BOP / 3D surface error · error

MSSD

Maximum Symmetry-Aware Surface Distance

Minimizes the maximum 3D surface deviation over all allowed global symmetry transformations.

MSSD is sensitive to the worst-aligned point and explicitly uses the model's symmetry set. It emphasizes 3D geometric precision and is often used in strict evaluations related to robotic manipulation.

Explore principles and formulas View related papers 45

Principle

What error does this metric penalize?

The formulas define the computation. The diagrams show whether the error concerns a 3D model, visible surfaces, the image plane, or aggregation across thresholds.

First try alignment under all allowed symmetry transformations S to avoid penalizing equivalent poses.

Then measure the displacement of the worst-aligned model vertex, so large local errors cannot be diluted by averaging.

e_{MSSD}=\min_{S\in\mathcal S_M}\ \max_{x\in\mathcal V_M}\left\lVert \hat P x-\bar P Sx\right\rVert_2

S denotes a global model symmetry and V_M the model vertex set; the maximum makes this a worst-case metric.

Illustration created for this site to explain the metric's error space; it does not show measured data or a figure from the original paper.

How to compute

Computation steps

01
Read discrete and continuous symmetry definitions from BOP models_info.json.
02
For each symmetry transformation, compute the maximum distance over all model vertices.
03
Take the minimum over symmetry candidates, then compute recall using BOP thresholds.

Strength

What it is useful for

Handles model symmetry explicitly and reproducibly.
Meaningful for clearance, insertion, and grasping tasks that cannot tolerate large local errors.

Caveat

Cautions when reading results

Sensitive to sampling and extreme vertices; its values cannot be directly equated with mean ADD errors.
A full-model metric does not establish whether occluded regions are distinguishable in the image.

Paper atlas

Which papers report this metric?

Links are derived by normalizing the metric names used in each paper. Directly reported metrics are distinguished from metrics associated through a broader protocol.

Filter the paper library

45Related papers

30Directly reported

15Linked through a protocol

2026 Directly reported

AlignPose: Generalizable 6D Pose Estimation via Multi-view Feature-metric Alignment

CVPR · Anna Šárová Mikeštíková, Médéric Fourmy, Martin Cifka et al.

Original terminology: BOP AR / MSSD

2026 Directly reported

COG: Confidence-aware Optimal Geometric Correspondence for Unsupervised Single-reference Novel Object Pose Estimation

CVPR · Yuchen Che, Jingtu Wu, Hao Zheng et al.

Original terminology: BOP AR / MSSD

2026 Via a broader protocol

ConceptPose: Training-Free Zero-Shot Object Pose Estimation using Concept Vectors

CVPR · Liming Kuang, Yordanka Velikova, Mahdi Saleh et al.

Original terminology: BOP AR

2026 Via a broader protocol

CoordAR: One-Reference 6D Pose Estimation of Novel Objects via Autoregressive Coordinate Map Generation

AAAI · Dexin Zuo, Ang Li, Wei Wang et al.

Original terminology: AR (MSSD/MSPD/VSD)

2026 Directly reported

Finding NeMO: A Geometry-Aware Representation of Template Views for Few-Shot Perception

3DV · Sebastian Jung, Leonard Klüpfel, Rudolph Triebel et al.

Original terminology: AR / MSSD

2026 Directly reported

HRDexDB: A Paired Human-Robot Dataset for Cross-Embodiment Dexterous Grasping

arXiv · Jongbin Lim, Taeyun Ha, Mingi Choi et al.

Original terminology: MSSD / AR_MSSD

2026 Directly reported

IndustryShapes: An RGB-D Benchmark Dataset for 6D Object Pose Estimation of Industrial Assembly Components and Tools

ICRA · Panagiotis Sapoutzoglou, Orestis Vaggelis, Athina Zacharia et al.

MSSD

What error does this metric penalize?

Computation steps

What it is useful for

Cautions when reading results

Which papers report this metric?

