Resel Count

Estimate the volume resel term R3 from a fractional search mask and axis-aligned anisotropic FWHM; boundary and lower-dimensional resel terms are not included.

Description

A volumetric resel count scales mask volume by the product of image smoothness widths.

A volumetric resel count scales mask volume by the product of image smoothness widths. Fractional mask values contribute partial voxel volume.

The tool returns maskVolumeMm3 (mask volume mm3); volumeReselCount (volume resel count). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use Resel Count

Use Resel Count when you already have maskFractions, voxelDimensionsMm, smoothnessFwhmMm and want maskVolumeMm3, volumeReselCount. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Resel Count and understand its results

Enter maskFractions, voxelDimensionsMm, smoothnessFwhmMm 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 maskVolumeMm3, volumeReselCount. 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
maskFractions	Mask fractions	list of number	Required
voxelDimensionsMm	Voxel dimensions mm	list of number	Required
smoothnessFwhmMm	Smoothness fwhm mm	list of number	Required

Use nonempty fractions in [0,1], three positive voxel dimensions and three positive smoothness widths in mm.

volume resels = ΣmaskFractions×dx×dy×dz / (FWHMx×FWHMy×FWHMz)

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "maskFractions": [
      1,
      0.5,
      1
    ],
    "voxelDimensionsMm": [
      2,
      2,
      2
    ],
    "smoothnessFwhmMm": [
      2,
      4,
      5
    ]
  },
  "output": {
    "maskVolumeMm3": 20,
    "volumeReselCount": 0.5
  }
}

Limitations and assumptions

Only the volumetric resel term is returned. Boundary terms, nonstationary smoothness and statistical thresholds are not calculated.

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. Lesion Volume: Integrate lesion voxel fractions using anisotropic voxel dimensions; segmentation and partial-volume probabilities must be supplied.

Methodological background: An Introduction to Random Field Theory.^[1]

References

An Introduction to Random Field Theory — Brett, Penny and Kiebel; University College London

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.
Lesion Volume
Integrate lesion voxel fractions using anisotropic voxel dimensions; segmentation and partial-volume probabilities must be supplied.