I want to convolve 2 images I1 and I2. Let's assume they have the same size. I know 2 methods: 1) Use direct definition of 2D convolution 2) i. Computer FFT of I1 (call it I1_FFT) and FFT of I2 (call it I2_FFT) ii. Multiply I1_FFT and I2_FFT (call it I1I2_FFT) iii. Compute inverse FFT of result I1I2_FFT
I want to know the number of multiplications and additions for each case. Note I don't want the Big O type of complexity.
It would be great if the answer includes a derivation.
In the end, I want to know for a specific NxM sized image, when I should use method 1 or 2.