[Paper Review] Hidden Markov Random Field Iterative Closest Point

John Stechschulte, Christoffer Heckman|arXiv (Cornell University)|Nov 7, 2017

Robotics and Sensor-Based Localization33 references3 citations

TL;DR

This paper proposes a Hidden Markov Random Field (HMRF) extension to the Iterative Closest Point (ICP) algorithm that models inlier and outlier states in depth maps using a Gaussian mixture model, with EM inference to estimate hidden states. The method improves registration accuracy and convergence speed in low-overlap scenarios, achieving sub-0.04 m translation and 0.2 rad rotation errors at 36% overlap, outperforming standard ICP and other outlier rejection methods.

ABSTRACT

When registering point clouds resolved from an underlying 2-D pixel structure, such as those resulting from structured light and flash LiDAR sensors, or stereo reconstruction, it is expected that some points in one cloud do not have corresponding points in the other cloud, and that these would occur together, such as along an edge of the depth map. In this work, a hidden Markov random field model is used to capture this prior within the framework of the iterative closest point algorithm. The EM algorithm is used to estimate the distribution parameters and the hidden component memberships. Experiments are presented demonstrating that this method outperforms several other outlier rejection methods when the point clouds have low or moderate overlap.

Motivation & Objective

• To address the challenge of poor ICP performance in low-overlap point cloud registration, especially when non-overlapping regions contain structured outliers.
• To model inlier and outlier states in depth maps as a hidden Markov random field (HMRF) to exploit spatial context and improve robustness.
• To use the EM algorithm with mean field approximation to infer hidden inlier/outlier states and estimate mixture model parameters.
• To demonstrate that HMRF-ICP achieves better registration accuracy and faster convergence than standard ICP and other outlier rejection techniques in low-overlap regimes.
• To enable more efficient 3D reconstruction from partial scans by reducing the number of required scans through improved alignment robustness.

Proposed method

• The method models observed distances from free cloud points to their nearest fixed cloud points as a Gaussian mixture: one component for inliers, one for outliers.
• A hidden Markov random field (HMRF) encodes spatial dependencies, where the state of each pixel (inlier/outlier) is influenced by its neighbors via a Potts-like potential.
• The EM algorithm is used for inference: the E-step estimates posterior probabilities of hidden states using mean field approximation, and the M-step updates mixture parameters.
• The HMRF model is initialized with a uniform prior and iteratively refined over 370 EM steps before the first ICP iteration.
• ICP is then applied using only the inferred inliers, minimizing sum of squared point-to-point distances via SVD-based closed-form solution.
• The method assumes a 2D grid structure (e.g., from structured light or stereo sensors), with neighbor relations defined on a 4-connected grid.

Experimental results

Research questions

• RQ1 Can a probabilistic HMRF model improve ICP performance in low-overlap point cloud registration by capturing spatial context in inlier/outlier states?
• RQ2 Does the use of EM inference with mean field approximation lead to more accurate and robust inlier detection than threshold-based or fixed-fraction outlier rejection?
• RQ3 How does HMRF-ICP compare to standard ICP and other outlier rejection methods in terms of convergence speed and transformation accuracy at varying overlap levels?
• RQ4 Can the HMRF model adapt effectively to sparse inlier distributions, such as in 36% overlap scenarios, without diverging?
• RQ5 What is the impact of spatial priors on outlier suppression in structured depth maps with occlusions and missing data?

Key findings

• At 36% overlap, HMRF-ICP achieved a translation error of 0.017 m and rotation error of 0.0776 radians, significantly outperforming other methods.
• For the shark sequence, HMRF-ICP maintained low error (max 0.036 m translation, 0.196 rad rotation) across all overlap levels, with faster convergence at low overlap.
• In the desk sequence, performance degraded below 20% overlap, with maximum errors of 1.55 m (translation) and 1.97 rad (rotation), indicating limitations in extreme low-overlap cases.
• The HMRF model reduced initial outlier estimates from 62% to 20% of pixels after 370 EM iterations, significantly improving alignment stability.
• HMRF-ICP showed minimal performance degradation with decreasing overlap, unlike other methods that slowed or diverged, indicating robustness in sparse data regimes.
• The method achieved faster convergence than standard ICP at low overlap, as the EM-inferred inlier set avoided divergence from local minima.