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CSCE 643 Computer Vision: Template Matching, Image Pyramids and Denoising Jinxiang Chai

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Today’s class Template matching Gaussian Pyramids Laplacian Pyramids Image denoising

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Template matching Goal: find in image

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Template matching Goal: find in image Main challenge: What is a good similarity or distance measure between two patches?

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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

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Matching with filters Goal: find in image Method 0: filter the image with eye patch Input Filtered Image What went wrong? f = image g = filter Slide: Hoiem

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Problem with Correlation

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Solution

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Slide: Hoiem Matching with filters Goal: find in image Method 1: filter the image with zero-mean eye Input Filtered Image (scaled) Thresholded Image True detections False detections mean of f

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Slide: Hoiem Matching with filters Goal: find in image Method 2: SSD Input 1- sqrt(SSD) Thresholded Image True detections

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Relationship SSD and Correlation

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Matching with filters Goal: find in image Method 2: SSD Input 1- sqrt(SSD) What’s the potential downside of SSD? Slide: Hoiem

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Matching with filters Goal: find in image Method 3: Normalized cross-correlation - subtracting the mean - dividing by the standard deviationstandard deviation

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Matching with filters Goal: find in image Method 3: Normalized cross-correlation Matlab: normxcorr2(template, im) mean image patch mean template

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

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

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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

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

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Gaussian Pyramid Low-Pass Filtered Image Image Gaussian Filter Sample Low-Res Image

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Gaussian Pyramid filter mask Repeat –Filter –Subsample Until minimum resolution reached –can specify desired number of levels (e.g., 3-level pyramid )

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Gaussian pyramid

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Template Matching with Image Pyramids Input: Image, Template 1.Match template at current scale 2.Downsample image 3.Repeat 1-2 until image is very small 4.Take responses above some threshold, perhaps with non-maxima suppression

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Laplacian pyramid

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Laplacian Filter The filtering kernel for Laplacian is Finite difference allows us to approximate the Laplacian using the following filtering kernel.

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Laplacian Pyramid Laplacian Pyramid (subband images) - Created from Gaussian pyramid by subtraction

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The Laplacian of Gaussian Kernel is the Laplacian operator:

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The Laplacian of Gaussian Filter Kernel

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Laplacian Pyramid What happens in frequency domain?

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Laplacian Pyramid What happens in frequency domain? Bandpass filters Can we reconstruct the original from the laplacian pyramid?

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Laplacian Pyramid What happens in frequency domain? Bandpass filters Can we reconstruct the original from the laplacian pyramid? - Yes, laplacian pyramid is a complete image representation which encodes fine to course structure in a different level

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Image representation Pixels: great for spatial resolution, poor access to frequency Fourier transform: great for frequency, not for spatial info such as locations. Pyramids/filter banks: balance between spatial and frequency information

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Major uses of image pyramids Compression Object detection – Scale search – Features Detecting stable interest points Image blending/mosaicing Registration – Course-to-fine

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Multi-resolution SIFT Feature Detection - Object recognition from local scale-invariant features [pdf link], ICCV 09pdf link - David G. Lowe, "Distinctive image features from scale- invariant keypoints," International Journal of Computer Vision, 60, 2 (2004), pp. 91-110

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Pyramid Blending

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laplacian level 4 laplacian level 2 laplacian level 0 left pyramidright pyramidblended pyramid

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Hierarchical Image Registration 1.Compute Gaussian pyramid 2.Align with coarse pyramid 3.Successively align with finer pyramids – Search smaller range Why is this faster? - Hierarchical Model-Based Motion Estimation- Hierarchical Model-Based Motion Estimation, ECCV 92

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Denoising Additive Gaussian Noise Gaussian Filter

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Gaussian inputGaussian filter

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Median Filter For each neighbor in image, sliding the window Sort pixel values Set the center pixel to the median

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Median Filter input Gaussian filterMedian filter

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Median Filter Examples inputMedian 7X7

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Median Filter Examples Median 11X11 Median 3X3

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Median Filter Examples Median 11X11 Median 3X3 Straight edges kept Sharp features lost

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Median Filter Properties Can remove outliers (peppers and salts) Window size controls size of structure Preserve some details but sharp corners and edges might get lost

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Comparison of Mean, Gaussian, and Median originalMean with 6 pixels

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Comparison of Mean, Gaussian, and Median originalGaussian with 6 pixels

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Comparison of Mean, Gaussian, and Median originalMedian with 6 pixels

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Common Problems Mean: blurs image, removes simple noise, no details are preserved

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Common Problems Mean: blurs image, removes simple noise, no details are preserved Gaussian: blurs image, preserves details only for small σ.

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Common Problems Mean: blurs image, removes simple noise, no details are preserved Gaussian: blurs image, preserves details only for small σ. Median: preserves some details, good at removing strong noise

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Common Problems Mean: blurs image, removes simple noise, no details are preserved Gaussian: blurs image, preserves details only for small σ. Median: preserves some details, good at removing strong noise Can we find a filter that not only smooths regions but preserves sharp features such as edges?

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Common Problems Mean: blurs image, removes simple noise, no details are preserved Gaussian: blurs image, preserves details only for small σ. Median: preserves some details, good at removing strong noise Can we find a filter that not only smooths regions but preserves sharp features such as edges? -yes, Tomasi's Bilateral Filter!Tomasi's Bilateral Filter

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Bilateral Filter Example Gaussian filter Bilateral filter

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Bilateral Filter Example Gaussian filter Bilateral filter

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1D Graphical Example Center Sample u It is clear that in weighting this neighborhood, we would like to preserve the step Neighborhood I(p) p

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The Weights p I(p)

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Filtered Values p I(p) Filtered value

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Edges Are Smoothed p I(p) Filtered value

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What Causes the Problem? p I(p) Filtered value

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What Causes the Problem? p I(p) Filtered value Same weights for these two pixels!!

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The Weights p I(p)

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Bilateral filter Denoise Feature preserving Normalization Bilateral Filtering

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Filter Parameters As proposed by Tomasi and Manduchi, the filter is controlled by 3 parameters: The filter can be applied for several iterations in order to further strengthen its edge-preserving smoothing N(u) – The neighbor size of the filter support, c – The variance of the spatial distances, s – The variance of the value distances,

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Bilateral Filter Results Original

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Bilateral Filter Results σ c = 3, σ s = 3

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Bilateral Filter Results σ c = 6, σ s = 3

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Bilateral Filter Results σ c = 12, σ s = 3

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Bilateral Filter Results σ c = 12, σ s = 6

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Bilateral Filter Results σ c = 15, σ s = 8

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Summary – 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 – Image denoising

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Recall: Gaussian smoothing/sampling G 1/4 G 1/8 Gaussian 1/2 Solution: filter the image, then subsample Filter size should double for each ½ size reduction.

Recall: Gaussian smoothing/sampling G 1/4 G 1/8 Gaussian 1/2 Solution: filter the image, then subsample Filter size should double for each ½ size reduction.

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