How Are Images Considered Non Stationary Signal When They Are Invariant to Time?
Stationarity is a statitical concept defined through stochastic processes. However the following is a practical account of why most typical images are nonstationary :

Throughout the image window, consider a small rectangular test block, say 16x16, and observe the frequency spectrum estimation of that block. Now move this test block accross the image and re-compute the resulting spectrum estimation each time. Now, if the spectrum does not change while the test block is moving accross the image, then you can loosely say that the image under concern is stationary.

Since for most natural images, such a moving block will be crossing unrelated distinct objects during its travesral of the image, the frequency spectrum will also be changing, i.e., image being nonstatinary

Basic Fourier type transforms are not very efficient and proper for this kind of local variations in spectra whereas wavelet or packets or short-space Fourier methods will be more efficiently indicating those local features.