AlignPose: Generalizable 6D Pose Estimation via Multi-view Feature-metric Alignment

COG: Confidence-aware Optimal Geometric Correspondence for Unsupervised Single-reference Novel Object Pose Estimation

ConceptPose: Training-Free Zero-Shot Object Pose Estimation using Concept Vectors

CoordAR: One-Reference 6D Pose Estimation of Novel Objects via Autoregressive Coordinate Map Generation

Finding NeMO: A Geometry-Aware Representation of Template Views for Few-Shot Perception

HRDexDB: A Paired Human-Robot Dataset for Cross-Embodiment Dexterous Grasping

IndustryShapes: An RGB-D Benchmark Dataset for 6D Object Pose Estimation of Industrial Assembly Components and Tools

InstantPose: Zero-Shot Instance-Level 6D Pose Estimation From a Single View

Deep Learning-Based Object Pose Estimation: A Comprehensive Survey

PoseGAM: Robust Unseen Object Pose Estimation via Geometry-Aware Multi-View Reasoning

PoseGaussian: 6D Pose Estimation for Unseen Objects via Sparse-View Object-Level 3D Gaussian Splatting

WALDO: Where Unseen Model-based 6D Pose Estimation Meets Occlusion

XYZ-IBD: Benchmarking Robust 6D Object Pose Estimation under Real-World Industrial Complexity

Any6D: Model-free 6D Pose Estimation of Novel Objects

Co-op: Correspondence-based Novel Object Pose Estimation

iG-6DoF: Model-free 6DoF Pose Estimation for Unseen Object via Iterative 3D Gaussian Splatting

JENGA: Object Selection and Pose Estimation for Robotic Grasping from a Stack

MixRI: Mixing Features of Reference Images for Novel Object Pose Estimation

One2Any: One-Reference 6D Pose Estimation for Any Object

Pos3R: 6D Pose Estimation for Unseen Objects Made Easy

Shape-Biased Texture Agnostic Representations for Improved Textureless and Metallic Object Detection and 6D Pose Estimation

RayPose: Ray Bundling Diffusion for Template Views in Unseen 6D Object Pose Estimation

Comparative Evaluation of 3D Reconstruction Methods for Object Pose Estimation

RefPose: Leveraging Reference Geometric Correspondences for Accurate 6D Pose Estimation of Unseen Objects

SCFlow2: Plug-and-Play Object Pose Refiner with Shape-Constraint Scene Flow

UA-Pose: Uncertainty-Aware 6D Object Pose Estimation and Online Object Completion with Partial References

UNOPose: Unseen Object Pose Estimation with an Unposed RGB-D Reference Image

ZeroPose: CAD-Prompted Zero-Shot Object 6D Pose Estimation in Cluttered Scenes

FoundationPose: Unified 6D Pose Estimation and Tracking of Novel Objects

FoundPose: Unseen Object Pose Estimation with Foundation Features

FreeZe: Training-free Zero-shot 6D Pose Estimation with Geometric and Vision Foundation Models

GenFlow: Generalizable Recurrent Flow for 6D Pose Refinement of Novel Objects

GigaPose: Fast and Robust Novel Object Pose Estimation via One Correspondence

MatchU: Matching Unseen Objects for 6D Pose Estimation from RGB-D Images

MRC-Net: 6-DoF Pose Estimation with MultiScale Residual Correlation

Open-Vocabulary Object 6D Pose Estimation

PACE: A Large-Scale Dataset with Pose Annotations in Cluttered Environments

Pseudo-keypoint RKHS Learning for Self-supervised 6DoF Pose Estimation

SAM-6D: Segment Anything Model Meets Zero-Shot 6D Object Pose Estimation

Confronting Ambiguity in 6D Object Pose Estimation via Score-Based Diffusion on SE(3)

ZS6D: Zero-Shot 6D Object Pose Estimation Using Vision Transformers

MegaPose: 6D Pose Estimation of Novel Objects via Render & Compare

GDR-Net: Geometry-Guided Direct Regression Network for Monocular 6D Object Pose Estimation

CosyPose: Consistent Multi-view Multi-object 6D Pose Estimation

EPOS: Estimating 6D Pose of Objects with Symmetries

Compare related metrics

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