JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III IMAGE PROCESSING Previous Question Paper (January/February - 2023 - R18)

Digital image processing refers to the use of a digital computer to process digital images through an algorithm. It involves the manipulation of image data to improve the quality of an image, extract information, or prepare it for further analysis, typically by converting an analog image into a discrete set of numerical values represented as pixels in a 2D matrix.

The 2-D Discrete Fourier Transform (DFT) possesses several fundamental properties that facilitate image analysis and processing:

• Separability: A 2-D DFT can be computed by performing 1-D DFTs sequentially along the rows and then along the columns of the image matrix, reducing computational complexity.
• Periodicity: The 2-D DFT is periodic in both frequency variables, with a period equal to the size of the image dimensions (N x M), meaning F(u, v) = F(u+N, v) = F(u, v+M).
• Translation (Shift) Property: Shifting an image in the spatial domain results in a phase shift in the frequency domain, while the magnitude spectrum remains invariant.
• Rotation Property: Rotating an image in the spatial domain by an angle results in an identical rotation of its Fourier transform in the frequency domain.
• Linearity: The DFT is a linear operator, meaning the DFT of a weighted sum of two images is equal to the weighted sum of their individual DFTs.