Interpolation

Building the Cantata Workspace

1. Display the original image (map-roi.viff and its Fourier Transform.
2. Create the image expanded by 4, without any interpolation:
   1. Resample the image by 4 using a pixel replication interpolation method.
   2. Create a grid image with impulses spaced by 4 using the Impulse operator.
   3. Multiply the grid image to the expanded image to obtain the image geometrically expanded by 4, with no interpolation.
3. Take and display the DFT of the expanded image.
4. Implement the spatial domain interpolation using convolution and the following kernels:
   1. Zero order interpolation: use the Constant to build a 4x4 kernel with constant 1
   2. Bilinear interpolation: multiply two Piecewise Linear operators both generating an image of size 9x9, from values ranging from 0 to 1 and the following parameters

            Period:     9
            Rise Time:  4 
            Fall Time:  4
            Pulse Width:0
      

      for X in one image and for Y in the other image.
5. Implement the frequency domain interpolation using FFT and the following frequency filters, using the operator Low-Pass
   1. Ideal filtering:
   2. Butterworth filtering, order 3

Exercises

1. What is the cutoff frequency of the filters as function of the scaling factor?
2. What is the result if we expand the DFT of the original image using pixel replication algorithm and take the inverse DFT? Use the expand property of the DFT and the convolution theorem to explain the results.