DFT: Linear Convolution

Building the Cantata Workspace

1. Get image gull.viff, reduce it to 1/2 its size (shrink), zero padded and display it using the following operators: User defined, Shrink , Pad and Display Image.
2. Import the ascii convolution kernel and zero padded to the same dimensions of the image. Use operators Import ASCII and Pad.
3. Take the forward Fourier transform of both the image and zero padded kernel and multiply the results. Now take the inverse Fourier transform and display the result, this is convolution in the frequency domain. Use the FFT and Display Image operators.
4. Perform the convolution and display the result, use operators Linear Operator and Display Image.
5. Take the absolute difference of the results obtained in the frequency domain and spatial domain.

Exercises

• Suggest another method for performing linear convolution where the output dimensions are the same of the original input image.
• Perform the same experiment but with different kernels (low pass, high pass).
• What happens if no zero padding is performed?
• Experiment with different images.