A median selects a position in the sorted neighborhood values. It does not average all those values in the same way as a mean filter.
Specify the rank operation
A median filter replaces a sample with the median of the specified neighborhood. For an odd number of samples, this is the central sorted value. The neighborhood shape, border handling and numerical output type remain part of the definition; they should not be inferred from a smoother-looking image. Primary reference: MathWorks median image filtering.
For an original worksheet, write out the sampled values and sort them before computing the result. Retain the arithmetic mean in a different column if it is being compared. A median’s rank selection and a mean’s sum-based calculation retain different information.
Compare fictional neighborhood values
Suppose an invented three-by-three neighborhood contains eight values of 10 and one value of 250. Its sorted fifth value is 10, so the median is 10. The arithmetic mean is (8 ×10 +250)/9 ≈36.67. The same input therefore yields different replacement values under the two operations.
This isolated high sample is a constructed array value, not a confirmed defect or noise cause. If a small genuine feature produces the same local values, replacing it could remove desired evidence. The operation’s arithmetic does not establish why the original sample was high.
Review feature retention separately
Prepare an original trial array containing both isolated variation and a selected small feature. Preserve the neighborhood definition and compare the resulting samples before running any classification. Do not label every removed isolated value unwanted solely because filtering removed it.
The guide does not prescribe an HM filter or certify that a median preserves all edges. Actual inspection performance needs application-specific evidence. The reader decision is whether the derived value was a rank statistic or a sum-based average, and whether that change fits the intended feature question.
Customer Questions
What is the fictional neighborhood’s median?
Ten, its fifth sorted value.
What is its mean?
Approximately 36.67.
Does removal prove the high sample was noise?
No. Its physical meaning needs separate evidence.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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