Primary Convolutions In Image Processing
Article 1
A convolution or a kernel is a simple mathematical operation which is fundamental to many common image processing applications. A Discrete convolution provides a way of multiplying together two arrays of numbers to produce 3rd array of numbers of the same dimentionality.
The output value depends on both image values and kernel values. If we take the resultant value as O(x,y) = O(1,1) , we can calculate the output value by
O(1,1) = I(1,1) x K(1,1) + I(1,2) x K(1,2) + I(2,1) x K(2,1) I(2,2) x K(2,2)
The general expression of a convolution is
For your notes :
Convolution is a simple mathematical operation which is fundamental to many common image processing operators.
Discrete Convolution provides a way of `multiplying together’ two arrays of numbers (generally of different sizes, but of the same dimensionality), to produce a third array of numbers of the same dimensionality.
This can be used in image processing to implement operators whose output pixel values are simple linear combinations of certain input pixel values.
In an image processing context, one of the input arrays is normally just a gray level image.
The second array is usually much smaller, and is also two dimensional (although it may be just a single pixel thick), and is known as the kernel.
The convolution is performed by sliding the kernel over the image, generally starting at the top left corner, so as to move the kernel through all the positions where the kernel fits entirely within the boundaries of the image.
Applying (convoluting) a 3x3 filter (mask)
More on Image Filters (Linear, Mean and Mode Filters in a future post)…
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