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xi-jia / Fourier-Net

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about the displacement field #4

Open kkkkkk123-ops opened 1 month ago

kkkkkk123-ops commented 1 month ago

I want to know why the the displacement filed φ is a low-pass filtered displacement field, and using ifft(fft(padding(φ,0))) [while φ is low-resolution] can correctly represent the full-resolution displacement field?

kkkkkk123-ops commented 1 month ago

sorry, typing wrong. should be ifft(padding(fft(φ),0))

xi-jia commented 1 month ago

Fourier-Net hypothesizes that the displacement is smooth, therefore the displacement can be represented by only the low frequencies. Learning the frequencies is difficult for a CNN, we instead learn a small spatial patch that shares the same low frequencies with the desired full displacement. Once the small patch is perfectly learned by the network, ->FFT->pad zero->iFFT will get the final displacement.

kkkkkk123-ops commented 1 month ago

thank you, it really helps a lot!