pith. sign in

arxiv: 2605.16779 · v1 · pith:65H2OCJHnew · submitted 2026-05-16 · 💻 cs.CV · cs.AI

A Holistic Method for Superquadric Fitting Using Unsupervised Clustering Analysis

Mingyang Zhao , Sipu Ruan , Xiaohong Jia This is my paper

Pith reviewed 2026-05-19 21:38 UTC · model grok-4.3

classification 💻 cs.CV cs.AI
keywords superquadric fittingpoint cloudunsupervised clusteringshape modelingnoise robustnessdeformable shapesgeometric fittingorthogonal distance
0
0 comments X

The pith

Superquadric fitting to noisy point clouds is reframed as unsupervised clustering where surface samples serve as dynamic centroids and input points as members.

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

This paper redefines superquadric fitting as an unsupervised clustering task to handle noise and outliers in point clouds. Samples drawn from the candidate superquadric surface act as clustering centroids while the observed points act as members. Updating the centroid locations during clustering directly optimizes the underlying superquadric parameters, creating a direct proxy between clustering dynamics and geometric fitting. The approach derives a relationship that replaces explicit surface sampling with orthogonal-distance computations and supplies closed-form expressions for membership degrees and covariance matrices.

Core claim

The paper claims that treating point-cloud data as clustering members and potential superquadric surface samples as centroids turns the clustering process with dynamic centroid updates into a direct proxy for optimizing superquadric parameters. This link unifies rigid and deformable fitting, removes the need for time-consuming surface sampling by relating pairwise centroid-member distances to orthogonal distances, supplies closed-form solutions for the fuzzy membership vector and covariance matrix, and yields a provably convergent procedure that escapes local minima through increased objective convexity.

What carries the argument

Unsupervised clustering formulation in which point-cloud points are members and superquadric surface samples are centroids, so that centroid-location updates serve as the mechanism for superquadric parameter optimization.

If this is right

  • Both rigid and deformable superquadrics are fit inside a single framework.
  • Explicit surface sampling is replaced by a closed-form relation to orthogonal distances.
  • Fuzzy membership degrees and covariance matrices admit closed-form updates, enabling fast iterations.
  • The objective function gains convexity, allowing the optimizer to escape some local minima.
  • A convergence certificate guarantees stability of the iterative process.

Where Pith is reading between the lines

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

  • The same clustering-to-fitting reduction could be tested on other parametric primitives such as superellipsoids or generalized cylinders.
  • Avoiding surface sampling may improve scalability for very large point clouds encountered in robotics or autonomous driving.
  • The explicit link to clustering dynamics opens the possibility of importing robust clustering variants to further improve outlier rejection.
  • Real-time implementations could be evaluated on streaming depth data to check whether the closed-form updates support online shape tracking.

Load-bearing premise

The derived mapping from pairwise centroid-member computations to orthogonal distances accurately captures the fitting objective without introducing approximation errors that would degrade parameter recovery.

What would settle it

Generate synthetic superquadric point clouds with controlled Gaussian noise and outliers, run the clustering-based fitter, and compare recovered parameters against ground truth; if the mean parameter error exceeds that of established surface-sampling methods by a large margin, the central equivalence claim is falsified.

Figures

Figures reproduced from arXiv: 2605.16779 by Mingyang Zhao, Sipu Ruan, Xiaohong Jia.

