Considering input images to a CNN that have a large dimension (e.g. 256X256), what are some possible methods to estimate the exact dimensions (e.g. 16X16 or 32X32) to which it can be condensed in the final pooling layer within the CNN network such that the important features are retained? I have found references to using linear dimensionality estimates (such as PCA) and the Riemannian Metric for non-linear estimation, but am not confident of how accurate the predicted dimensions may be.
One paper that explores this issue in Deep Neural Networks in a better way can be found here. Answers specifically pertaining to processing of SAR images would be more helpful.