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For local enhancement using mean and variance, the condition is:

The local variance must be sufficiently high to apply meaningful enhancement.

Explanation:

  • Mean: The local mean helps adjust the overall brightness in a region by calculating the average intensity of the neighboring pixels.
  • Variance: The variance measures the spread of pixel intensities within the local neighborhood. High variance indicates a region with contrast, edges, or texture, while low variance indicates a uniform or smooth region.

Condition:

  • High Variance: Enhancement should be applied more effectively in regions with high variance because these areas have more variation in intensity and therefore contain more useful information (e.g., edges or details).
  • Low Variance: For regions with low variance, which are typically smooth or uniform, enhancement might either be avoided or applied less intensively to prevent exaggerating noise or creating artificial contrast.

In summary, only regions with high variance should undergo significant enhancement, as they contain more detail that can benefit from contrast enhancement.

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