Obtaining Motion Blur Parameters Form The Frequency Spectrum

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Obtaining Motion Blur Parameters Form The Frequency Spectrum

Fourier transform is applied on digital images to interprets their content in terms frequency information. To illustrate, Flat areas, where the intensity is slowly changing, result in low frequencies. Rough areas, on the other hand, result in high frequencies because of the dramatic change in the intensity value. this paper discusses the impact of manipulating the frequency information of digital images and how the frequency spectrum can be used to address a real world situation.

Filtering an image in the frequency domain is usually composed of three steps. First, the Fourier transform is calculated (DCT or DFT). Then, a certain operation is performed on the frequencies
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Huei and Kun [2] proposed that the speed of moving objects in a single image can be estimated using the blur parameters, the camera parameters and imaging geometry. To illustrate, the displacement of a moving object (d) can be determined using similar triangles according to the blur length (k) Figure2. And by knowing the shutter speed of the camera (T), the speed of the object is v =d/T(1). Since this paper is concerned with Fourier Transform, the details of equation (1) are omitted and calculating the blur parameter is detailed below.

The blur parameters, including the blurs’ direction and length, can be determined by examining their impact on the Fourier spectrum. As shown in figure, the Fourier spectrum of the motion blur contains strips of dark lines that are parallel and uniformly separated. Note that the Fourier spectrum depends on the objects’ orientation; so the direction of the motion blur could be extracted from the frequency spectrum. Also, as the blurs’ length increase, the edges get smoother, resulting in lower frequency response. These observations suggest that the frequency spectrum has all the needed information to determine the blurs parameters. In particular, the object shown in the figure is moving along the horizontal axis, and this caused the vertical orientation of the dark lines in the frequency spectrum. Furthermore, increasing the blurs length, which can be achieved by increasing the object’s speed, lessens the distance

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