Digital Image Processing

Assignment #1

Assignment Report By:

Ashish Gupta 98131
Ashish Gupta 98130

# Part B : Frequency Domain Methods

1. Write FFT routine to be used for Fourier transform and its inverse for 2D images. Draw a graph between N (number of points) and the Cutoffmputation time.

The Graph Showing Performance of 2D FFT module designed for Image Manipulation
Graph is time (us)  vs.  N

1. Ideal low/high pass filter and Butterworth low/high pass filter. Examine the effects when the cutoff frequency is changed, plot the Fourier spectrum (you may have to use Compression of dynamic range). For Butterworth see what happens when the order is changed.

Click on the following links :

The Ant example

1. Demonstrate the properties of translation and rotation of Fourier transform.

Properties of Translation

#### The original Block Image and its Fourier

The block image                                                           Fourier of block image

Fourier of block image after applying the translation transform the translate the block by 50x50 units
Note that the magnitude of the Fourier Plot doesn’t change

Fourier Plot after translation                                          The translated block image ( Inverse FFT of the left Fourier Plot )

Rotation of Fourier Transform

The block image rotated by 45 degrees                              The Fourier plot of the left image

The Fourier plot is also rotated by 45 degrees.

Code : freq.cpp

End of Report