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
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