For local enhancement using mean and variance, the condition is:
The size of the local window or neighborhood should be chosen appropriately to avoid including edges or regions with abrupt intensity changes.
This condition ensures that the mean and variance are calculated over a region that is homogeneous enough to produce reliable statistical values, leading to effective enhancement. If the local neighborhood is too large, it may include regions that smooth out important features. If the region is too small, the statistics may not be meaningful due to noise or lack of sufficient data points. Therefore, the region should be balanced in size to properly capture the local variations while avoiding the influence of edges or large variations in intensity.