BUG: ScaleLogarithmicTransform Jacobian ignores the center

[physwkim]

ScaleLogarithmicTransform's Jacobian dropped the transform center: d/dLog(scale[i]) is scale[i] * (p[i] - center[i]), not scale[i] * p[i]. Adds the missing Jacobian test case. Split out of #6569 per review.

Root cause

itkScaleLogarithmicTransform.hxx computed

jacobian(dim, dim) = scales[dim] * p[dim];

but the transform (inherited from ScaleTransform) maps
p -> scale * (p - center) + center. itkScaleTransform.hxx already
differentiates about the center (j(dim, dim) = p[dim] - center[dim]), so
the log-scale chain rule gives scale[dim] * (p[dim] - center[dim]). With a
non-zero center, any Optimizerv4 driving this transform received a wrong
gradient.

itkScaleLogarithmicTransformTest exercised no Jacobian at all. The added
case: center (5, 6, 7), scales (2, 3, 4), point (10, 10, 10) — expected
diagonal (10, 12, 12); the old code returns (20, 30, 40).

AI assistance

• Tool: Claude Code (claude-opus-4-8)
• Role: found the defect while cross-checking an independent reimplementation
  of ITKv4 registration against this source
• Contribution: the patch and the new Jacobian test case
• Testing: this commit (same SHA) passed CI in BUG: Fix JointHistogramMutualInformation metric marginals and derivative #6569's previous run,
  including itkScaleLogarithmicTransformTest

[greptile-apps]

Greptile Summary

This PR fixes the ScaleLogarithmicTransform Jacobian for transforms with a non-zero center. The main changes are:

• Uses p - center when computing each log-scale Jacobian diagonal entry.
• Adds a regression test with a non-zero center and non-unit scales.
• Verifies the expected Jacobian values for the centered transform case.

Confidence Score: 5/5

Safe to merge with minimal risk.

The change is small, matches ScaleTransform::TransformPoint behavior, and is covered by a focused regression test.

No files require special attention.

T-Rex Logs

What T-Rex did

• The initial CTest run for the scale_logarithmic_transform completed successfully, with exit code 0, and its transcript was preserved in the first log.
• A PIPESTATUS portability issue was observed after the initial run, so the command was rerun under bash to achieve a clean harness exit.
• The CTest rerun under bash completed successfully, with exit code 0, and its transcript was captured in the rerun log.

_{Ran code and verified through T-Rex}

Important Files Changed

Filename	Overview
Modules/Core/Transform/include/itkScaleLogarithmicTransform.hxx	Updates the log-scale Jacobian to differentiate around the transform center; no issues found.
Modules/Core/Transform/test/itkScaleLogarithmicTransformTest.cxx	Adds a non-zero-center Jacobian regression test using log-scale parameters; no issues found.

_{Reviews (1): Last reviewed commit: "BUG: ScaleLogarithmicTransform Jacobian ..." | Re-trigger Greptile}

[hjmjohnson]

ITK.Linux.Python failed with "We stopped hearing from agent Azure Pipelines 5" (agent VM died mid-build) — infrastructure flake, no code issue; CDash shows 0 errors / 0 test failures for this revision. Retriggering.

[hjmjohnson]

/azp run ITK.Linux.Python