Computer Linear Algebra-Individual Assignment
Topic: Image Sharpening and softening (blurring and deblurring).
Nowadays, technology has become very important in the society and so does image processing. People may not realize that they use this application everyday in the real life to makes life easier in many areas, such as business, medical, science, law enforcement. Image processing is an application where signal information of an image is analyzed and manipulated to transform it to a different stage. This technique can be done simply by changing the nature of the image using change of basis. In most situations, people prefer a better image with high resolution, sharper, more detail, etc. Image can be describes as a collection of pixels that have different component depends on the digital signals that digitized as a matrix. These signals came from different energy such as wavelength, frequency. Fourier basis manipulate the image by changing the signal in the pixels. Some signals that give a similar coefficient can be eliminated so that the picture become blurrier or vice versa. These kind functions are found in many situations such as the speeding camera. Speeding camera capture high-speed object, which in return give a result of, blur image. It is almost impossible for human eye to see or track the plate number of the fast moving vehicle without deblurring the image because the range is too high. Fourier change basis is the easiest way to transform the image. Eigenvector change basis will probably give the best result of transformation, but the problem is it will cost a lot of time, effort, and also expensive.
The development of image processing applications has many impacts on the society. Television for example, in the early century, television can only transmit and receive monochromatic moving images that give people black and white or grayscales images. This kind of television was not comfortable for human eye because it is not clear, detail...
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