Registration Cost Function MI
Score supplied image-pair joint histograms with MI and Studholme NMI=(H1+H2)/Hjoint; does not perform registration search or select bin edges.
Description
A joint histogram summarizes paired image-intensity bins.
A joint histogram summarizes paired image-intensity bins. Mutual information measures statistical dependence; normalized MI here divides the sum of marginal entropies by joint entropy.
The tool returns mutualInformationBits (mutual information bits); firstEntropyBits (first entropy bits); secondEntropyBits (second entropy bits); normalizedMutualInformation (normalized mutual information). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Registration Cost Function MI
Use Registration Cost Function MI when you already have jointBinCounts and want mutualInformationBits, firstEntropyBits, secondEntropyBits, normalizedMutualInformation. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Registration Cost Function MI and understand its results
- Enter jointBinCounts 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 mutualInformationBits, firstEntropyBits, secondEntropyBits, normalizedMutualInformation. 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 |
|---|---|---|---|
| jointBinCounts | Joint bin counts | list of list of number | Required |
Use a rectangular nonnegative integer count matrix with positive total and positive joint entropy. Compute probabilities and base-two entropies, treating zero-probability terms as zero.
MIbits = H(first)+H(second)−H(joint); NMI = (H(first)+H(second))/H(joint) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"jointBinCounts": [
[
5,
0
],
[
0,
5
]
]
},
"output": {
"mutualInformationBits": 1,
"firstEntropyBits": 1,
"secondEntropyBits": 1,
"normalizedMutualInformation": 2
}
}Limitations and assumptions
No image sampling, histogram bin selection or registration optimization occurs. A histogram with zero joint entropy is rejected.
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
Affine Spatial Normalization: Apply a supplied nonsingular voxel-to-world image affine including translations; voxel indexing and world-axis convention must match the image header, and registration is not fitted. Temporal SNR tSNR: Compute per-voxel temporal SNR using sample SD without detrending; constant series have undefined infinite tSNR and return an error, not a fabricated finite value.
Methodological background: Multimodality image registration by maximization of mutual information.1
References
-
Multimodality image registration by maximization of mutual information — Maes et al.; IEEE Transactions on Medical Imaging
Similar or alternative tools
- Affine Spatial Normalization
Apply a supplied nonsingular voxel-to-world image affine including translations; voxel indexing and world-axis convention must match the image header, and registration is not fitted.
- Temporal SNR tSNR
Compute per-voxel temporal SNR using sample SD without detrending; constant series have undefined infinite tSNR and return an error, not a fabricated finite value.