Posted: May 22nd, 2023
In this study, the behavior of the image in the frequency domain also known as the Fourier Transform has been shown . Fourier Transform facilitates the analysis and observation of different frequency components and thus revealing their respective effects or contributions to an image. The study has also revealed how various operations are carried out in the Fourier Domain. The different effects imparted on an image after processing have also been shown .
It has been shown that using the surf and mesh plots a 2D data matrix can easily be displayed in a 3D plot. Thus a better observation and understanding is achieved by observing the 2D data in a 3D perspective. This function is particularly vital in observing the Fourier spectrum of an image and analyzing the behavior of the different designs of filters. For instance, the magnitude of the responses of the cut-off frequencies and other similar properties can be analyzed clearly in a 3D display. In this study three filters were designed; two ideal low pass filters and a Gaussian low pass filter. It has been shown that when a low pass filter is applied to an image it produces a blurring effect.
This is seen in all the low pass filters (Gaussian, Ideal, Butterworth, and others) . However, the different types of filters have other specific effects which may be advantageous or disadvantageous and thus they vary in usage. The smaller the radii of the low pass filters greater the blurring effect. The high pass filters produce an effect that is opposite to this. For instance, when an image is passed through the high pass filter the resultant image will have objects with sharper edges, this is because high pass filters allow high-frequency elements to pass. The larger the radius of a filter the sharper the image, however, this may lead to loss of color information because the color is contributed by low-frequency components (slowly changing values of the signal) .
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