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ActiveReg: Information-Driven Active Regional Probing for Partial-to-Full Bone Registration

Tiancheng Li, Yingyu Wang, Peter Walker, Liang Zhao, Shoudong Huang

arXiv:2610.11003v1cs.RO

TL;DR

ActiveReg addresses bone registration when limited surgical exposure makes prescribed-point probing difficult and free probing leaves contact selection unguided. It recommends informative probing regions, updates registration with each actual contact, and assesses whether further acquisition is needed. Simulations and phantom experiments report competitive accuracy with substantially fewer acquired points than baseline methods.

  • Problem

    Bone registration must map pre-operative plans to patient anatomy, but prescribed-point acquisition can be difficult under limited exposure and reducing contacts must retain sufficient geometric constraints.

    Source: §I · p. 1

  • Method

    ActiveReg uses current registration information to recommend probing regions, updates correspondence-free SDF registration with actual contacts, and assesses completion using innovation consistency and task-space uncertainty.

    Source: §I · p. 2

  • Results

    Across four exposure scenarios, ActiveReg used 13.1–28.5 contacts on average, including retries, and had lower mean rotation and translation errors than Gradient-SDF with 30 and 100 contacts and other baselines with 30, 100, and 200 contacts.

    Source: B. Closed-Loop Registration Performance · p. 5

  • Takeaways & Limitations

    Simulations and phantom experiments with two tracking systems showed competitive accuracy against baseline methods while using substantially fewer acquired points.

    Source: §V · p. 8

    Future work will assess acquisition time, surgeon effort, and registration accuracy under realistic surgical conditions.

    Source: §V · p. 8

Abstract

from arXiv · show

Accurate bone registration is essential for orthopedic surgical navigation and robotic assistance. In a common workflow, the surgeon needs to identify and probe a number of prescribed locations on the exposed bone surface to obtain data points for registration, which can be difficult and time-consuming under limited surgical exposure. Reducing the number of required points while providing clear probing guidance would ease the surgeon's acquisition task intra-operatively. We present ActiveReg, a closed-loop framework that recommends probing regions rather than individual points, allowing flexibility in the exact contact location. A D-optimal planner that takes into account the already acquired points and the uncertainty of current registration information helps achieve accurate registration with fewer points. An online assessment combines pre-update innovation consistency with uncertainty at predefined surgical task locations improves the reliability of completion decision, without requiring ground truth. Simulations across four anatomical scenarios demonstrated that ActiveReg can achieve competitive accuracy compared with baseline registration methods while using substantially fewer acquired points. Real phantom experiments with optical and electromagnetic tracking demonstrated comparable mean target registration error to the Gradient-SDF framework, using only 24-28 acquired points instead of 771-1263.

I. INTRODUCTION

Bone registration maps pre-operative plans to patient anatomy, but probing exposed bone creates a trade-off between clear guidance and flexible, low-effort acquisition. ActiveReg addresses this with information-driven regional recommendations and online completion assessment.

I. INTRODUCTION

  • Bone registration aligns the pre-operative model with the intra-operative patient frame, supporting bone preparation and implant placement in hip and knee arthroplasty.Source: §I · p. 1
  • MAKO’s enhanced workflow specifies three initial landmarks plus 32 prescribed points for each of the acetabulum and femur, which are difficult to contact under limited exposure.Correspondence-free methods allow free contact placement, but leave probe selection to the surgeon and require many contacts.Source: §I · p. 1
  • A recommended region lets the surgeon choose the exact contact location while directing acquisition toward geometric information that complements previous contacts.The region recommendation is updated using the actual acquired points to address remaining registration uncertainty.Source: §I · pp. 1–2
  • ActiveReg uses the current registration estimate and information matrix to recommend an informative surface region, then incorporates the actual probe point into SDF registration and replans if needed.Online completion assessment determines whether acquisition ends or continues.Source: §I · p. 2
  • ActiveReg’s contributions combine closed-loop probing, D-optimal region construction with connectivity and minimum-area requirements, and completion assessment using innovation consistency and task-space uncertainty.Source: §I · p. 2

A. Registration for Orthopedic Surgery

Orthopedic bone registration must work with sparse measurements and partial surface overlap. ActiveReg couples registration, regional probing guidance, and online assessment so actual contacts inform both the current estimate and subsequent acquisition.

