Conformal forecasting for surgical instrument trajectory

TL;DR

This paper addresses uncertainty quantification in forecasting surgical instrument trajectories within endoscopic video by applying conformal prediction (CP) and conformalized quantile regression (CQR) to produce predictive intervals for the angle $\angle v$ and magnitude $||v||$ of the future motion vector $v$, with joint coverage guaranteed under exchangeability. It demonstrates that CQR yields sharper, more adaptive intervals than standard CP, and that applying multiple-testing corrections (e.g., Bonferroni, Sidak, Max-Rank) is essential to maintain valid joint coverage for angle and magnitude. The authors validate these approaches on a pituitary surgery dataset, showing practical uncertainty heatmaps and analyzing computational efficiency for real-time guidance. The work establishes a principled path toward principled prediction intervals with formal coverage guarantees in surgical guidance and highlights directions for extending to autoregressive models and handling exchangeability violations.

Abstract

Forecasting surgical instrument trajectories and predicting the next surgical action recently started to attract attention from the research community. Both these tasks are crucial for automation and assistance in endoscopy surgery. Given the safety-critical nature of these tasks, reliable uncertainty quantification is essential. Conformal prediction is a fast-growing and widely recognized framework for uncertainty estimation in machine learning and computer vision, offering distribution-free, theoretically valid prediction intervals. In this work, we explore the application of standard conformal prediction and conformalized quantile regression to estimate uncertainty in forecasting surgical instrument motion, i.e., predicting direction and magnitude of surgical instruments' future motion. We analyze and compare their coverage and interval sizes, assessing the impact of multiple hypothesis testing and correction methods. Additionally, we show how these techniques can be employed to produce useful uncertainty heatmaps. To the best of our knowledge, this is the first study applying conformal prediction to surgical guidance, marking an initial step toward constructing principled prediction intervals with formal coverage guarantees in this domain.

Figures (2)

• Figure 1: Qualitative illustration of how Conformal Prediction (CP) for instrument trajectory forecasting. a): CP applied independently to the angle and the length. b): Joint intervals obtained by merging the independent ones without corrections, here failing to cover the angle. c): Multiple-test corrections restore valid coverage for both quantities.
• Figure 2: Heatmaps from CP (top) and CQR (bottom). The black vector denotes the GT trajectory. Target coverage ranges from 10% (yellow) to 80% (blue). Left: Angle-only intervals—CQR yields sharper intervals and better coverage than CP. Center: Joint intervals without correction—coverage fails as expected. Right: Sidak-corrected joint intervals—recalibration restores validity, with CQR providing tighter bounds.