Image Processing in The Frequency Domain (Biomedical Image Analysis)

In previous topics the image was introduced as a spatial arrangement of discrete values: image values that represent a physical metric. Neighboring pixels relate to each other in a defined spatial relationship. The human eye is very adept at recognizing spatial relationships, such as repeat patterns, irregularities (noise), edges, or contiguous features. For image processing software, this task is more difficult, because the analysis of large neighborhoods is usually very time consuming. In Section 2.3, filters were introduced that modified an image in a specific manner: for example, by enhancing discontinuities (sharpening) or attenuating detail (blurring). These filters act differently on different spatial frequencies. The term spatialfrequency refers to the rate of change of the image values. An intensity trend that continues over most of the image consists of low spatial frequencies; conversely, an edge (a rapid change of intensity over a few pixels) contains high-frequency components. The frequency domain is a different representation of the same image data where the strength of periodic components (such as a pattern that repeats every 20 pixels) is extracted. The Fourier transform is a tool that converts the image with spatially arranged data into the same data arranged by periodicity, and thus, frequency. Any transform is characterized by the existence of an inverse transform that allows us to restore the original arrangement of the data. By using the Fourier transform, image data can be presented in a way that makes a number of image manipulations easier (or possible, in the first place): Images can be manipulated or filtered in the frequency domain. With the inverse Fourier transform, the filtered image is restored to its original spatial arrangement.

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