Figure 1
Figure 1. Figure 1: Gallery of superquadrics. Left: Rigid superquadrics. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Visualization of the fuzzy clustering-inspired su [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Flowchart of the proposed superquadric fitting method. Given an input point cloud, we first perform PCA initialization, followed by iterative optimization, where the fuzzy membership vector u, superquadric parameters Θ, and covariance matrix Σ are updated sequentially. The algorithm outputs the fitted superquadric upon convergence. 4.5.1 Update of u First, we fix Θ and Σ to update u, which reduces to a con… view at source ↗
Figure 4
Figure 4. Figure 4: Qualitative comparisons of rigid superquadric fitting under severe occlusion with a partial ratio of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Quantitative comparisons of accuracy (left) and effi [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Robustness comparison in terms of accuracy (left) and efficiency (right) between RANSAC and the proposed method under increasing outlier ratios. For each outlier ratio, we report the average result over 1,000 random trials, along with the standard deviation (shown as the band￾width). demonstrating superior efficiency across all levels of occlu￾sion [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Qualitative comparisons of deformable superquadric fitting under tapering deformations with occlusion. [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Robustness comparisons of deformable tapering superquadric fitting under noise (top) and outlier (bottom) [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Quantitative comparisons for fitting tapering de [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Qualitative comparisons of deformable superquadric fitting under bending deformations. [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Robustness comparisons against external distur [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Quantitative comparisons of bending deformable [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Qualitative comparisons of deformable superquadric fitting ( [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Visualization of the convergence process for fitting rigid (first two columns), tapered (third column), and bent (last [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Ablation study on the effect of the ui log ui regu￾larization term (weighted by λ) for escaping local minima in superquadric fitting. The mean (left) and median (right) fitting deviations are reported. three initializations to avoid local minima when the PCA result deviates significantly from the correct orientation. 5.9 Adaptation to Type-Specific Fitting While the proposed method is designed for general… view at source ↗
Figure 17
Figure 17. Figure 17: Adaptation of the proposed method to type-specific fitting (spherical and cylindrical primitives) under heavy [PITH_FULL_IMAGE:figures/full_fig_p012_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Adaptation of the proposed method to sphere-specific primitive fitting under various occluded scenarios. [PITH_FULL_IMAGE:figures/full_fig_p012_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Sensitivity analysis of PCA-based initialization. (a) PCA initialization; (b) rotation by 45◦ about the x-axis; (c) rotation by 90◦ about the x-axis; (d) fitting result using PCA initialization; (e) fitting result under 45◦ rotation; (f) fitting result under 45◦ rotation with three different axis initializations; (g) fitting result under 90◦ rotation. To ensure consistently high-quality fitting, we recomm… view at source ↗
Figure 20
Figure 20. Figure 20: Qualitative results on the shape approximation for objects from the ShapeNet dataset [42] by superquadrics. Both rigid and deformable (e.g., the wing of an airplane and the buttstock of a gun) superquadrics are accurately fitted. 5.10 Applications After showing the accuracy and robustness of our algo￾rithm, in this section, we further demonstrate its versatility by applying the proposed superquadric fitti… view at source ↗
Figure 21
Figure 21. Figure 21: Qualitative comparisons with SuperDec on the ShapeNet dataset. The first row presents the initial segmentation [PITH_FULL_IMAGE:figures/full_fig_p014_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Shape approximation using type-specific superquadrics, i.e., ellipsoid primitives (left); application of the proposed method to medical modeling using bent superquadrics (right) [PITH_FULL_IMAGE:figures/full_fig_p015_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Geometry editing based on our proposed su [PITH_FULL_IMAGE:figures/full_fig_p015_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Investigation of the proposed method against structured noise. 12 OPTIMIZATION BOUND SETTING During the optimization of the unknown superquadric parameters Θ, we set different upper and lower bounds (abbreviated as ub and lb) for each parameter to boost the convergence of the interior trust region method. Specifically, (1) for rigid superquadrics, we have lb = [0.0 0.0 0.00001 0.00001 0.00001 -2*pi -2*pi … view at source ↗
read the original abstract

This work presents a novel method for fitting superquadrics to point clouds under the contamination of noise and outliers, which has many applications for shape modeling across diverse fields. Unlike prior approaches that either exclusively focus on fitting rigid or deformable superquadrics, or suffer from robustness and numerical instability issues, our method redefines the problem from a new unsupervised clustering perspective, enabling the holistic fitting of both rigid and deformable superquadrics within a unified framework. Central to our approach is a stable optimization function inspired by unsupervised clustering analysis, where we formulate the point cloud data and samples from the potential parametric surface as clustering members and centroids, respectively. Then, the clustering process with dynamic updates to centroid locations serves as a direct proxy for optimizing superquadric parameters, establishing a principled link between geometric fitting and clustering dynamics. We further derive the relationship between pairwise computations of clustering centroids and clustering members to orthogonal distances, effectively eliminating the need for the time-consuming surface sampling process. Moreover, our formulation provides closed-form analytical solutions for both the fuzzy membership degree vector and the covariance matrix, ensuring efficient iteration optimization and enabling more effective handling of geometric deformations. In addition, we provide a theoretical certificate of convergence analysis and demonstrate that the clustering-inspired fitting method can escape local minima by inherently increasing the convexity of the objective function. The implementation is publicly available at https://github.com/zikai1/SuperquadricFitting.

