Image processing free open source libraries This is the first time that I post a question  here so excuse me for asking such a beginner question.
what free open source 3rd party libraries which have good documentation(because I'm new to using 3rd party libraries) would you suggest me for fourier transform,inverse fourier transform , meshgrids , dynamic arrays and etc to have a better performance and higher speed in visualC++ when implementing image processing filters? 
Note that I'm not permitted to use openCV. In fact I'm going to compare the results of my code with results of openCV
For Fourier transforms go get fftw.  I don't know what meshgrids are, so I can't answer that.  For dynamic arrays: that's what std::vector is, it's built into the language.

For a wider variety of image transformations you might look at GEGL and the library underlying Imagemagick.

There's also this question about filtering software: Use Butterworth and Chebychev filters.