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arxiv: 2606.01545 · v1 · pith:GWZEKW4Q · submitted 2026-06-01 · cs.RO

Hierarchical Object Representation for Spatial Robot Perception: Points, Meshes, and Superquadrics

Ceng Zhang , Wan Su , Mohamed Samshad , Gregory S. Chirikjian , Rajat Talak This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 reserved 2026-06-28 14:50 UTCgrok-4.3pith:GWZEKW4Qrecord.jsonopen to challenge →

Figure 1
Figure 1. Figure 1: Hierarchical Object Representation. (a) Our object representation is composed of four layers: Layer 1 (point cloud), Layer 2 (dense 3D mesh), Layer 3 (Superquadric), and Layer 4 (Inflated Superquadric). (b) Layer 1 (point cloud) is obtained by aggre￾gating object point cloud trackied from… reproduced from arXiv: 2606.01545
classification cs.RO
keywords hierarchical object representationsuperquadrics3D scene graphsRGB-D perceptionmap alignmentcollision checkingrobot navigationobject reconstruction
0
0 comments X

The pith

A four-layer hierarchy from RGB-D data to superquadrics supports high-fidelity reconstruction, map alignment, and analytical collision checking.

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

The paper introduces a hierarchical object representation organized into four layers that progressively abstract raw sensor data into point clouds, dense 3D meshes, and superquadric analytical primitives. This structure targets high-fidelity object-level reconstruction, robust re-localization via map alignment, and efficient collision checking for robot navigation in cluttered spaces. The authors build a pipeline from RGB-D image streams and validate it on indoor and outdoor real-world datasets, including demonstrations of improved map alignment over the ROMAN baseline.

Core claim

The representation is structurally organized into four distinct layers, progressively abstracting the scene from raw sensor data to dense 3D meshes to analytical primitives such as superquadrics, which provide a sparse and analytical representation for object geometry. A pipeline builds this from RGB-D streams captured by a robot and is shown to work in real-world open-set scenes indoors and outdoors, with superquadric-based alignment outperforming prior object-based methods.

What carries the argument

Four-layer hierarchical object representation that abstracts from raw RGB-D data through point clouds and meshes to superquadrics as the analytical primitive layer.

If this is right

  • Enables high-fidelity object-level reconstruction directly from RGB-D image streams.
  • Supports robust object-based re-localization and map alignment.
  • Permits efficient analytical collision checking for navigation planning in dense environments.
  • Achieves higher map alignment accuracy than the prior ROMAN method on tested datasets.

Where Pith is reading between the lines

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

  • The layered structure could reduce memory use in large maps by storing sparse superquadrics instead of full meshes at the top level.
  • Analytical superquadric parameters might allow closed-form solutions for certain planning queries that dense representations cannot.
  • Extending the pipeline to fuse semantic labels at the mesh or superquadric layer could link geometry to higher-level scene understanding.

Load-bearing premise

That fitting superquadrics to real-world open-set objects yields representations sufficiently accurate for high-fidelity reconstruction, robust map alignment, and analytical collision checking.

What would settle it

A controlled test in which superquadric fits on open-set objects produce collision-checking errors or map-alignment accuracy below that achieved by bounding-box or point-cloud baselines in the same cluttered scenes.

Figures

Figures reproduced from arXiv: 2606.01545 by Ceng Zhang, Gregory S. Chirikjian, Mohamed Samshad, Rajat Talak, Wan Su.

Figure 2
Figure 2. Figure 2: Hickory: Pipeline for building the hierarchical object representation from posed RGB-D image stream. (a) Layer 1 performs object segmentation and feature-variance￾based best-view selection. (b) Layer 2 reconstructs object meshes and estimates their poses to build an object-level scene. (c) Layer 3 abstracts each object mesh into a compact superquadric representations and shows its applicability in map alig… view at source ↗
Figure 3
Figure 3. Figure 3: Visualization of Dataset for Map Alignment Evaluation: (a) Four indoor scenes in ReplicaCAD [13], featuring distinct object configurations. The two independent camera trajectories for each scene are highlighted in blue and orange. (b) Three outdoor scenes in Kimera-Multi [15], where two robots traverse shared locations either in the same direction (Scenes 1 and 2) or in opposite directions (Scene 3). Note … view at source ↗
Figure 4
Figure 4. Figure 4: As detailed in Table 3, our superquadric-based matching achieves accu [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 4
Figure 4. Figure 4: Visualization of Map alignment Result. (a) Evaluation in simulation on Repli￾caCAD dataset. (b) Demonstration in real world on NUS-CLB scene. the coarse dimensions of mesh bounding boxes, it fundamentally fails to dis￾tinguish geometrically different objects that coincidentally share similar spatial volumes, leading to brutally wrong matching and degrading its performance es￾pecially under scenes with fewe… view at source ↗
Figure 5
Figure 5. Figure 5: Evaluation on Robot Navigation. (a) Simulation evaluation. Comparison of 2D occupancy grid maps generated by different representation methods (left), and the corresponding planned navigation paths given the start and end positions (right). (b) Real-world demonstration. The occupy map by Mesh-OBB representation (red) fails to plan a valid path while our inflated superquadric representation (green) is able f… view at source ↗
read the original abstract

