Spatial Smoothing FWHM
Build a normalized truncated 1D Gaussian kernel from physical FWHM and voxel spacing; distinct from estimating residual smoothness from derivative covariance.
Description
A Gaussian smoothing kernel uses FWHM to determine standard deviation.
A Gaussian smoothing kernel uses FWHM to determine standard deviation. Truncation to a finite radius requires renormalizing the sampled weights.
The tool returns offsetsVoxels (offsets voxels); normalizedWeights (normalized weights); sigmaVoxels (sigma voxels). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Spatial Smoothing FWHM
Use Spatial Smoothing FWHM when you already have fwhmMm, voxelSpacingMm, radiusVoxels and want offsetsVoxels, normalizedWeights, sigmaVoxels. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Spatial Smoothing FWHM and understand its results
- Enter fwhmMm, voxelSpacingMm, radiusVoxels using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read offsetsVoxels, normalizedWeights, sigmaVoxels. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| fwhmMm | Fwhm mm | number | Required |
| voxelSpacingMm | Voxel spacing mm | number | Required |
| radiusVoxels | Radius voxels | integer | Required |
Use positive FWHM and voxel spacing with nonnegative integer radius. Generate offsets −radius through +radius and normalize weights to sum to one.
sigmaVoxels = FWHMmm/(2sqrt(2ln2)×spacingMm); weight[j] ∝ exp(−0.5(j/sigma)²) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"fwhmMm": 2.3548200450309493,
"voxelSpacingMm": 1,
"radiusVoxels": 1
},
"output": {
"offsetsVoxels": [
-1,
0,
1
],
"normalizedWeights": [
0.274068619061197,
0.45186276187760605,
0.274068619061197
],
"sigmaVoxels": 1
}
}Limitations and assumptions
The tool returns a one-dimensional kernel and does not apply it to an image. Radius zero produces [1]; truncation and boundary handling affect later smoothing.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Smoothness FWHM: Infer coordinate-axis Gaussian-equivalent residual FWHM and determinant-based resel density from residual variance and physical gradient covariance; not the applied smoothing-kernel width. Gibbs Ringing Checker: Screen overshoot/undershoot around a caller-selected intensity edge relative to plateau contrast; this finds ringing-compatible features, not a specific Gibbs-artifact diagnosis.
Methodological background: Measures of scale: sample variance and standard deviation.1
References
-
Measures of scale: sample variance and standard deviation — NIST/SEMATECH
Similar or alternative tools
- Smoothness FWHM
Infer coordinate-axis Gaussian-equivalent residual FWHM and determinant-based resel density from residual variance and physical gradient covariance; not the applied smoothing-kernel width.
- Gibbs Ringing Checker
Screen overshoot/undershoot around a caller-selected intensity edge relative to plateau contrast; this finds ringing-compatible features, not a specific Gibbs-artifact diagnosis.