Convolution Theorem I

Building the Cantata Workspace

Images

1. Input: lenina.viff
2. Kernel: roberts_y.ascii

First process the image in the spatial domain using Linear Operator. Since the kernel has negative values, convert the input image to float in order to support negative values in the resultant image.

Do the same processing in the frequency domain

1. Take the DFT of the input image.
2. Extend the kernel to the size of the input image. Use the Pad operator.
3. Take the DFT of the padded kernel.
4. Multiply both DFTs using Multiply.
5. Take the inverse DFT of the result of the multiplication.
6. Due to numerical roundoff, the resultant image should be a real image. Verify that the imaginary part is very small. Discard the imaginary part of the resultant image using Complex to Real.