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

1 major / 2 minor

Summary. The paper proposes a novel unsupervised clustering approach to fit superquadrics to noisy and outlier-contaminated point clouds. It recasts the fitting task by treating input points as cluster members and samples drawn from the parametric superquadric surface as centroids; dynamic centroid updates then serve as a proxy for optimizing the superquadric parameters. The authors claim to derive an exact relationship between pairwise centroid-member distances and orthogonal surface distances that removes any need for explicit surface sampling, supply closed-form expressions for the fuzzy membership vector and covariance matrix, prove convergence, and show that the formulation inherently increases convexity to escape local minima. A public implementation is provided.

Significance. If the claimed exact equivalence between pairwise distances and true orthogonal distances holds without approximation, the method would constitute a meaningful advance: a single, stable framework that unifies rigid and deformable superquadric fitting while improving robustness and eliminating costly surface sampling. The public code release is a clear strength that supports reproducibility and further testing.

major comments (1)
  1. [Derivation of the pairwise-to-orthogonal distance relationship] The central technical claim is that the relationship between pairwise centroid-member computations and orthogonal distances to the superquadric surface is exact and therefore eliminates surface sampling. For an implicit surface F(x; a,b,c,r,s,...) = 1 the orthogonal distance is the length of the shortest vector satisfying the normal condition; this generally requires a nonlinear minimization and does not reduce to a closed-form expression involving only distances to a discrete set of surface points. If the derived relationship is instead an approximation, linearization, or holds only under restrictive assumptions on the exponents or axis ratios, the resulting objective no longer minimizes geometric error and the claimed robustness and convexity benefits become unreliable. This derivation must be shown in full detail (including any intermediate steps or assumptions) before the method can
minor comments (2)
  1. [Abstract] The abstract states that a 'theoretical certificate of convergence analysis' is provided; the manuscript should clarify whether this is a formal proof or an empirical observation supported by the convexity argument.
  2. [Introduction / Method] Notation for the superquadric parameters (a, b, c, r, s, …) and the implicit function F should be introduced consistently at the first appearance and used uniformly thereafter.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and for recognizing the potential significance of the work if the central equivalence holds. We address the major comment on the derivation below and will incorporate additional details in the revision.

read point-by-point responses

  1. Referee: [Derivation of the pairwise-to-orthogonal distance relationship] The central technical claim is that the relationship between pairwise centroid-member computations and orthogonal distances to the superquadric surface is exact and therefore eliminates surface sampling. For an implicit surface F(x; a,b,c,r,s,...) = 1 the orthogonal distance is the length of the shortest vector satisfying the normal condition; this generally requires a nonlinear minimization and does not reduce to a closed-form expression involving only distances to a discrete set of surface points. If the derived relationship is instead an approximation, linearization, or holds only under restrictive assumptions on the exponents or axis ratios, the resulting objective no longer minimizes geometric error and the claimed robustness and convexity benefits become unreliable. This derivation must be shown in full detail (includ

    Authors: We thank the referee for highlighting the need to present this derivation with full rigor. In the manuscript we derive an exact equivalence: by treating surface samples as dynamic centroids constrained to the superquadric parametric form and points as cluster members, the clustering objective becomes mathematically identical to the sum of squared orthogonal distances. The key step is showing that the normal condition for orthogonality is satisfied implicitly through the centroid update rule derived from the superquadric equation, so that the pairwise distance computation equals the true orthogonal distance without approximation or iterative per-point minimization. This identity holds for arbitrary exponents and axis ratios because no linearization is introduced. We agree that the current presentation condenses some algebraic steps. In the revised manuscript we will expand the relevant section with every intermediate equation, the explicit mapping from pairwise to orthogonal distance, and a clear statement of assumptions (standard superquadric parametrization only). This will confirm that geometric error is minimized and that the robustness and convexity claims remain valid. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation chain is self-contained with explicit reformulation and closed-form results

full rationale

The paper redefines superquadric fitting as an unsupervised clustering task by treating point-cloud members and surface samples as centroids, then derives a relationship between pairwise centroid-member distances and orthogonal distances while supplying closed-form expressions for membership vectors and covariance matrices plus a convergence certificate. These steps are presented as explicit derivations within the unified framework rather than reductions to prior fitted parameters or self-citation chains. No load-bearing claim reduces by construction to its own inputs; the method remains independently verifiable via the public implementation and external geometric benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central approach rests on the domain assumption that clustering dynamics can serve as a direct proxy for geometric parameter optimization; no explicit free parameters or invented entities are described in the abstract.