A. Registration for Orthopedic Surgery

  • Sparse measurements and partial overlap make intra-operative bone registration challenging; prior approaches add geometric constraints from point normals or tangents.SPNR methods use point positions and surface normals, while Min et al. combine point tangents with pre-operative surface normals.Source: A. Registration for Orthopedic Surgery · p. 2

B. Active Acquisition and Registration Assessment

  • Active acquisition methods have selected informative points or touch actions, but were not designed for bone registration; task-relevant uncertainty also matters because low fiducial error can coexist with high target error.ActiveReg combines uncertainty assessment at task-relevant locations with pre-update innovation consistency.Source: B. Active Acquisition and Registration… · p. 2

III. METHODOLOGY

  • Each actual acquired point updates registration and geometric information, which inform completion assessment and the next recommended region when more probing is needed.Source: §III · p. 2

A. Problem Statement

  • Registration minimizes robust signed-distance residuals of transformed probe contacts against the model surface, without requiring predefined point correspondences.Source: A. Problem Statement · p. 2
  • The strategy seeks required accuracy with few points by using the current estimate and uncertainty to guide probing, recommending a connected accessible-surface region of at least Amin when further probing is needed.The surgeon chooses the exact contact location within the region, and the strategy must also determine when accumulated measurements suffice.Source: A. Problem Statement · pp. 2–3

B. Registration and Geometric Information

ActiveReg derives geometric information from the SDF registration objective and uses it to assess pose uncertainty and plan informative contacts. Each contact contributes a position- and surface-gradient-dependent constraint.

B. Registration and Geometric Information

  • Each contact provides a scalar constraint determined by its position and local SDF gradient, and complementary contacts can constrain pose directions that remain weakly observed.The residual Jacobian’s first three columns correspond to rotational increments and its remaining three to translational increments.Source: B. Registration and Geometric… · p. 3
  • The Cauchy robust loss downweights residuals according to their scale, and residuals, weights, and Jacobians are recomputed at each updated estimate.The resulting weighted Gauss–Newton matrix summarizes geometric constraints from the actual measurements under the current alignment.Source: B. Registration and Geometric… · p. 3
  • The approximate information matrix predicts candidate-contact information gain, while pose covariance is propagated to task-relevant locations for completion assessment.Source: B. Registration and Geometric… · p. 3

C. Geometry-Guided Bootstrap Initialization

Six geometry-guided contacts initialize the registration estimate and information matrix. ActiveReg then evaluates candidate locations by D-optimality and uses the resulting information field to construct a connected region.

C. Geometry-Guided Bootstrap Initialization

  • Six bootstrap contacts initialize both SDF registration and information-driven planning, which otherwise require an initial estimate and geometric information.Source: C. Geometry-Guided Bootstrap… · p. 3
  • The first bootstrap region is centered near the mean exposed-surface position, and five more centers are selected by geodesic farthest-point sampling for spatial coverage.A contact is acquired within each region; approximate correspondences between contacts and region centers provide coarse alignment before SDF refinement.Source: C. Geometry-Guided Bootstrap… · p. 3

D. Information-Driven Regional Acquisition Planning

  • D-optimality evaluates candidate surface locations, and the resulting information field guides construction of a connected region subject to a minimum-area requirement.Source: D. Information-Driven Regional… · p. 3

1) D-optimal information gain:

  • A candidate contact has greater information gain when it constrains pose directions that remain uncertain; evaluating gain at accessible mesh vertices produces the field for region construction.Source: 1) D-optimal information gain · p. 4

2) Connected region construction:

ActiveReg converts pointwise information gain into a connected, sufficiently large surface region for flexible probing. It selects a high-gain component and replans from the registration state updated with the actual contact.

