Definition
- changes in image position correspond to changes in the spatial frequency
- this is the rate at which image intensity values are changing in the spatial domain image
- transform the image to its frequency representation
- perform image processing
- compute inverse transform back to the spatial domain
Methods
FD can be obtained through the transformation from one (time or spatial) domain to the other (frequency) via
- Discrete Cosine Transform
- Fourier Transform
It helps to separate the image into parts of differing importance. It is similar to discrete Fourier transform; it transform a signal or image from the spatial domain to the frequency domain.
Basic operation of the DCT is as folows:
- the input image is N by M
- f ( i , j ) is the intensity of the pixel in row i and column j
- F ( u , v ) is the DCT coefficient in row k1 and column k2 of the DCT matrix.
- for most images, much of the signal energy lies at low frequencies; these appear in the upper left corner of the DCT.
- compression is achieved since the lower right values represent higher frequencies, and are often small - small enough to be neglected with little visible distortion.
- the DCT input is an 8 by 8 array of integers. this array contain ah pixel's gray scale level
- 8 bits pixels have level from 0 to 255.
The Two-Dimensional DCT
Fourier Transform (FT)
Brief Description
It is used to decompose image into its sine and cosine components. The output represent the image in frequency domain while the input is the spatial domain.
Widely used in image analysis image filtering, image reconstruction and image compression.
Properties of the Fourier Transform
- The FT is a linear operator
- some other useful properties include
Filtering - scheme
Filtering Example
Smooth an Image with a Gaussian Kernel
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