Hierarchical 3D Scene Graphs (3DSG) have emerged as an actionable and scalable representation for long-term autonomy incorporating metric, semantic, and topological information in the scene. However, the question of geometric representation of objects in 3DSG has been overlooked as most methods use simplified geometric models such as partial point clouds or 3D bounding boxes. In this work, we introduce a hierarchical object representation that can be leveraged for high-fidelity object-level reconstruction, object-based robust re-localization or map alignment, and efficient and analytical collision checking for safe robot navigation planning in dense and cluttered environments. The representation is structurally organized into four distinct layers, progressively abstracting the scene from raw sensor data to dense 3D meshes to analytical primitives such as superquadrics, which provide a sparse and analytical representation for object geometry. We develop a pipeline that builds the hierarchical object representation from RGB-D image stream captured by a robot, and demonstrate its working in real-world open-set object scenes in both indoor and outdoor environments. Extensive experiments across diverse datasets including HOPE, ReplicaCAD, Kimera-Multi, and NUS Campus Dataset collected using Unitree B2 Robot validate our pipeline in both indoor and outdoor environments. We show that our superquadric-based map alignment method outperforms the current state-of-the-art object based map alignment method ROMAN. Our code can be found at https://github.com/perceptica-robotics/Hickory.

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 / 2 minor

Summary. The paper introduces a four-layer hierarchical object representation for 3D scene graphs in robotics: raw RGB-D points, dense meshes, and analytical superquadric primitives. A pipeline constructs this representation from robot-captured RGB-D streams and is evaluated on HOPE, ReplicaCAD, Kimera-Multi, and NUS Campus datasets (indoor/outdoor), claiming utility for high-fidelity reconstruction, robust object-based map alignment (outperforming ROMAN), and analytical collision checking, with code released at the provided GitHub link.

Significance. If the superquadric approximations prove sufficiently accurate for the claimed tasks, the hierarchy could provide a useful sparse, analytical alternative to point clouds or bounding boxes for object-level long-term autonomy. The open-source code release supports reproducibility and is a clear strength.

major comments (2)
  1. [Abstract; experimental validation (datasets HOPE, ReplicaCAD, Kimera-Multi, NUS Campus)] Abstract and experimental validation sections: the central claims of high-fidelity reconstruction, robust map alignment, and analytical collision checking rest on superquadric fitting yielding representations accurate enough for these uses, yet no quantitative fitting metrics (Hausdorff distance, volume error, surface deviation, or similar) against ground-truth meshes are reported for the open-set objects across the four datasets. Without these, it is impossible to determine whether approximation residuals remain within tolerance relative to sensor noise or object scale.
  2. [Map alignment experiments] Method and results on map alignment: the reported outperformance over ROMAN is stated without accompanying superquadric-specific error analysis, ablation on fitting parameters, or statistical details (e.g., variance across runs or object categories), which is load-bearing for the claim that the analytic layer enables robust re-localization.
minor comments (2)
  1. [Introduction] Notation for the four layers could be made more consistent when first introduced to aid readability.
  2. [Figure 1] The pipeline diagram would benefit from explicit arrows indicating data flow between layers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive comments. We agree that the manuscript would benefit from additional quantitative validation of the superquadric fitting accuracy and more detailed analysis of the map alignment results. Below we respond point-by-point and indicate the revisions we will make.

read point-by-point responses

  1. Referee: Abstract and experimental validation sections: the central claims of high-fidelity reconstruction, robust map alignment, and analytical collision checking rest on superquadric fitting yielding representations accurate enough for these uses, yet no quantitative fitting metrics (Hausdorff distance, volume error, surface deviation, or similar) against ground-truth meshes are reported for the open-set objects across the four datasets. Without these, it is impossible to determine whether approximation residuals remain within tolerance relative to sensor noise or object scale.

    Authors: We agree that explicit quantitative fitting metrics are needed to substantiate the accuracy claims for the superquadric layer. The original submission prioritized demonstrating the end-to-end pipeline and its robotics applications over detailed per-object fitting error analysis. In the revised manuscript we will add a new subsection under Experiments that reports Hausdorff distance, volume error, and mean surface deviation for superquadric fits against ground-truth meshes on ReplicaCAD and HOPE. For NUS Campus and Kimera-Multi we will report fitting residuals and compare them to sensor noise levels. These additions will allow readers to assess whether approximation errors remain within acceptable bounds. revision: yes

  2. Referee: Method and results on map alignment: the reported outperformance over ROMAN is stated without accompanying superquadric-specific error analysis, ablation on fitting parameters, or statistical details (e.g., variance across runs or object categories), which is load-bearing for the claim that the analytic layer enables robust re-localization.

    Authors: The map alignment section currently shows aggregate success rates and pose errors comparing our superquadric method to ROMAN. We acknowledge the lack of ablations and statistical breakdowns. In revision we will expand the results to include (i) an ablation on key fitting parameters (point sampling density, optimization iterations), (ii) standard deviation across repeated runs, and (iii) performance stratified by object category on the Kimera-Multi and NUS Campus sequences. These additions will strengthen the evidence that the analytic layer contributes to robust re-localization. revision: yes

Circularity Check

0 steps flagged

No circularity: pipeline and experiments are self-contained

full rationale

The paper presents an engineering pipeline for building a four-layer hierarchical object representation (points → meshes → superquadrics) from RGB-D streams and validates it via experiments on HOPE, ReplicaCAD, Kimera-Multi, and NUS Campus datasets, including a comparison showing outperformance versus ROMAN on map alignment. No equations, fitted parameters, or predictions are defined in terms of themselves; no self-citations are invoked as load-bearing uniqueness theorems; and no ansatz or renaming of known results is presented as a derivation. The central claims rest on described implementation and empirical results rather than any reduction to prior inputs by construction. This is the expected non-finding for a systems paper whose value is in the implemented pipeline and reported comparisons.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; superquadrics are referenced as known analytical primitives rather than newly postulated.

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discussion (0)

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