2) Connected region construction:

  • The planner thresholds accessible faces by mean vertex information gain, selecting the highest threshold that still leaves a connected component of at least Amin.Faces are connected when they share an edge.Source: 2) Connected region construction · p. 4
  • Among qualifying components, it chooses the one with the highest area-weighted mean information gain, accounting for unequal mesh face sizes.Component area sums the constituent face areas.Source: 2) Connected region construction · p. 4
  • After a contact within the recommended region, the planner uses the registration state updated from that actual contact if probing continues.Source: 2) Connected region construction · p. 4

E. Online Completion Assessment

ActiveReg assesses completion by combining pre-update innovation consistency with uncertainty at task-relevant locations. The innovation check uses a recent window and an approximate independent, zero-mean Gaussian model.

E. Online Completion Assessment

  • Completion assessment combines whether new contacts agree with preceding registration estimates and whether measurements constrain task-relevant locations.Source: E. Online Completion Assessment · p. 4

1) Pre-update innovation consistency:

  • Before registration updates, ActiveReg stores each contact’s innovation and predicted variance, then calculates a normalized innovation statistic over the last W measurements.The predicted variance accounts for pose uncertainty and measurement noise.Source: 1) Pre-update innovation consistency · p. 4
  • The innovation consistency threshold uses an approximate independent, zero-mean Gaussian innovation model and a chi-squared quantile with W degrees of freedom.Source: 1) Pre-update innovation consistency · p. 4

2) Task-space uncertainty:

Task-space uncertainty evaluates registration uncertainty at selected pre-operative model locations relevant to surgical tasks. The completion condition requires every selected target to satisfy its assigned tolerance.

2) Task-space uncertainty:

  • Task-space locations may be landmarks, planned resection sites, or implant-related targets, and require no additional intra-operative probing.Registration error at these locations directly affects surgical execution.Source: 2) Task-space uncertainty · p. 4
  • The method propagates pose uncertainty through target displacement sensitivity to estimate positional uncertainty under a local zero-mean model.The predicted measure is RMS displacement uncertainty at each task target.Source: 2) Task-space uncertainty · p. 4
  • The task-space condition ηK ≤1 requires all selected targets to meet their assigned uncertainty tolerances.Source: 2) Task-space uncertainty · p. 4

3) Joint Completion Criterion:

Completion requires a minimum contact count, consistent innovations, and acceptable uncertainty at selected task targets; reaching the contact budget alone does not count as completion. The evaluation uses four anatomical exposure scenarios across 144 model–exposure configurations.

3) Joint Completion Criterion:

  • Acquisition is complete only when K ≥Kmin, the innovation consistency condition holds, and ηK ≤1; reaching Kmax without these conditions is budget exhaustion, not completion.Kmin ≥6 + W ensures a full innovation window after the six-contact bootstrap.Source: 3) Joint Completion Criterion · p. 4

A. Datasets and Experimental Setup

  • The study used 37 femoral and 40 hip models from RWTHmediTEC and 30 right tibial models from SSM-Tibia, yielding 144 configurations across four exposure scenarios.Scenarios were acetabular, proximal femoral, distal femoral, and proximal tibial exposure.Source: A. Datasets and Experimental Setup · p. 5, Figure 3 · p. 5
  • 0.5 mm zero-mean Gaussian noise was added per coordinate; simulated rotations ranged from −45° to 45° per axis and translations from −1000 mm to 1000 mm.The inverse applied transformation served as ground truth.Source: A. Datasets and Experimental Setup · p. 5

B. Closed-Loop Registration Performance

ActiveReg achieved competitive registration accuracy across four exposure scenarios with substantially fewer contacts than the baselines. Its information-driven planning improved fixed-budget accuracy and target attainment, although planning alone did not prevent occasional large errors.

