Convolution and Fourier Transforms in Image Processing

CONVOLUTION AND FOURIER TRANSFORMS IN IMAGE PROCESSING
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Convolution
Convolution is considered to be a filter that generally filters images. Besides, it is regarded as a matrix incorporated within a print consisting of integer mathematical operations. Convolution goes along achieving its objective by establishing the value of a central pixel by summing up the weighted values of all its neighbors before an output (filtered image) is obtained.
Process of image convolution
The whole process of image convolution is achieved by multiplying a pixel's and its neighboring pixels' color value by a matrix. A kernel usually consists of a small matrix of numbers applied in image convolutions. With different sizes of kernels having various patterns, different results are acquired within a convolution. The size of a kernel is usually designed to be a 3*3 matrix.
Example of a kernel
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The main reasons why images are convoluted are to; Smoothen, sharpen, intensify, and enhance them. There are three main steps taken into consideration in working out a convolutional kernel. First, in the process of convolution, the image undergoes a series of manipulations by rolling kernels over convolutional, and as a result, the convolution is delineated over a source pixel. After that, the kernel values are then multiplied by a factor of the corresponding value of the pixel it is covering. Lastly, the summation of all the values that have been multiplied is then recorded and is thus considered as the first value (center pixel value). Another patch of source pixel is taken to fill new pixel values, leaving behind a brand changed pixel values having similar characteristics as that of the original image and fewer dimensions and transformation.
Fourier Transform and its application in Image processing
Fourier transform is a unique image processing technique applied to its individual sine and cosine elements during image decomposition. Usually, the transformation output symbolizes the image in the Fourier or frequency domain, whereas the image that is input represents the equivalent spatial domain. The Fourier transform has been used in sectors such during analytical examination, filtering, reconstruction and compression of images.
One way through which Fourier transforms processes images is by decomposing them into their respective cosine and sine constituents. The transformation output signifies the image in its Fourier domain, whereas on the other hand, the input represents spatial domain equivalent. Considering the Fourier domain image, each of the points stands for a given frequency incorporated within the spatial domain image.
In an actual situation, images can be represented as a summation of sin waves. Still, instead of representing one-dimensional waves, Fourier transform does represent them as waves that differ in two ways just like variations on a sheet.
These 2-D waves can be considered to be:...