I would guess most images that follow some strict pattern could have only a few non-zero points in the frequency domain (like the sine/cosine images from earlier in lecture), which would make multiplication in the frequency domain very fast. When an image is more random frequency-wise (like a photograph) It might be faster to filter by convolution.
joshua16266261
I think filters with small kernels would be faster to implement by convolution because even though the asymptotic time complexity is worse than just multiplying in the frequency domain, the small size probably means that it will still be faster. However, for large kernels, multiplying in frequency will probably be faster since we can use FFT to take the Fourier transform and multiplying is faster than convolution.
yfz3357
I think for larger inputs, filtering is faster in the frequency domain because of slower-growing time complexity(frequency is NlogN while spatial is N^2 if I am not wrong). However, due to the extra step of the Fourier Transform, it is faster to use convolution in the spatial domain when inputs are small.
I would guess most images that follow some strict pattern could have only a few non-zero points in the frequency domain (like the sine/cosine images from earlier in lecture), which would make multiplication in the frequency domain very fast. When an image is more random frequency-wise (like a photograph) It might be faster to filter by convolution.
I think filters with small kernels would be faster to implement by convolution because even though the asymptotic time complexity is worse than just multiplying in the frequency domain, the small size probably means that it will still be faster. However, for large kernels, multiplying in frequency will probably be faster since we can use FFT to take the Fourier transform and multiplying is faster than convolution.
I think for larger inputs, filtering is faster in the frequency domain because of slower-growing time complexity(frequency is NlogN while spatial is N^2 if I am not wrong). However, due to the extra step of the Fourier Transform, it is faster to use convolution in the spatial domain when inputs are small.