Box smoothing replaces local values with a neighborhood average. A larger averaging support can change the contribution of a small feature.
State the averaging support
A normalized box filter gives equal weight to the samples in its chosen neighborhood and computes their local mean. Neighborhood dimensions and normalization are therefore part of the operation. A local sum without normalization is another quantity even when the same samples are included. Primary reference: MathWorks box filtering and mean normalization.
For an original processing worksheet, retain the input array, support shape, numerical type and border rule. Use floating arithmetic for the teaching calculation so rounding or saturation is not silently added. A visually smoother result does not specify which neighborhood produced it.
Calculate a fictional isolated feature
Suppose a hypothetical image neighborhood has a center value of 90 and every other sample is zero. A three-by-three mean uses nine samples, giving 90/9 = 10 at the center. A five-by-five mean uses twenty-five samples, giving 90/25 = 3.6 under the same constructed surroundings.
The different center values follow the averaging support, not a changed original feature. Both windows are fully inside the image in this illustration. The numbers are mathematical output before any integer storage conversion and do not describe measured contrast on an actual pack.
Review the downstream measurement
Prepare an original before-and-after array and retain the filter dimensions beside any later threshold or feature measurement. If the measurement uses the filtered image, identify that derived input rather than implying it came directly from the sensor samples. Compare changes using the same support convention.
This guide does not recommend a universal kernel size or promise improved defect detection. A larger average can suppress desired small structure as well as unwanted variation. Actual inspection choices need their own images and evaluation; the decision here is whether local averaging has changed the values being interpreted.
Customer Questions
What is the three-by-three center result in the example?
Ten using the stated floating mean.
What changes for five-by-five support?
The same value 90 is divided among 25 samples, giving 3.6.
Is a local sum the same as a mean?
No. A mean includes the defined normalization.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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