Computing cross-correlation function

Question

In R  I am using ccf or acf to compute the pair-wise cross-correlation function so that I can find out which shift gives me the maximum value  From the looks of it  R gives me a normalized sequence of values  Is there something similar in Python s scipy or am I supposed to do it using the fft module  Currently  I am doing it as follows   xcorr   lambda x y   irfft rfft x  rfft y   -1    x   numpy array  0 0 1 1   y   numpy array  1 1 0 0   print xcorr x y

User · Answer

I just finished writing my own optimised implementation of normalized cross-correlation for N-dimensional arrays. You can get it from here.

It will calculate cross-correlation either directly, using scipy.ndimage.correlate, or in the frequency domain, using scipy.fftpack.fftn/ifftn depending on whichever will be quickest.

User · Answer

If you are looking for a rapid  normalized cross correlation in either one or two dimensions I would recommend the openCV library  see http   opencv willowgarage com wiki  http   opencv org     The cross-correlation code maintained by this group is the fastest you will find  and it will be normalized  results between -1 and 1    While this is a C   library the code is maintained with CMake and has python bindings so that access to the cross correlation functions is convenient   OpenCV also plays nicely with numpy   If I wanted to compute a 2-D cross-correlation starting from numpy arrays I could do it as follows   import numpy import cv   Create a random template and place it in a larger image templateNp   numpy random random   100 100    image   numpy random random   400 400    image  100   100    templateNp   create a numpy array for storing result resultNp   numpy zeros   301  301      convert from numpy format to openCV format templateCv   cv fromarray numpy float32 template   imageCv   cv fromarray numpy float32 image   resultCv    cv fromarray numpy float32 resultNp     perform cross correlation cv MatchTemplate templateCv  imageCv  resultCv  cv CV TM CCORR NORMED    convert result back to numpy array resultNp   np asarray resultCv    For just a 1-D cross-correlation create a 2-D array with shape equal to  N  1     Though there is some extra code involved to convert to an openCV format the speed-up over scipy is quite impressive

User · Answer

For 1D array  numpy correlate is faster than scipy signal correlate  under different sizes  I see a consistent 5x peformance gain using numpy correlate  When two arrays are of similar size  the bright line connecting the diagonal   the performance difference is even more outstanding  50x           a simple benchmark res      for x in range 1  1000       list x          for y in range 1  1000               generate different sizes of series to compare         l1   np random choice range 1  100   size x          l2   np random choice range 1  100   size y           time start   datetime now           np correlate a l1  v l2          t np   datetime now   - time start          time start   datetime now           scipy signal correlate in1 l1  in2 l2          t scipy   datetime now   - time start          list x append t scipy   t np      res append list x  plt imshow np matrix res       As default  scipy signal correlate calculates a few extra numbers by padding and that might explained the performance difference     gt  gt  l1    1 2 3 2 1 2 3   gt  gt  l2    1 2 3   gt  gt  print numpy correlate a l1  v l2    gt  gt  print scipy signal correlate in1 l1  in2 l2     14 14 10 10 14    3  8 14 14 10 10 14  8  3     the first 3 is  0 0 1 dot 1 2 3

User · Answer

To cross-correlate 1d arrays use numpy correlate   For 2d arrays  use scipy signal correlate2d   There is also scipy stsci convolve correlate2d   There is also matplotlib pyplot xcorr which is based on numpy correlate   See this post on the SciPy mailing list for some links to different implementations   Edit   user333700 added a link to the SciPy ticket for this issue in a comment

[python] Computing cross-correlation function?

Examples related to python

Examples related to r

Examples related to statistics

Examples related to numpy

Examples related to scipy