Templates, Image Pyramids, and Filter Banks

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1 Templates, Image Pyramids, and Filter Banks 09/9/ Computer Vision James Hays, Brown Slides: Hoiem and others

2 Review. Match the spatial domain image to the Fourier magnitude image B A C D E Slide: Hoiem

3 Reminder Project due in one week

4 Today s class Template matching Image Pyramids Filter banks and texture Denoising, Compression

5 Template matching Goal: find in image Main challenge: What is a good similarity or distance measure between two patches? Correlation Zero-mean correlation Sum Square Difference Normalized Cross Correlation Slide: Hoiem

6 Matching with filters Goal: find in image Method 0: filter the image with eye patch h[ m, n] g[ k, l] k, l f [ m k, n l] f = image g = filter What went wrong? Input Filtered Image Slide: Hoiem

7 Matching with filters Goal: find in image Method : filter the image with zero-mean eye h[ m, n] ( k, l f [ k, l] f ) ( g[ m k, n l]) mean of f True detections False detections Input Filtered Image (scaled) Thresholded Image Slide: Hoiem

8 Matching with filters Goal: find in image Method 2: SSD h[ m, n] ( g[ k, l] f [ m k, n l]) k, l 2 True detections Input - sqrt(ssd) Thresholded Image Slide: Hoiem

9 Matching with filters Goal: find Method 2: SSD in image h[ m, n] ( g[ k, l] f [ m k, n l]) k, l What s the potential downside of SSD? 2 Input - sqrt(ssd) Slide: Hoiem

10 Matching with filters Goal: find in image Method 3: Normalized cross-correlation 0.5, 2,, 2,, ) ], [ ( ) ], [ ( ) ], [ )( ], [ ( ], [ l k m n l k m n l k f l n k m f g l k g f l n k m f g l k g m n h Matlab: normxcorr2(template, im) mean image patch mean template Slide: Hoiem

11 Matching with filters Goal: find in image Method 3: Normalized cross-correlation True detections Input Normalized X-Correlation Thresholded Image Slide: Hoiem

12 Matching with filters Goal: find in image Method 3: Normalized cross-correlation True detections Input Normalized X-Correlation Thresholded Image Slide: Hoiem

13 Q: What is the best method to use? A: Depends SSD: faster, sensitive to overall intensity Normalized cross-correlation: slower, invariant to local average intensity and contrast

14 Q: What if we want to find larger or smaller eyes? A: Image Pyramid

15 Review of Sampling Image Gaussian Filter Low-Pass Filtered Image Sample Low-Res Image Slide: Hoiem

16 Gaussian pyramid Source: Forsyth

17 Template Matching with Image Pyramids Input: Image, Template. Match template at current scale 2. Downsample image 3. Repeat -2 until image is very small 4. Take responses above some threshold, perhaps with non-maxima suppression Slide: Hoiem

18 Coarse-to-fine Image Registration. Compute Gaussian pyramid 2. Align with coarse pyramid 3. Successively align with finer pyramids Search smaller range Why is this faster? Are we guaranteed to get the same result? Slide: Hoiem

19 Laplacian filter unit impulse Gaussian Laplacian of Gaussian Source: Lazebnik

20 2D edge detection filters Laplacian of Gaussian Gaussian derivative of Gaussian is the Laplacian operator:

21 Laplacian pyramid Source: Forsyth

22 Computing Gaussian/Laplacian Pyramid Can we reconstruct the original from the laplacian pyramid?

23 Hybrid Image Slide: Hoiem

24 Hybrid Image in Laplacian Pyramid High frequency Low frequency Slide: Hoiem

25 Image representation Pixels: great for spatial resolution, poor access to frequency Fourier transform: great for frequency, not for spatial info Pyramids/filter banks: balance between spatial and frequency information Slide: Hoiem

26 Major uses of image pyramids Compression Object detection Scale search Features Detecting stable interest points Registration Course-to-fine Slide: Hoiem

27 Denoising Gaussian Filter Additive Gaussian Noise Slide: Hoiem

28 Reducing Gaussian noise Smoothing with larger standard deviations suppresses noise, but also blurs the image Source: S. Lazebnik

29 Reducing salt-and-pepper noise by Gaussian smoothing 3x3 5x5 7x7

30 Alternative idea: Median filtering A median filter operates over a window by selecting the median intensity in the window Is median filtering linear? Source: K. Grauman

31 Median filter What advantage does median filtering have over Gaussian filtering? Robustness to outliers Source: K. Grauman

32 Median filter Salt-and-pepper noise Median filtered MATLAB: medfilt2(image, [h w]) Source: M. Hebert

33 Median vs. Gaussian filtering 3x3 5x5 7x7 Gaussian Median

34 Other non-linear filters Weighted median (pixels further from center count less) Clipped mean (average, ignoring few brightest and darkest pixels) Bilateral filtering (weight by spatial distance and intensity difference) Bilateral filtering Image:

35 Review of last three days

36 Review: Image filtering g[, ] f [.,.] h[.,.] h[ m, n] k, l f [ k, l] g[ m k, n l] Credit: S. Seitz

37 Image filtering g[, ] f [.,.] h[.,.] h[ m, n] k, l f [ k, l] g[ m k, n l] Credit: S. Seitz

38 Image filtering g[, ] f [.,.] h[.,.] h[ m, n] k, l f [ k, l] g[ m k, n l] Credit: S. Seitz

39 Filtering in spatial domain * =

40 Filtering in frequency domain FFT FFT = Inverse FFT Slide: Hoiem

41 Review of Last 3 Days Linear filters for basic processing Edge filter (high-pass) Gaussian filter (low-pass) [- ] Gaussian FFT of Gradient Filter FFT of Gaussian Slide: Hoiem

42 Review of Last 3 Days Derivative of Gaussian Slide: Hoiem

43 Review of Last 3 Days Applications of filters Template matching (SSD or Normxcorr2) SSD can be done with linear filters, is sensitive to overall intensity Gaussian pyramid Coarse-to-fine search, multi-scale detection Laplacian pyramid More compact image representation Can be used for compositing in graphics Downsampling Need to sufficiently low-pass before downsampling

44 Next Lectures Machine Learning Crash Course

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