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cs685-perception-2

# cs685-perception-2 - ICRA 2003 Tutorial 1 Image Brightness...

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10/15/09 1 1 ICRA 2003 Tutorial Image Brightness values I(x,y)

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10/15/09 2 Local, meaningful, detectable parts of the image. Edge detection Line detection Corner detection Motivation Information content high Invariant to change of view point, illumination Reduces computational burden Uniqueness Can be tuned to a task at hand Given a noisy image How do we reduce noise ? How do we find useful features ? Today: Filtering Point-wise operations Edge detection
10/15/09 3 1D signal and its sampled version f = { f(1), f(2), f(3), …, f(n)} f = {0, 1, 2, 3, 4, 5, 5, 6, 10 } The output of the linear filtering (system) is related to the input via convolution Convolution sum: Notation for convolution: filter h f g f – input signal (image), h – filter, g-output signal (image) Convolution general concept behind linear filtering operations Linear Filters – one means of processing 1D signals Notice weird order of indices: it’s a result of the derivation expressing any shift-invariant linear operator as a convolution.

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10/15/09 4 Averaging filter Box filter Averaging filter center pixel weighted more and 0 everywhere else Ex. cont. Original image Smoothed image
10/15/09 5 CS223b, Jana Kosecka

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10/15/09 6
10/15/09 7 The bigger the mask, more neighbors contribute. smaller noise variance of the output. bigger noise spread. more blurring. more expensive to compute. Signal frequencies shared with noise are lost, resulting in blurring. Impulsive noise is diffused but not removed. The secondary lobes of the sinc let noise into the filtered image (frequency domain interpretation) It spreads the noise, resulting in blurring. Impulsive noise is diffused but not removed.

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10/15/09 8 Computer Vision - A Modern Approach Set: Linear Filters Slides by D.A. Forsyth A particular case of averaging The coefficients are samples of a 1D Gaussian. Gives more weight at the central pixel and less weights to the neighbors. The further away the neighbors, the smaller the weight. Sample from the continuous Gaussian
10/15/09 9 Computer Vision - A Modern Approach Set: Linear Filters Slides by D.A. Forsyth The std. dev of the Gaussian σ determines the amount of smoothing. The samples should adequately represent a Gaussian For a 98.76% of the area, we need m = 5 σ 5.(1/ σ ) 2 π σ 0.796, m 5 g[x] = [0.136, 0.6065, 1.00, 0.606, 0.136] 5-tap filter

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10/15/09 10 Convolution with a 2D Gaussian filter Gaussian filter is separable, convolution can be accomplished as two 1-D convolutions The bigger the mask, more neighbors contribute. smaller noise variance of the output. bigger noise spread. more blurring. more expensive to compute.
10/15/09 11 Signal frequencies shared with noise are lost, resulting in blurring.

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