axioms (1)
  • domain assumption Clustering members and centroids can be formulated to directly optimize superquadric parameters via dynamic updates.
    Central to the method as described in the abstract.

pith-pipeline@v0.9.0 · 5782 in / 1099 out tokens · 43931 ms · 2026-05-19T21:38:38.715768+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages · 2 internal anchors

  1. [1]

    Supervised fitting of geometric primitives to 3d point clouds,

    L. Li, M. Sung, A. Dubrovina, L. Yi, and L. J. Guibas, “Supervised fitting of geometric primitives to 3d point clouds,” inProc. IEEE Conf. Comput. Vis. Pattern Recog., pp. 2652–2660, 2019. 1

    work page 2019

  2. [2]

    Error of fit measures for recovering parametric solids,

    A. D. Gross and T. E. Boult, “Error of fit measures for recovering parametric solids,” inProc. IEEE Int. Conf. Comput. Vis., pp. 690– 691, 1988. 1, 2, 5, 7, 9, 18

    work page 1988

  3. [3]

    Superquadrics with ra- tional and irrational symmetry,

    J. Gielis, B. Beirinckx, and E. Bastiaens, “Superquadrics with ra- tional and irrational symmetry,” inProc. ACM Symp. Solid. Model. Appl., pp. 262–265, 2003. 1

    work page 2003

  4. [4]

    Superquadric glyphs for sym- metric second-order tensors,

    T. Schultz and G. L. Kindlmann, “Superquadric glyphs for sym- metric second-order tensors,”IEEE Trans. Vis. Comput. Graph., vol. 16, no. 6, pp. 1595–1604, 2010. 1

    work page 2010

  5. [5]

    3doodle: Compact abstraction of objects with 3d strokes,

    C. Choi, J. Lee, J. Park, and Y. M. Kim, “3doodle: Compact abstraction of objects with 3d strokes,”ACM Trans. Graph., vol. 43, no. 4, pp. 1–13, 2024. 1

    work page 2024

  6. [6]

    Effi- cient path planning in narrow passages for robots with ellipsoidal components,

    S. Ruan, K. L. Poblete, H. Wu, Q. Ma, and G. S. Chirikjian, “Effi- cient path planning in narrow passages for robots with ellipsoidal components,”IEEE Trans. Robot., vol. 39, no. 1, pp. 110–127, 2022. 1

    work page 2022

  7. [7]

    Sq-slam: Monocular semantic slam based on superquadric object representation,

    X. Han and L. Yang, “Sq-slam: Monocular semantic slam based on superquadric object representation,” vol. 109, no. 2, p. 29, 2023. 1

    work page 2023

  8. [8]

    Object-based slam using superquadrics,

    Y. Xing, N. Samano, W. Fan, and A. Calway, “Object-based slam using superquadrics,” inIEEE/RSJ Int. Conf. Intell. Robot. Syst., pp. 10198–10205, 2024. 1

    work page 2024

  9. [9]

    A bayesian approach toward robust multidimensional ellipsoid-specific fitting,

    M. Zhao, X. Jia, L. Ma, Y. Shi, J. Jiang, Q. Li, D.-M. Yan, and T. Huang, “A bayesian approach toward robust multidimensional ellipsoid-specific fitting,”IEEE Trans. Pattern Anal. Mach. Intell.,

    work page

  10. [10]

    Superquadrics revisited: Learning 3d shape parsing beyond cuboids,

    D. Paschalidou, A. O. Ulusoy, and A. Geiger, “Superquadrics revisited: Learning 3d shape parsing beyond cuboids,” inProc. IEEE Conf. Comput. Vis. Pattern Recog., pp. 10344–10353, 2019. 1, 3, 13

    work page 2019

  11. [11]

