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Unformatted text preview: Linear Filtering CS / ECE 181B Ack: Prof. Matthew Turk for the slides Monday, January 11, 2010 Linear Filtering CS / ECE 181B ® Convolution, Fourier Transforms and Correlation Today Ack: Prof. Matthew Turk for the slides Monday, January 11, 2010 2 Area operations: Linear filtering • Point, local, and global operations – Each kind has its purposes • Much of computer vision analysis starts with local area operations and then builds from there – Texture, edges, contours, shape, etc. – Perhaps at multiple scales • Linear filtering is an important class of local operators – Convolution – Correlation – Fourier (and other) transforms – Sampling and aliasing issues Monday, January 11, 2010 3 Convolution • The response of a linear shiftinvariant system can be described by the convolution operation R ij = H i − u , j − v F uv u , v ∑ Input image Convolution filter kernel Output image Convolution notations Monday, January 11, 2010 4 Convolution • Think of 2D convolution as the following procedure • For every pixel (i,j): – Line up the image at (i,j) with the filter kernel – Flip the kernel in both directions (vertical and horizontal) – Multiply and sum (dot product) to get output value R ( i,j ) Monday, January 11, 2010 4 Convolution • Think of 2D convolution as the following procedure • For every pixel (i,j): – Line up the image at (i,j) with the filter kernel – Flip the kernel in both directions (vertical and horizontal) – Multiply and sum (dot product) to get output value R ( i,j ) (i,j) Monday, January 11, 2010 4 Convolution • Think of 2D convolution as the following procedure • For every pixel (i,j): – Line up the image at (i,j) with the filter kernel – Flip the kernel in both directions (vertical and horizontal) – Multiply and sum (dot product) to get output value R ( i,j ) Monday, January 11, 2010 4 Convolution • Think of 2D convolution as the following procedure • For every pixel (i,j): – Line up the image at (i,j) with the filter kernel – Flip the kernel in both directions (vertical and horizontal) – Multiply and sum (dot product) to get output value R ( i,j ) Monday, January 11, 2010 4 Convolution • Think of 2D convolution as the following procedure • For every pixel (i,j): – Line up the image at (i,j) with the filter kernel – Flip the kernel in both directions (vertical and horizontal) – Multiply and sum (dot product) to get output value R ( i,j ) Monday, January 11, 2010 4 Convolution • Think of 2D convolution as the following procedure • For every pixel (i,j): – Line up the image at (i,j) with the filter kernel – Flip the kernel in both directions (vertical and horizontal) – Multiply and sum (dot product) to get output value R ( i,j ) Monday, January 11, 2010 4 Convolution • Think of 2D convolution as the following procedure • For every pixel (i,j): – Line up the image at (i,j) with the filter kernel – Flip the kernel in both directions (vertical and horizontal) – Multiply and sum (dot product) to get output value R ( i,j ) Monday, January 11, 2010 4...
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This note was uploaded on 12/29/2011 for the course ECE 181b taught by Professor Staff during the Fall '08 term at UCSB.
 Fall '08
 Staff

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