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U of I CS 498 - Image features: Histograms

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Image features: Histograms, Aliasing, Filters, Orientation and HOGD.A. ForsythSimple color features•Histogram of image colors in a window•Opponent color representations•R-G•B-Y=B-(R+G)/2•Intensity=(R+G+B)/3•Percentage of blue pixels•Blue pixel mapMatlab slideScaled representations•Represent one image with many different resolutions•Why?•find bigger, smaller swimming poolsCarelessness causes aliasingObtained pyramid of images by subsamplingMatlab slide: subsamplingAliasing and fast changing signalsMore aliasing examples•Undersampled sine wave ->•Color shimmering on striped shirts on TV•Wheels going backwards in movies•temporal aliasingAnother aliasing example•location of a sharp change is known poorly0 50100150200250 300 35040000.10.20.30.40.50.60.70.80.91Fundamental facts•A sine wave will alias if sampled less often than twice per period01020 3040 50 6070 80 90100ï1ï0.8ï0.6ï0.4ï0.200.20.40.60.8101020 3040 50 6070 80 90100ï1ï0.8ï0.6ï0.4ï0.200.20.40.60.8101020 3040 50 6070 80 90100ï1ï0.8ï0.6ï0.4ï0.200.20.40.60.8101020 3040 50 6070 80 90100ï1ï0.8ï0.6ï0.4ï0.200.20.40.60.8101020 3040 50 6070 80 90100ï1ï0.8ï0.6ï0.4ï0.200.20.40.60.8101020 3040 50 6070 80 90100ï1ï0.8ï0.6ï0.4ï0.200.20.40.60.8101020 3040 50 6070 80 90100ï1ï0.8ï0.6ï0.4ï0.200.20.40.60.8101020 3040 50 6070 80 90100ï1ï0.8ï0.6ï0.4ï0.200.20.40.60.81Fundamental facts•Sample(A+B)=Sample(A)+Sample(B)•if a signal contains a high frequency sine wave, it will alias01020 3040 50 6070 80 90100ï1ï0.8ï0.6ï0.4ï0.200.20.40.60.8101020 3040 50 6070 80 90100ï1ï0.8ï0.6ï0.4ï0.200.20.40.60.8101020 3040 50 6070 80 90100ï1ï0.8ï0.6ï0.4ï0.200.20.40.60.81Weapons against aliasing•Filtering•or smoothing•take the signal, reduce the fast-changing/high-frequency content•can do this by weighted local averagingPrefiltering (Ideal case)ContinuousImageSamplingContinuousImageDiscreteSamplesReconstructionppReconstructionKernel1 1SamplingFunctionFilterSmoothing by AveragingNij=1NΣuvOi+u,j+vwhere u, v, is a window of N pixels in total centered at 0, 0• A Gaussian gives a good model of a fuzzy blobSmoothing with a Gaussian•Notice “ringing” •apparently, a grid is superimposed•Smoothing with an average actually doesn’t compare at all well with a defocussed lens•what does a point of light produce?Gaussian filter kernelKuv=�12πσ2�exp�−�u2+ v2�2σ2�We’re assuming the index can take negative valuesNij=�uvOi−u,j−vKuvNotice the curious looking formSmoothing with a GaussianMatlab slide: convolution in 2DLinear Filters•Example: smoothing by averaging•form the average of pixels in a neighbourhood•Example: smoothing with a Gaussian•form a weighted average of pixels in a neighbourhood•Example: finding a derivative•form a weighted average of pixels in a neighbourhoodFinding derivativesNij=1∆x(Ii+1,j− Iij)•Each of these involves a weighted sum of image pixels•The set of weights is the same •we represent these weights as an image, H•H is usually called the kernel•Operation is called convolution•it’s associative•Any linear shift-invariant operation can be represented by convolution•linear: G(k f)=k G(f)•shift invariant: G(Shift(f))=Shift(G(f))•Examples: •smoothing, differentiation, camera with a reasonable, defocussed lens systemConvolutionNij=�uvHuvOi−u,j−vFilters are templates•At one point•output of convolution is a (strange) dot-product•Filtering the image involves a dot product at each point• Insight •filters look like the effects they are intended to find•filters find effects they look likeNij=�uvHuvOi−u,j−vSmoothing reduces noise•Generally expect pixels to “be like” their neighbours•surfaces turn slowly•relatively few reflectance changes•Expect noise to be independent from pixel to pixel•Implies that smoothing suppresses noise, for appropriate noise models•Scale•the parameter in the symmetric Gaussian•as this parameter goes up, more pixels are involved in the average•and the image gets more blurred•and noise is more effectively suppressedKuv=�12πσ2�exp�−�u2+ v2�2σ2�Representing image changes: Edges• Idea:• points where image value change very sharply are important• changes in surface reflectance• shadow boundaries• outlines• Finding Edges:• Estimate gradient magnitude using appropriate smoothing• Mark points where gradient magnitude is• Locally biggest and• bigMatlab slide: gradientsMatlab slide: smoothed gradients1 pixel 3 pixels 7 pixelsScale affects derivativesScale affects gradient magnitudeSmoothing and Differentiation•Issue: noise•smooth before differentiation•two convolutions to smooth, then differentiate?•actually, no - we can use a derivative of Gaussian filterMatlab slide: orientations and arrow plotsMatlab slide: rose plotsHog features•Take a window•subdivide into boxes, each with multiple pixels•these might overlap•for each box, build a histogram of gradient orientations•possibly weighting by distance from center•possibly normalizing by intensity over the box•string these histograms together to a vector•Extremely strong at spatial codingVlfeat pointerImage HOG featuresPositive termsin linear classifierNegative termsin linear


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U of I CS 498 - Image features: Histograms

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