Filtering (II)
Dr. Chang Shu
COMP 4900CWinter 2008
Image FilteringModifying the pixels in an image based on some
functions of a local neighbourhood of the pixels
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Linear Filtering – convolution
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Filter Output
The output is the linear combination of the neighbourhood pixels
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The coefficients come from a constant matrix A, called kernel.This process, denoted by ‘*’, is called (discrete) convolution.
Handle Border Pixels
• Set the value of all non-included pixels to zero.
• Set all non-included pixels to the value of the corresponding pixel in the input image.
Near the borders of the image, some pixels do not have enoughneighbours. Two possible solutions are:
Smoothing by Averaging
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Convolution can be understood as weighted averaging.
Gaussian Filter
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Discrete Gaussian kernel:
Gaussian Filter
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Gaussian Kernel is Separable
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Gaussian Kernel is SeparableConvolving rows and then columns with a 1-D Gaussian kernel.
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Gaussian vs. Average
Gaussian Smoothing Smoothing by Averaging
Noise Filtering
Gaussian Noise
After Gaussian Smoothing
After Averaging
Noise Filtering
Salt-and-pepper noise
After Gaussian smoothing
After averaging
Nonlinear Filtering – median filter
Replace each pixel value I(i, j) with the median of the valuesfound in a local neighbourhood of (i, j).
Median Filter
Salt-and-pepper noise After median filtering
Salt-and-Pepper Noise Removal by Median-type Noise Detectors and Edge-preserving Regularization Raymond H. Chan, Chung-Wa Ho, and Mila NikolovaIEEE Transactions on Image Processing, 14 (2005), 1479-1485.
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