Optimization and Registration

Metrics only become registration algorithms once ritk couples them to an optimizer. On the differentiable side, ritk-registration::metric::autodiff supplies a reusable gradient_descent driver configured by GradientDescentConfig, rebuilding a transform from trainable Coeus Vars each iteration and stepping parameters with the native SGD helper. On the classical side, ImageRegistration uses ClassicalConfig and MutualInformationMetric to run deterministic CPU optimization over rigid or affine parameters. This chapter covers that seam: parameterization, iteration budgets, tolerances, step sizes, and why optimizer behavior must be read together with the chosen similarity metric.

Atlas integration is split but coherent. Coeus provides the autodiff graph, tensor execution, and backend flexibility for learning-style registration loops, while Leto supports the classical numeric path where predictable CPU array behavior is preferred. RITK keeps those implementation details behind a common image boundary so callers can reason about transforms, convergence, and output geometry without rewriting file I/O or preprocessing around each optimizer family.

Bounded rigid capture and refinement

search_rigid_pose searches a six-degree-of-freedom rigid transform in physical millimetres. It starts from a validated RigidSearchAnchor, performs four coarse-to-fine coordinate-descent levels, and polishes the capture objective with bounded Nelder–Mead. A second structural objective defaults to a half-range of one terminal capture cell. with_structural_half_range_cells accepts a NonZeroU8 when a consumer needs to test a wider local basin. The configured radius scales both the structural bounds and initial simplex, but the original global rigid bounds remain authoritative. The effective interval is their intersection. When capture ends on a global boundary, each simplex edge points toward the side with available room rather than constructing an invalid outward vertex. This separation supports multimodal registration where normalized mutual information (NMI) finds the broad basin and MIND-SSC or Normalized Gradient Fields (NGF) resolves local soft-tissue structure without enabling an unbounded second search. The tested Rustdoc on RigidSearchConfig::with_structural_half_range_cells is the copyable API example.

The capture schedule and all simplex operations preserve finite proposals and their bounded-objective rejection semantics. If an otherwise valid finite resolution multiplied by a schedule factor would overflow, only that non-finite proposal is replaced by the finite endpoint in its direction before an objective sees it. A separate finite-transform check converts overflow from centroid and residual composition into a typed numerical failure before metric evaluation.

RigidSearchResult::capture_saturated and structural_saturated report when an optimum touches its permitted boundary. Structural saturation covers either the configured local half-range or a tighter global bound. Saturation is a quality-control signal: it means the configured search region may have clipped the optimum, not that the transform is invalid. The caller still owns image sampling, fixed-domain support, overlap acceptance, and the final choice between the capture and structural candidates.

Objective errors propagate through the search result. A malformed or empty metric sample set therefore cannot be converted into a plausible pose.

When centroids alone do not place the orientation inside this bounded search, fit_symmetric_trimmed_rigid estimates the complete anchor from direction- specific FixedToMovingCorrespondence and MovingToFixedCorrespondence physical-space matches. It fits each direction independently, retains the half with smallest Euclidean residual under a deterministic LTS fit, inverts the reverse result, and combines the two fixed-to-moving transforms with a log-Euclidean mean. Exact endpoint pairs with conflicting directions are discarded because selecting either would make the directional schedules depend on image-role ordering. The fit requires a strict majority supporting one non-collinear rigid consensus; exactly two equal half-population consensuses are not identifiable. See the robust rigid capture initializer for the executable known-transform and outlier case.

Example Summary