Convolution?
in [Matlab]
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From: Nick on 20 Feb 2006 16:39 matrix A [3 0 0 0] matrix B [1 0 3 0] Ive been trying to have a patch image of A passed through B and generate a peak when the two 3's match each other. Ive been told its a convolution which broken down is A1=fft(A); B1=fft(B); A2=real(A1); B2=real(B1); R=A2.*B2; IR=ifft(R); I dont really understand it and cant get anything resembling a bright peak in teh correct place other than by chance any help would be much appreciated Nick
From: ysriraja on 20 Feb 2006 16:50 Try xcorr. xcorr2 for 2D cases or normxcorr2. Raja Nick wrote: > matrix A [3 0 0 0] > matrix B [1 0 3 0] > > Ive been trying to have a patch image of A passed through B and > generate a peak when the two 3's match each other. > > Ive been told its a convolution which broken down is > > A1=fft(A); > B1=fft(B); > > A2=real(A1); > B2=real(B1); > > R=A2.*B2; > IR=ifft(R); > > I dont really understand it and cant get anything resembling a bright > peak in teh correct place other than by chance > > any help would be much appreciated > > Nick
From: Matthew Crema on 20 Feb 2006 16:50 Nick wrote: > Ive been told its a convolution What you're describing sounds more like cross-correlation 'help xcorr' or 'help xcorr2' > which broken down is > A1=fft(A); > B1=fft(B); > > A2=real(A1); > B2=real(B1); You should not be taking the real part here. Convolution is equivalent to multiplying the Fourier Transforms, and then taking the inverse Fourier Transform of the result. It is incorrect to take the real part. http://www.mathworks.com/access/helpdesk/help/techdoc/ref/conv.html > R=A2.*B2; > IR=ifft(R); It is good practice to take the real part here. It is not a problem in your case, but IR can have a small imaginary part (very close to zero) due to round-off error. However, why not just use "conv" which should give you the same result (with some extra zeros)? IR1=conv(A,B) IR2=real(ifft(fft(A).*fft(B))) -Matt
From: Dave Robinson on 21 Feb 2006 04:58 Matthew Crema wrote: > > > Nick wrote: >> Ive been told its a convolution > What you're describing sounds more like cross-correlation > 'help xcorr' or 'help xcorr2' > >> which broken down is >> A1=fft(A); >> B1=fft(B); >> >> A2=real(A1); >> B2=real(B1); > You should not be taking the real part here. Convolution is > equivalent > to multiplying the Fourier Transforms, and then taking the inverse > Fourier Transform of the result. It is incorrect to take the real > part. > > <http://www.mathworks.com/access/helpdesk/help/techdoc/ref/conv.html> > >> R=A2.*B2; >> IR=ifft(R); > It is good practice to take the real part here. It is not a > problem in > your case, but IR can have a small imaginary part (very close to > zero) > due to round-off error. > > However, why not just use "conv" which should give you the same > result > (with some extra zeros)? > > IR1=conv(A,B) > IR2=real(ifft(fft(A).*fft(B))) > > -Matt > If you use Matt's second equation for IR2, you need to be careful of a nasty problem that can catch the unwary user out. You can get what is known as overlap error, which distorts the output convolution. It is wise to embed both A and B into zero filled buffers of size length(A) + length(B) - 1 prior to doing the transform stuff, this way you can guarantee that the distortion doesn't occur. Regards Dave Robinson
From: nick on 22 Feb 2006 06:18 thanks, i'll give all this a try. only thing is i'm eventually working up to 3d ie spaial and temporal. But i'll give ur suggestions a go first cheers Nick Dave Robinson wrote: > > > Matthew Crema wrote: >> >> >> Nick wrote: >>> Ive been told its a convolution >> What you're describing sounds more like cross-correlation >> 'help xcorr' or 'help xcorr2' >> >>> which broken down is >>> A1=fft(A); >>> B1=fft(B); >>> >>> A2=real(A1); >>> B2=real(B1); >> You should not be taking the real part here. Convolution is >> equivalent >> to multiplying the Fourier Transforms, and then taking the > inverse >> Fourier Transform of the result. It is incorrect to take the > real >> part. >> >> <http://www.mathworks.com/access/helpdesk/help/techdoc/ref/conv.html> >> >>> R=A2.*B2; >>> IR=ifft(R); >> It is good practice to take the real part here. It is not a >> problem in >> your case, but IR can have a small imaginary part (very close to >> zero) >> due to round-off error. >> >> However, why not just use "conv" which should give you the same >> result >> (with some extra zeros)? >> >> IR1=conv(A,B) >> IR2=real(ifft(fft(A).*fft(B))) >> >> -Matt >> > If you use Matt's second equation for IR2, you need to be careful > of > a nasty problem that can catch the unwary user out. You can get > what > is known as overlap error, which distorts the output convolution. > > It is wise to embed both A and B into zero filled buffers of size > > length(A) + length(B) - 1 > > prior to doing the transform stuff, this way you can guarantee that > the distortion doesn't occur. > > Regards > > Dave Robinson
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