From: Joseph Greer on 21 Apr 2010 14:03 Hello, I'm using phase correlation to perform motion estimation on video and am trying to find some sort of metric for the quality of a peak (which corresponds to a candidate motion vector) in a given phase correlation block. I know that performing phase correlation on duplicate images gives a result that has a peak at (0, 0) with magnitude 1 and 0 elsewhere. Obviously, in real video there is noise, multiple instances of object motion, and sub-pixel motion that causes there to be multiple peaks that which are smeared over several bins. Does anyone know of any equalities in general, e.g. the sum of all the bins in a phase correlation block equals 1 or the sum of the squares of all the bins in a phase correlation block equals 1, or something along those lines for the result of doing phase correlation on any two frames? The closest statement I've seen to broaching this subject is in Watkinson, J., "An Engineer's Guide to Motion Compensation" where he says "The volume of the peak corresponds to the amount of the area of the window (i.e. the number of pixels) having that motion." Does anyone know anything more along these lines? Thanks, Joey From: dvsarwate on 21 Apr 2010 14:25 On Apr 21, 1:03 pm, Joseph Greer wrote:> Hello, > > I'm using phase correlation to perform motion estimation on video and > am trying to find some sort of metric for the quality of a peak (which > corresponds to a candidate motion vector) in a given phase correlation > block.  I know that performing phase correlation on duplicate images > gives a result that has a peak at (0, 0) with magnitude 1 and 0 > elsewhere.  Obviously, in real video there is noise, multiple > instances of object motion, and sub-pixel motion that causes there to > be multiple peaks that which are smeared over several bins.  Does > anyone know of any equalities in general, e.g. the sum of all the bins > in a phase correlation block equals 1 or the sum of the squares of all > the bins in a phase correlation block equals 1, or something along > those lines for the result of doing phase correlation on any two > frames?  The closest statement I've seen to broaching this subject is > in Watkinson, J., "An Engineer's Guide to Motion Compensation" where > he says "The volume of the peak corresponds to the amount of the area > of the window (i.e. the number of pixels) having that motion."  Does > anyone know anything more along these lines? > > Thanks, > Joey For correlations in general (not necessarily applicable to phase correlations), the sum of all the cross-correlation values equals the product of the sums of x and y. That is, sum(over all l) C_{x,y}(l) = [sum(over all l) x(l)][sum over all l) y(l)] and sum(over all l) [C{x,y}(l)^2 = sum(over all l) C{x,x}(l).C{y,y}(l) that is, the squared length of the C_{x,y} sequence equals the inner product of the autocorrelation sequences. Hope this helps --Dilip Sarwate