Image processing free open source libraries
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.