Difference between revisions of "Image Convolution"

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|ImageIntro=Image Convolution is the process of applying a filter to images
 
|ImageIntro=Image Convolution is the process of applying a filter to images
 
|ImageDescElem=Images can be convolved by applying a function to each pixel of the image. Usually, this function is precalculated inside a small two dimensional array called a kernel.
 
|ImageDescElem=Images can be convolved by applying a function to each pixel of the image. Usually, this function is precalculated inside a small two dimensional array called a kernel.
|ImageDesc=<math>F(x) = \sum{ \sum{ f(x) * k(x) } }</math>
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|ImageDesc=Most generally, the convolution of two functions f and g is defined as the following: <math>(f * g)(x,y) = \sum_{v=-\infty}^{\infty} \sum_{u=-\infty}^{\infty} f(x,y) g(x - u,y - v)</math>
 +
In this case <math>f(x,y)</math> is a function that represents the image. In most cases, images are only defined over a set of points, <math>[0,width] \times [0,height]</math>
 
|Field=Other
 
|Field=Other
 
|InProgress=Yes
 
|InProgress=Yes
 
}}
 
}}

Revision as of 11:59, 14 August 2009

Inprogress.png
Image Convolution
Field: Other
Image Created By: [[Author:| ]]

Image Convolution

Image Convolution is the process of applying a filter to images


Basic Description

Images can be convolved by applying a function to each pixel of the image. Usually, this function is precalculated inside a small two dimensional array called a kernel.

A More Mathematical Explanation

Most generally, the convolution of two functions f and g is defined as the following: '"`UNIQ--math- [...]

Most generally, the convolution of two functions f and g is defined as the following: (f * g)(x,y) = \sum_{v=-\infty}^{\infty} \sum_{u=-\infty}^{\infty} f(x,y) g(x - u,y - v) In this case f(x,y) is a function that represents the image. In most cases, images are only defined over a set of points, [0,width] \times [0,height]




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