Window dimensions do not fully define Gaussian smoothing. The relative weights also depend on the stated Gaussian scale and normalization.
Retain the coefficient definition
Gaussian smoothing uses a Gaussian-weighted neighborhood rather than uniform box weights. The coefficient scale and finite support both matter. Sampled coefficients are normalized for an averaging operation, so the center’s contribution cannot be inferred from the window width alone. Primary reference: MathWorks Gaussian image filtering.
For an original worksheet, keep the selected support, standard deviation, coefficient normalization and boundary treatment. Compare coefficient arrays directly when checking whether two proposed filters are equivalent. A shared description such as three samples is not enough to establish equal weighting.
Compare a fictional one-dimensional slice
Use an invented three-sample slice [0,90,0]. For Gaussian sample positions −1,0,1 with standard deviation 1, unnormalized weights are exp(−0.5),1,exp(−0.5). Normalizing their sum gives the center weight about 0.4519, so its output contribution is about 40.67.
A uniform three-sample mean gives 30 instead. This calculation demonstrates a one-dimensional sampled Gaussian, not the exact default two-dimensional output of a software call. Both examples use floating values and the same support; their different coefficient weights explain the different center results.
Review scale and implementation
Prepare a trial record with the actual coefficient matrix or explicit generator parameters. If a software function chooses support automatically, retain that resulting size rather than assuming it from the standard deviation alone. Also record any output-type conversion that follows the mathematical operation.
A smoother display does not prove preserved feature geometry or greater inspection accuracy. The original slice supplies no HM imaging specification and recommends no universal scale. Its purpose is to make the weighting behind a derived image explicit before values or feature contrast are compared.
Customer Questions
Does equal window width imply equal weights?
No. Gaussian scale and normalization also matter.
What is the fictional Gaussian center contribution?
About 40.67 for the defined normalized three-sample slice.
Is that a software-default two-dimensional result?
No. It is an explicitly defined one-dimensional illustration.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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