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## Computer and Robot Vision I

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**Computer and Robot Vision I**Chapter 7 Conditioning and Labeling Presented by: 傅楸善 & 江祖榮 r02922085@ntu.edu.tw 指導教授: 傅楸善 博士**Recognition Methodology**• Conditioning • Labeling • Grouping • Extracting • Matching**7-1 Introduction**• Conditioning: noise removal, background normalization,… • Labeling: thresholding, edge detection, corner finding,… dDC & CV Lab. CSIE NTU**7-2 Noise Cleaning**• noise cleaning: • uses neighborhood spatial coherence • uses neighborhood pixel value homogeneity**7-2 Filter**Xaxis image Filter Yaxis**7.2 Noise Cleaning**box filter: computes equally weighted average box filter: separable box filter: recursive implementation with “two+”, “two-”, “one/” per pixel**filter: separable*** =* 3 multiplications 9 multiplications 3 multiplications * =* 3 multiplications 9 multiplications 3 multiplications**7.2 Noise Cleaning**=* = ***7.2 Noise Cleaning**=* = ***7.2 Noise Cleaning**• Gaussian filter: linear smoother weight matrix: for all where size of W: two or three from center linear noise-cleaning filters: defocusing images, edges blurred**A Statistical Framework for Noise Removal**• Idealization assumption: if there were no noise, the pixel values in each image neighborhood would be the same constant**Outlier or Peak Noise**• outlier: peak noise: pixel value replaced by random noise value • neighborhood size: larger than noise, smaller than preserved detail • center-deleted: neighborhood pixel values in neighborhood except center**Outlier or Peak Noise**Decide whether y is an outlier or not center-deleted neighborhood center pixel value**Outlier or Peak Noise**center-deleted neighborhood center pixel value mean of center-deleted neighborhood minimizes**Outlier or Peak Noise**output value of neighborhood outlier removal not an outlier value if reasonably close to use mean value when outlier threshold for outlier value too small: edges blurred too large: noise cleaning will not be good**Outlier or Peak Noise**center-deleted neighborhood variance use neighborhood mean if pixel value significantly far from mean**7-2-3 Outlier or Peak Noise**• smooth replacement: instead of complete replacement or not at all convex combination of input and mean use neighborhood mean weighting parameter use input pixel value**7-2-4K-Nearest Neighbor**• K-nearest neighbor: average equally weighted average of k-nearest neighbors**7-2-5 Gradient Inverse weighted**• gradient inverse weighted: reduces sum-of-squares error within regions**7-2-6 Order Statistic Neighborhood Operators**• order statistic: linear combination of neighborhood sorted values • neighborhood pixel values sorted neighborhood values from smallest to largest**7-2-6 Order Statistic Neighborhood Operators**• Median Operator median: most common order statistic operator median root: fixed-point result of a median filter median roots: comprise only constant-valued neighborhoods, sloped edges**Median Root Image**Original Image**7-2-6 Order Statistic Neighborhood Operators**• median: effective for impulsive noise (salt and pepper) • median: distorts or loses fine detail such as thin lines**7-2-6 Order Statistic Neighborhood Operators**• Running-median Operator inter-quartile distance**7-2-6 Order Statistic Neighborhood Operators**• Trimmed-Mean Operator trimmed-mean: first k and last k order statistics not used trimmed-mean: equal weighted average of central N-2k order statistics**7-2-6 Order Statistic Neighborhood Operators**• Midrange operator midrange: noise distribution with light and smooth tails**7-2-7 Hysteresis Smoothing**• hysteresis smoothing: removes minor fluctuations, preserves major transients • hysteresis smoothing: • finite state machine with two states: UP, DOWN • applied row-by-row and then column-by-column**7-2-7 Hysteresis Smoothing**• if state DOWN and next one larger, if next local maximum does not exceed threshold then stays current value i.e. small peak cuts flat • otherwise state changes from DOWN to UP and preserves major transients**7-2-7 Hysteresis Smoothing**• if state UP and next one smaller, if next local minimum does not exceed threshold then stays current value i.e. small valley filled flat • otherwise state changes from UP to DOWN and preserves major transients**Sigma Filter**• sigma filter: average only with values within two-sigma interval**Selected-Neighborhood Averaging**• selected-neighborhood averaging: assumes pixel a part of homogeneous region (not required to be squared, others can be diagonal, rectangle, three pixels vertical and horizontal neighborhood) • noise-filtered value: mean value from lowest variance neighborhood**Minimum Mean Square Noise Smoothing**• minimum mean square noise smoothing: additive or multiplicative noise • each pixel in true image: regarded as a random variable**Noise-Removal Techniques-Experiments**• uniform • Gaussian • salt and pepper • varying noise (the noise energy varies across the image) types of noise**Noise-Removal Techniques-Experiments**• salt and pepper minimum/ maximum gray value for noise pixels fraction of image to be corrupted with noise uniform random variable in [0,1] gray value at given pixel in input image gray value at given pixel in output image**Noise-Removal Techniques-Experiments**• Generate salt-and-pepper noise I(nim, i , j) = 0 if uniform(0,1) < 0.05 I(nim, i , j) = 255 if uniform(0,1) > 1- 0.05 I(nim, i, j) = I(im, i ,j) otherwise uniform(0,1) : random variable uniformly distributed over [0,1]**Noise-Removal Techniques-Experiments**• S/N ratio (signal to noise ratio): • VS: image gray level variance • VN: noise variance**Noise-Removal Techniques-Experiments**uniform noise Gaussian noise salt and pepper noise varies