Camera shake * = Source: Fergus, et al. “ Removing Camera Shake from a Single Photograph”, SIGGRAPH 2006 Bokeh : Blur in out-of-focus regions of image Slide credit: C. Dyer Source: http://lullaby.homepage.dk/diy-camera/bokeh.html

  11. Image Correlation Filtering o Select a filter g n g is called a filter , mask , kernel , or template o Center filter g at each pixel in image f o Multiply weights by corresponding pixels o Set resulting value in output image h o Linear filtering is sum of dot product at each pixel position o Filtering operation called cross-correlation , and denoted h = f  g Slide credit: C. Dyer

  12. Example: Box Filter   g [ , ] 1 1 1 1 1 1 1 1 1 Slide credit: David Lowe

  13. Image Filtering 1 1 1   g [ , ] 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     h [ m , n ] g [ k , l ] f [ m k , n l ] k , l Credit: S. Seitz

  14. 1 1 1 Image Filtering   g [ , ] 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 0 0 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     h [ m , n ] g [ k , l ] f [ m k , n l ] k , l Credit: S. Seitz

  15. 1 1 1 Image Filtering   g [ , ] 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 0 0 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     h [ m , n ] g [ k , l ] f [ m k , n l ] k , l Credit: S. Seitz

  16. 1 1 1 Image Filtering   g [ , ] 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 0 0 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     h [ m , n ] g [ k , l ] f [ m k , n l ] k , l Credit: S. Seitz

  17. 1 1 1 Image Filtering   g [ , ] 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 10 20 30 30 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     h [ m , n ] g [ k , l ] f [ m k , n l ] k , l Credit: S. Seitz

  18. 1 1 1 Image Filtering   g [ , ] 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 10 20 30 30 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 ? 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     h [ m , n ] g [ k , l ] f [ m k , n l ] k , l Credit: S. Seitz

  19. 1 1 1 Image Filtering   g [ , ] 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 10 20 30 30 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 ? 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 50 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     h [ m , n ] g [ k , l ] f [ m k , n l ] k , l Credit: S. Seitz

  20.   g [ , ] 1 1 1 Image Filtering 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 30 30 30 20 10 0 0 0 90 90 90 90 90 0 0 0 20 40 60 60 60 40 20 0 0 0 90 90 90 90 90 0 0 0 30 60 90 90 90 60 30 0 0 0 90 90 90 90 90 0 0 0 30 50 80 80 90 60 30 0 0 0 90 0 90 90 90 0 0 0 30 50 80 80 90 60 30 0 0 0 90 90 90 90 90 0 0 0 20 30 50 50 60 40 20 0 0 0 0 0 0 0 0 0 0 10 20 30 30 30 30 20 10 0 0 90 0 0 0 0 0 0 0 10 10 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     h [ m , n ] g [ k , l ] f [ m k , n l ] k , l Credit: S. Seitz

  21. Box Filter What does it do? • Replaces each pixel with   g [ , ] an average of its neighborhood 1 1 1 • Achieves smoothing 1 1 1 effect (i.e., removes 1 1 1 sharp features) • Weaknesses: • Blocky results • Axis-aligned streaks Slide credit: David Lowe

  22. Smoothing with Box Filter Slide credit: C. Dyer

  23. Properties of Smoothing Filters o Smoothing n Values all positive n Sum to 1  constant regions same as input n Amount of smoothing proportional to mask size n Removes “high-frequency” components n “low-pass” filter Slide credit: C. Dyer

  24. Gaussian Filtering Weight contributions of neighboring pixels by nearness o 0.003 0.013 0.022 0.013 0.003 0.013 0.059 0.097 0.059 0.013 0.022 0.097 0.159 0.097 0.022 0.013 0.059 0.097 0.059 0.013 0.003 0.013 0.022 0.013 0.003 5 x 5,  = 1 o Constant factor at front makes volume sum to 1 o Convolve each row of image with 1D kernel to produce new image; then convolve each column of new image with same 1D kernel to yield output image Slide credit: Christopher Rasmussen

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