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arxiv: 1907.09133 · v1 · pith:LVFS5EW2new · submitted 2019-07-22 · 💻 cs.RO · cs.LG

Speeding Up Iterative Closest Point Using Stochastic Gradient Descent

Fahira Afzal Maken , Fabio Ramos , Lionel Ott This is my paper

Pith reviewed 2026-05-24 18:23 UTC · model grok-4.3

classification 💻 cs.RO cs.LG
keywords iterative closest pointstochastic gradient descentpoint cloud registration3d alignmentroboticsslampose estimationsensor data
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The pith

Stochastic gradient descent solves the ICP optimization problem to reach accurate point cloud alignments faster than standard solvers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper proposes solving the optimization in Iterative Closest Point registration by using stochastic gradient descent instead of conventional methods. The central aim is to reduce the number of iterations needed for convergence while producing alignments of equivalent quality. A sympathetic reader would care because ICP remains the default tool for aligning 3D point clouds in robotics tasks such as model registration, pose estimation, and SLAM, where sensor data from devices like Kinect and Velodyne must be processed quickly. Experiments on real sensor data are presented to show that the SGD variant runs faster and requires less parameter adjustment across different sensors.

Core claim

The paper claims that applying stochastic gradient descent to the ICP objective improves convergence speed without sacrificing solution quality. Experiments using Kinect and Velodyne data confirm that the proposed method is faster than existing ICP variants while obtaining comparable alignments, with an added benefit of greater robustness to parameter choices when data come from different sensors.

What carries the argument

Stochastic gradient descent applied directly to the ICP point correspondence error objective.

If this is right

  • The SGD formulation converges in fewer iterations than standard ICP solvers.
  • Final alignment accuracy remains comparable to conventional ICP on real sensor data.
  • The approach exhibits reduced sensitivity to parameter settings across Kinect and Velodyne datasets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method could allow ICP to be used in tighter real-time loops inside SLAM pipelines where iteration count directly limits frame rate.
  • Because SGD naturally handles noisy gradients, the same substitution might improve robustness when ICP is applied to sparse or partially overlapping clouds.
  • The formulation might be combined with modern robust kernels or learned feature matching without changing the core SGD loop.

Load-bearing premise

The non-convex ICP objective can be optimized reliably by SGD without introducing new local minima or instability that standard ICP solvers avoid.

What would settle it

A direct comparison on identical point-cloud pairs in which the SGD version consistently produces higher final alignment error or fails to reach solutions of similar quality to deterministic ICP.

Figures

Figures reproduced from arXiv: 1907.09133 by Fabio Ramos, Fahira Afzal Maken, Lionel Ott.

Figure 1
Figure 1. Figure 1: Comparison of the amount of points needed by different methods to [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of the ability to handle errors in the initial transform by the different methods. The two plots show sensitivity to translational error [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example cloud pairs showing failure cases due to partial overlap [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Effect of batch-size on the performance of SGD-ICP algorithm in terms of accuracy and run-time using a fixed step-size (vanilla-SGD) and [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Sensors producing 3D point clouds such as 3D laser scanners and RGB-D cameras are widely used in robotics, be it for autonomous driving or manipulation. Aligning point clouds produced by these sensors is a vital component in such applications to perform tasks such as model registration, pose estimation, and SLAM. Iterative closest point (ICP) is the most widely used method for this task, due to its simplicity and efficiency. In this paper we propose a novel method which solves the optimisation problem posed by ICP using stochastic gradient descent (SGD). Using SGD allows us to improve the convergence speed of ICP without sacrificing solution quality. Experiments using Kinect as well as Velodyne data show that, our proposed method is faster than existing methods, while obtaining solutions comparable to standard ICP. An additional benefit is robustness to parameters when processing data from different sensors.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims that solving the ICP optimization problem via stochastic gradient descent (SGD) improves convergence speed without sacrificing solution quality relative to standard ICP, with supporting experiments on Kinect and Velodyne data demonstrating faster performance, comparable solutions, and greater parameter robustness across sensors.

Significance. If the central claim holds, the method could provide a practical speed-up for point-cloud registration in robotics applications such as SLAM and pose estimation. The approach is noteworthy for attempting to apply SGD directly to the non-convex ICP objective (pose parameters plus correspondence updates) rather than relying solely on alternating closed-form rigid transforms.

major comments (2)
  1. [Abstract] Abstract: the claim that SGD yields 'solutions comparable to standard ICP' is load-bearing for the central contribution, yet the text provides no explicit comparison of final residual distributions, failure rates, or error metrics (point-to-point vs. point-to-plane) under matched initializations, leaving the assumption that SGD avoids inferior local minima untested.
  2. [Abstract] Abstract: no equations, objective function, or derivation is shown for how the 6-DoF pose is optimized by SGD while handling correspondence updates, preventing assessment of whether the stochastic gradient estimates preserve the monotonic descent property of standard ICP's SVD/quaternion steps.
minor comments (1)
  1. The abstract refers to 'existing methods' without naming the baselines (e.g., standard ICP, Go-ICP, or others) used for speed and quality comparisons.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive comments on our manuscript. We address each major comment below, indicating where we agree that revisions are warranted to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that SGD yields 'solutions comparable to standard ICP' is load-bearing for the central contribution, yet the text provides no explicit comparison of final residual distributions, failure rates, or error metrics (point-to-point vs. point-to-plane) under matched initializations, leaving the assumption that SGD avoids inferior local minima untested.

    Authors: We agree that more explicit quantitative support is needed for the claim of comparable solution quality. The experiments section reports average final alignment errors and success rates on Kinect and Velodyne datasets under varied initializations, indicating performance comparable to standard ICP. However, we did not include detailed residual distribution histograms, failure rate breakdowns, or direct point-to-point vs. point-to-plane metric comparisons. We will revise the manuscript to add these analyses and figures to more rigorously test whether SGD-ICP avoids inferior local minima. revision: yes

  2. Referee: [Abstract] Abstract: no equations, objective function, or derivation is shown for how the 6-DoF pose is optimized by SGD while handling correspondence updates, preventing assessment of whether the stochastic gradient estimates preserve the monotonic descent property of standard ICP's SVD/quaternion steps.

    Authors: The abstract is a high-level summary and conventionally omits equations. The full manuscript (Section 3) defines the ICP objective, describes the 6-DoF parameterization, and explains the stochastic gradient computation with iterative correspondence updates. That said, we acknowledge the value of a more explicit derivation addressing monotonic descent properties. We will expand the methods section with additional equations and discussion of the stochastic approximation in the revision. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical validation of SGD-ICP with no self-referential derivations

full rationale

The paper presents an algorithmic proposal to replace standard ICP's alternating closed-form solves with direct SGD on the 6-DoF pose, then reports wall-clock speedups and comparable final alignment quality on Kinect and Velodyne point clouds. No equations, uniqueness theorems, or parameter fits are shown that would make any claimed improvement equivalent to its own inputs by construction. The central result is an empirical performance comparison rather than a derived identity or self-cited premise, so the derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The approach rests on standard assumptions of SGD convergence for non-convex problems and the standard ICP formulation; no free parameters, axioms, or invented entities are described in the abstract.

pith-pipeline@v0.9.0 · 5671 in / 858 out tokens · 15992 ms · 2026-05-24T18:23:46.867622+00:00 · methodology

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Reference graph

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