Correlation Performed by Convolution Background: The question here is related to images in particular and not signal/waveforms.

I have been reading a lot of answers about the difference between convolution and correlation but I am stuck on my doubt as to how are they related to each other while performing operations. Most of the answers are individual answers for each of these terms.

For example:

A statement I am trying to understand says 


  Here correlation operations are performed by replacing the exhausted
  convolutions with element-wise multiplications using Discrete Fourier 
  Transform (DFT).


I am not able to relate the individual definitions here. Can anyone please explain this?
What that statement is saying that 

a. Correlation is performed the same way as one would perform convolution (you must implicitly know that one of the sequences is conjugated and time reversed to express a correlation as a convolution, as it was not stated there),

and

b. Mathematically the convolution is performed using this relationship

$$x[n]*h[n] = \mathscr{F}^{-1}\left\{\mathscr{F}\left\{x[n]\right\}\cdot\mathscr{F}\left\{h[n]\right\}\right\}$$

Where $*$ denotes convolution, $\mathscr{F}\left\{f[n]\right\}$ denotes the Discrete Fourier Transform of $f[n]$, and $\mathscr{F}^{-1}\left\{F[k]\right\}$ denotes the Inverse Discrete Fourier Transform of $F[k]$.

Note that these operations with Discrete Fourier Transforms actually yield the "circular" convolution of $x[n]$ and $h[n]$, which is equal to the linear convolution of $x[n]$ and $h[n]$ only under a certain condition: there must be enough zero padding to avoid aliasing.