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Images Camera models Digital images Colour images Noise Smoothing Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014Slide 1

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Camera models Components: A photosensitive image plane A housing A lenses Mathematical model needed The simple pinhole camera model Distortions Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 2

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Camera models Simple Pinhole Model Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 3

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Camera models Simple Pinhole Model 3-D point 2-D image point Scaling factor Combination of focal length and image coordinate system Location of the optical centre Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 4

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Digital Images Theoretically images are continuous 2D functions of reflected scene brightness. (i, j) or (column, row) or (x, y) To process on a computer we need a discrete representation Sample Quantise Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 5

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Digital Images Sampling Sample the continuous 2D function into discrete elements. Sensor 2D array Photosensitive elements Non photosensitive gaps Issues Elements have a fixed area Gaps Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 6

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Digital Images Sampling How many samples do we need ? Wasted space and computation time Enough for the objects of interest Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 7 Mat image, smaller_image; resize( image, smaller_image, Size( image1.cols/2, image.rows/2 ));

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Digital Images Quantisation Represent the individual image points as digital values. Typically 8 bits Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 8

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Digital Images Quantisation How many bits do we need ? Wasted space ? Losing the ability to distinguish objects Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 9 void ChangeQuantisationGrey( Mat &image, int num_bits ) { CV_Assert( (image.type() == CV_8UC1) && (num_bits >= 1) && (num_bits

Colour Images Skin detection (S >= 0.2) AND (0.5 < L/S = 50) && (LS_ratio > 0.5) && (LS_ratio = 165));

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Colour Images Red eye detection (L >= 0.25) AND (S >= 0.4) AND (0.5 < L/S = 64) && (S >= 100) && (LS_ratio > 0.5) && (LS_ratio < 1.5) && ((H = 162));

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Noise Affects most images Degrades the image Can cause problems with processing Causes? Measuring noise: Correcting noise Types Gaussian Salt and Pepper Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 23

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Noise - Models Additive noise f(i,j) = g(i,j) + v(i,j) Multiplicative noise f(i,j) = g(i,j) + g(i,j).v(i,j) Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 24

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Noise Salt and Pepper Noise Impulse noise Noise is maximum or minimum values Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 25

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Noise Salt and Pepper Noise Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 26 int noise_points = (int) (((double) image_rows* image.cols*image.channels())*noise_percentage/100.0); for (int count = 0; count < noise_points; count++) { int row = rand() % image.rows; int column = rand() % image.cols; int channel = rand() % image.channels(); uchar* pixel = image.ptr (row) + (column*image.channels()) + channel; *pixel = (rand()%2 == 1) ? 255 : 0; }

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Noise Gaussian Noise Good approximation to real noise Distribution is Gaussian (mean & s.d.) Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 27

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Noise Gaussian Noise Generation Select value for Determine distribution -(i) 2 p(i) = 1.e 2 2 i = -(G-1),..,-1,0,1,,G-1 2 P cum (-(G-1)) = p(-(G-1)) P cum (i) = P cum (i-1) + p(i) For every pixel (x,y) f*(x,y) = g(x,y) + argmin i (abs( rand() - P cum [i] )) Set f(x,y) = 0 if f*(x,y) < 0 f(x,y) = G-1 if f*(x,y) > G-1 f(x,y) = f*(x,y) otherwise Truncation attenuates Gaussian nature of noise Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 28

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Noise Gaussian Noise Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 29 Mat noise_image(image.size(), CV_16SC3); randn(noise_image, Scalar::all(average), Scalar::all(standard_deviation)); Mat temp_image; image.convertTo(temp_image,CV_16SC3); addWeighted(temp_image, 1.0, noise_image, 1.0, 0.0, temp_image); temp_image.convertTo(image,image.type());

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Smoothing Removing or reducing noise Linear smoothing transformations Image Averaging Local Averaging Gaussian Smoothing Non-linear transformations Rotating Mask Median Filter Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 30

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Smoothing Image Averaging (linear) Average of n images f(i,j) = (1/ n). (g k (i,j) + v k (i,j)) k = 1..,n Additive noise model v k (i,j) St. Dev. = / n Assumptions? Static Statistical independence Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 31 addWeighted(image1,0.5,image2,0.5,0.0,average_image);

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Smoothing Image Averaging Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 32

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Smoothing Convolution Filtering / Convolution Linear transformation: f( i,j ) = h( i-m, j-n ).g( m,n ) (m,n) Convolution mask Non-linear transformation: Some logical operation based on a local region Smoothing Suppression of image noise Blurring sharp edges Large degradations? Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 33

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Smoothing Averaging Filters (linear) Available images? Local neighbourhood f( i,j ) = h( i-m, j-n ).g( m,n ) (m,n) Different masks Local Average Gaussian Acceptable results? Size of noise Blurring of edges Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 34 blur(image,smoothed_image,Size(3,3)); GaussianBlur(image,smoothed_image,Size(5,5),1.5);

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Smoothing Examples Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 35

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Smoothing Rotating Mask (non-linear) Define a number of masks/regions Mask size & shape Alternatives: Use the average of one of the masks But which mask?? The most homogeneous Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 36

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Smoothing Rotating Mask (non-linear) Algorithm: For each image point (i,j) Calculate dispersions Assign output point average of mask with minimum dispersion Iterative application Convergence Effects of mask size Effects Noise suppression Image sharpening Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 37

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Smoothing Rotating Mask (non-linear) Dispersion 2 Lower computational complexity Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 38

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Smoothing Median Filter (non-linear) Use the median value Not affected by noise Doesnt blur edges much Can be applied iteratively Damages thin lines and sharp corners Change region shape Computational expensive Standard O(r 2 log r) Huang O(r) Perreault (2007) O(1) Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 39 11 18 20 21 23 25 25 30 250 Median = 23 Average = 47 medianBlur(image, smoothed_image, 5);

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Smoothing Median Filter (Huang O(r)) Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 40 Input image X (m * n), kernel radius k, Output image Y for row = 1 to m Initialise histogram H: X(-k, row-k).. X(k, row+k) for column = 1 to n Y(column, row) = Median of H Remove leftmost column from H: X(column-k, row-k).. X(column-k, row+k) Add new column to right of H: X(column+k+1, row-k).. X(column+k+1, row+k) Can determine median efficiently by maintaining and updating: - Median value - Number of points less than the median

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Smoothing Median Filter (Perreault O(1)) Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 41 Input image X (m * n), kernel radius k, Output image Y for row = 1 to m Initialise column histograms h 1..n and histogram H for column = 1 to n Y(column, row) = Median of H Remove X(column+k+1, row-k-1) from h column+k+1 Add X(column+k+1, row+k) from h column+k+1 Remove leftmost column from H: h column-k Add new column to right of H: h column+k+1

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Smoothing Examples Images Based on A Practical Introduction to Computer Vision with OpenCV by Kenneth Dawson-Howe Wiley & Sons Inc. 2014 Slide 42