lec12 - Convolution: R= K*I Filtering and Edge Detection *...

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1 CS252A, Fall 2010 Computer Vision I Filtering and Edge Detection Computer Vision I CSE252A Lecture 12 CS252A, Fall 2010 Computer Vision I Image (I) Kernel (K) * Note: Typically Kernel is relatively small in vision applications. -2 1 1 2 -1 -1 Convolution: R= K*I CS252A, Fall 2010 Computer Vision I Convolution: R= K*I I R Kernel size is m+1 by m+1 m=2 CS252A, Fall 2010 Computer Vision I Filters are templates • Applying a filter at some point can be seen as taking a dot- product between the image and some vector • Filtering the image is a set of dot products • Insight – filters look like the effects they are intended to find – filters find effects they look like CS252A, Fall 2010 Computer Vision I Properties of convolution Let f,g,h be images and * denote convolution • Commutative: f*g=g*f • Associative: f*(g*h)=(f*g)*h • Linear: for scalars a & b and images f,g,h (af+bg)*h=a(f*h)+b(g*h) • Differentiation rule CS252A, Fall 2010 Computer Vision I Filtering to reduce noise • Noise is what we’re not interested in. – We’ll discuss simple, low-level noise today: Light fluctuations; Sensor noise; Quantization effects; Finite precision – Not complex: shadows; extraneous objects. • A pixel’s neighborhood contains information about its intensity. • Averaging noise reduces its effect.
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2 CS252A, Fall 2010 Computer Vision I Additive noise • I = S + N. Noise doesn’t depend on signal. • We’ll consider: CS252A, Fall 2010 Computer Vision I Smoothing 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? • A Gaussian gives a good model of a fuzzy blob CS252A, Fall 2010 Computer Vision I Smoothing by Averaging Kernel: CS252A, Fall 2010 Computer Vision I An Isotropic Gaussian • The picture shows a smoothing kernel proportional to (which is a reasonable model of a circularly symmetric fuzzy blob) CS252A, Fall 2010 Computer Vision I Smoothing with a Gaussian Kernel: CS252A, Fall 2010 Computer Vision I The effects of smoothing Each row shows smoothing with gaussians of different width; each column shows different realizations of an image of gaussian noise.
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3 CS252A, Fall 2010
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lec12 - Convolution: R= K*I Filtering and Edge Detection *...

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