B. Closed-Loop Registration Performance

  • With 13.1–28.5 contacts on average, ActiveReg had lower mean rotation and translation errors than Gradient-SDF at 30 and 100 contacts and all other baselines at 30, 100, and 200 contacts.It had the lowest rotation errors in both femoral scenarios and second-lowest errors in the remaining measures; 200-contact Gradient-SDF slightly improved six error measures but used substantially more contacts.Source: B. Closed-Loop Registration Performance · p. 5, Table I · p. 6

C. Effect of Acquisition Planning

  • The acquisition-planning comparison tested ActiveReg against random, geodesically uniform, and feature-guided sampling using the same SDF registration backend.The strategies shared initial poses and ground truth in paired trials; each strategy had 720 trials, and registration began after six points.Source: C. Effect of Acquisition Planning · p. 5
  • At 10, 15, and 20 contacts, ActiveReg achieved the lowest median rotation and translation errors across all four scenarios.Geodesically uniform and feature-guided sampling generally reduced median errors relative to random sampling.Source: C. Effect of Acquisition Planning · p. 5, Figure 4 · p. 6
  • With completion assessment disabled, fixed-budget trials showed occasional large errors across all strategies, and planning alone did not ensure accurate registration.The authors note that information-driven planning based on an extreme incorrect estimate may not provide measurements needed to recover accurate alignment.Source: C. Effect of Acquisition Planning · pp. 5–6
  • ActiveReg had the highest target-attainment rates in both femoral scenarios and the proximal tibia, and required the fewest contacts in the proximal femur, proximal tibia, and pelvis.The comparison used shared initial values and ground-truth transformations across paired trials; completion assessment was disabled.Source: C. Effect of Acquisition Planning · pp. 5, 7, Table II · p. 6

D. Ablation Studies

ActiveReg's regional probing retained similar median accuracy to pointwise D-optimal probing while allowing flexible contact placement. In completion-assessment ablations, combining innovation consistency with task-space uncertainty produced the lowest errors across four scenarios.

1) Pointwise vs Regional Probing; 2) Online Completion Assessment

  • The regional-probing comparison used paired trials at a fixed budget of 20 contacts, while completion-criterion variants shared a budget of Kmax = 30.The completion assessment compared innovation consistency alone, task-space uncertainty alone, and their conjunction; task-space uncertainty used five locations per bone model as surrogate targets.Source: 1) Pointwise vs Regional Probing · p. 7, 2) Online Completion Assessment · p. 7

1) Pointwise vs Regional Probing

  • Across four scenarios, regional probing's largest median-error increases over pointwise probing were 0.20° in rotation and 0.21 mm in translation, with recommended regions covering 2.9%–3.3% of exposed surface.The regions measured 180 to 188 mm2, allowing acquisition within a region rather than precise alignment with a point target; neither variant consistently achieved lower P90 errors across scenarios and metrics.Source: 1) Pointwise vs Regional Probing · p. 7

2) Online Completion Assessment

  • The Joint completion criterion achieved the lowest mean and maximum rotation and translation errors across all four scenarios.Compared with Uncertainty alone, mean contact count increased by at most 1.03, with one to three fewer completed trials per scenario.Source: 2) Online Completion Assessment · p. 7, Table IV · p. 7

E. Real Phantom Experiments

Phantom experiments compared ActiveReg with baseline registration methods using optical and electromagnetic tracking, finding Gradient-SDF-comparable mean TRE with far fewer acquired points. The conclusions also report competitive accuracy across simulations and phantom experiments, plus ablation findings on probing guidance and completion assessment.

E. Real Phantom Experiments

  • Phantom testing used four pelvic and three femoral Sawbones models, with optical and electromagnetic tracking systems.Source: E. Real Phantom Experiments · p. 8
  • 24–28 acquired points yielded mean TRE comparable to Gradient-SDF using 771–1263 points for dense sampling; the mean TRE difference stayed below 1 mm across all four conditions.Registration accuracy was evaluated at ten anatomical landmarks excluded from registration.Source: E. Real Phantom Experiments · p. 8

V. CONCLUSIONS

  • ActiveReg uses information from acquired contacts to plan recommended probing regions and assess whether further probing is needed, allowing flexibility in exact contact location.Source: §V · p. 8
  • Across four anatomical simulation scenarios and phantom experiments with two tracking systems, ActiveReg achieved competitive accuracy versus baselines while using substantially fewer points.Future work will assess acquisition time, surgeon effort, and registration accuracy under realistic surgical conditions.Source: §V · p. 8
  • Ablations found regional guidance balanced registration accuracy with tolerance to contact-placement variation, while innovation consistency plus task-space uncertainty improved completion-decision reliability.Source: §V · p. 8
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