Filtering (II) Dr. Chang Shu COMP 4900C Winter 2008.
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Filtering (II) Dr. Chang Shu COMP 4900C Winter 2008
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Linear Filtering – convolution Image Kernel = 5 Filter Output The output is the linear combination of the neighbourhood pixels The coefficients come from a constant matrix A, called kernel. This process, denoted by ‘*’, is called (discrete) convolution.
Transcript of Filtering (II) Dr. Chang Shu COMP 4900C Winter 2008.
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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The complexity increases linearly with instead of with .m 2m
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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