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02/04/10Applications of Image FiltersComputer VisionCS 543 / ECE 549University of IllinoisDerek Hoiem
Review: Image filteringg[ , ]111111111h[.,.]f 00909000000000000000000000000000000000000h[m, n] f [k , l ] g[m k , n l ]k ,lCredit: S. Seitz
Image filteringg[ , ]111111111h[.,.]f 000000000009000000000000000000010h[m, n] f [k , l ] g[m k , n l ]k ,lCredit: S. Seitz
Image filteringg[ , ]111111111h[.,.]f 00000000000900000000000000000001020h[m, n] f [k , l ] g[m k , n l ]k ,lCredit: S. Seitz
Filtering in spatial domain* 10-120-210-1
Filtering in frequency domainFFTFFTInverse FFT
Sharpening revisited What does blurring take away?– detailsmoothed (5x5)originalLet’s add it back: αoriginal detailsharpened
Application: Hybrid Images A. Oliva, A. Torralba, P.G. Schyns,“Hybrid Images,” SIGGRAPH 2006
Application: Hybrid Images A. Oliva, A. Torralba, P.G. Schyns,“Hybrid Images,” SIGGRAPH 2006
Today’s class How to use filters for– Matching– Denoising– Anti‐aliasing Image representation with pyramids Texture– What is it?– How to represent it?
Matching with filters Goal: findin image
Matching with filters Goal: findin image Method 1: SSDInput1- sqrt(SSD)Threshold at 0.8
Matching with filters Goal: findin image Method 1: SSD Method 2: Normalized cross‐correlationInputNormalized X-CorrelationThreshold at 0.5
Noise Gaussian Additive NoiseNoisy Image
Gaussian noise Mathematical model: sum of many independentfactors Assumption: independent, zero‐mean noiseSource: M. Hebert
NoiseOriginalSalt and pepper noiseImpulse noiseGaussian noise Salt and peppernoise: containsrandom occurrencesof black and whitepixels Impulse noise:contains randomoccurrences of whitepixels Gaussian noise:variations inintensity drawn froma Gaussian normaldistributionSource: S. Seitz
DenoisingGaussianFilterAdditive Gaussian Noise
Reducing Gaussian noiseSmoothing with larger standard deviations suppresses noise, but also blurs theimageSource: S. Lazebnik
Reducing salt‐and‐pepper noise byGaussian smoothing3x35x57x7
Alternative idea: Median filtering A median filter operates over a window byselecting the median intensity in the window Is median filtering linear?Source: K. Grauman
Median filter What advantage does median filtering haveover Gaussian filtering?– Robustness to outliersSource: K. Grauman
Median filterSalt-and-pepper noiseMedian filtered MATLAB: medfilt2(image, [h w])Source: M. Hebert
Median vs. Gaussian filtering3x3GaussianMedian5x57x7
Subsampling by a factor of 2Throw away every other row andcolumn to create a 1/2 size image
Aliasing problem 1D example (sinewave):Source: S. Marschner
Aliasing problem 1D example (sinewave):Source: S. Marschner
Aliasing problem Sub‐sampling may be dangerous . Characteristic errors may appear:– “Wagon wheels rolling the wrong way inmovies”– “Checkerboards disintegrate in ray tracing”– “Striped shirts look funny on color television”Source: D. Forsyth
Aliasing in videoSlide by Steve Seitz
Aliasing in graphicsSource: A. Efros
Sampling and aliasing
Nyquist‐Shannon Sampling Theorem When sampling a signal at discrete intervals, thesampling frequency must be 2 fmax; fmax max frequency of the input signal. This will allows to reconstruct the originalperfectly from the sampled versionvvvgoodbad
Anti‐aliasingSolutions: Sample more often Get rid of all frequencies that are greaterthan half the new sampling frequency– Will lose information– But it’s better than aliasing– Apply a smoothing filter
Algorithm for downsampling by factor of 21. Start with image(h, w)2. Apply low‐pass filterim blur imfilter(image, fspecial(‘gaussian’, 7, 1))3. Sample every other pixelim small im blur(1:2:end, 1:2:end);
Anti‐aliasingForsyth and Ponce 2002
Subsampling without pre‐filtering1/21/4(2x zoom)1/8(4x zoom)Slide by Steve Seitz
Subsampling with Gaussian pre‐filteringGaussian 1/2G 1/4G 1/8Slide by Steve Seitz
Gaussian pyramidSource: Forsyth
Laplacian filterunit impulseGaussianLaplacian of GaussianSource: Lazebnik
Laplacian pyramidSource: Forsyth
Computing Gaussian/Laplacian PyramidCan we reconstruct the originalfrom the laplacian pyramid?http://sepwww.stanford.edu/ morgan/texturematch/paper html/node3.html
Related idea: 2d wavelets
2d WaveletsMatlab: wavemenu
Image representation Pixels: great for spatial resolution, poor access tofrequency Fourier transform: great for frequency, not for spatialinfo Pyramids/wavelets: balance between spatial andfrequency information
Major uses of image pyramids Compression Object detection– Scale search– Features Detecting stable interest points Registration– Course‐to‐fine
TextureSource: Forsyth
Texture and Materialhttp://www-cvr.ai.uiuc.edu/ponce grp/data/texture database/samples/
Texture and Orientationhttp://www-cvr.ai.uiuc.edu/ponce grp/data/texture database/samples/
Texture and Scalehttp://www-cvr.ai.uiuc.edu/ponce grp/data/texture database/samples/
What is texture? Regular or stochastic patterns caused bybumps, grooves, and/or markings
How can we represent texture? Measure frequencies at various orientationsand scales
Overcomplete representation: filter banksLM Filter BankCode for filter banks: www.robots.ox.ac.uk/ vgg/research/texclass/filters.html
Filter banks Process image with each filter and keepresponses (or squared/abs responses)
Representing texture Idea 1: take simple statistics (e.g., mean, std)of various absolute filter responses
Can you match the texture to theresponse?FiltersAB12C3Mean abs responses
Representing texture by mean absresponseFiltersMean abs responses
Representing texture Idea 2: take vectors of filter responses at each pixel andcluster them, then take histograms (more on in comingweeks)
Things to remember When matching using a filter, normalized crosscorrelation is preferred Use Gaussian or median filter for denoising Beware of aliasing – use lowpass filter to downsample Laplacian pyramids and wavelets providespatial/frequency information Filter banks provide overcomplete representation,good for modeling/recognizing texture
Next class Edges and lines
Questions
over Gaussian filtering? - Robustness to outliers Source: K. Grauman. Median filter Salt-and-pepper noise Median filtered. Source: M. Hebert MATLAB: medfilt2(image, [h w]) Median vs. Gaussian filtering 3x3 5x5. 7x7. Gaussian. Median. Throw away every other row and column to create a 1/2