    Robust and accurate superquadric recovery: A probabilistic approach,

    W. Liu, Y. Wu, S. Ruan, and G. S. Chirikjian, “Robust and accurate superquadric recovery: A probabilistic approach,” inProc. IEEE Conf. Comput. Vis. Pattern Recog., pp. 2676–2685, 2022. 1, 2, 5, 6, 7, 9, 13, 18

    work page 2022

  12. [12]

    Shared latent membership enables joint shape abstraction and segmentation with deformable superquadrics,

    J. Li, H. Wang, J. Tan, and J. Yuan, “Shared latent membership enables joint shape abstraction and segmentation with deformable superquadrics,”IEEE Trans. Image Process., 2024. 1

    work page 2024

  13. [13]

    Superquadrics and angle-preserving transforma- tions,

    A. H. Barr, “Superquadrics and angle-preserving transforma- tions,”IEEE Computer graphics and Applications, vol. 1, no. 01, pp. 11–23, 1981. 2, 3

    work page 1981

  14. [14]

    Three dimensional object representation revisited,

    F. Solina and R. Bajcsy, “Three dimensional object representation revisited,” inProc. IEEE Int. Conf. Comput. Vis., pp. 231–240, 1987. 2

    work page 1987

  15. [15]

    Recovery of parametric models from range images: The case for superquadrics with global deforma- tions,

    F. Solina and R. Bajcsy, “Recovery of parametric models from range images: The case for superquadrics with global deforma- tions,”IEEE Trans. Pattern Anal. Mach. Intell., vol. 12, no. 2, pp. 131– 147, 1990. 2, 7, 9, 18

    work page 1990

  16. [16]

    Experimental comparison of superquadric fitting objec- tive functions,

    Y. Zhang, “Experimental comparison of superquadric fitting objec- tive functions,”Pattern Recogn. Lett., vol. 24, no. 14, pp. 2185–2193,

    work page

  17. [17]

    Robust 3d part extraction from range images with deformable superquadric models,

    Y.-L. Hu and W. G. Wee, “Robust 3d part extraction from range images with deformable superquadric models,” inSignal Process. Sens. Fusion Target Recognit., vol. 2484, pp. 524–535, 1995. 2, 7, 9, 18

    work page 1995

  18. [18]

    Fitting undeformed su- perquadrics to range data: improving model recovery and classifi- cation,

    E. R. Van Dop and P . P . Regtien, “Fitting undeformed su- perquadrics to range data: improving model recovery and classifi- cation,” inProc. IEEE Conf. Comput. Vis. Pattern Recog., pp. 396–401,

    work page

  19. [19]

    Revisiting superquadric fitting: A numerically stable formulation,

    N. Vaskevicius and A. Birk, “Revisiting superquadric fitting: A numerically stable formulation,”IEEE Trans. Pattern Anal. Mach. Intell., vol. 41, no. 1, pp. 220–233, 2017. 2, 5, 6, 7, 18

    work page 2017

  20. [20]

    Segmentation and recovery of su- perquadric models using convolutional neural networks,

    J. ˇSircelj, T. Oblak, K. Grm, U. Petkovi ´c, A. Jakli ˇc, P . Peer, V . ˇStruc, and F. Solina, “Segmentation and recovery of su- perquadric models using convolutional neural networks,”arXiv preprint arXiv:2001.10504, 2020. 2

    work page arXiv 2001

  21. [21]

    Learn- ing to predict superquadric parameters from depth images with explicit and implicit supervision,

    T. Oblak, J. ˇSircelj, V .ˇStruc, P . Peer, F. Solina, and A. Jakliˇc, “Learn- ing to predict superquadric parameters from depth images with explicit and implicit supervision,”IEEE Access, vol. 9, pp. 1087– 1102, 2020. 2

    work page 2020

  22. [22]

    Dsqnet: a deformable model-based supervised learning algorithm for grasping unknown occluded objects,

    S. Kim, T. Ahn, Y. Lee, J. Kim, M. Y. Wang, and F. C. Park, “Dsqnet: a deformable model-based supervised learning algorithm for grasping unknown occluded objects,”IEEE Trans. Autom. Sci. Eng., vol. 20, no. 3, pp. 1721–1734, 2022. 2

    work page 2022

  23. [23]

    Superquadrics for segment- ing and modeling range data,

    A. Leonardis, A. Jaklic, and F. Solina, “Superquadrics for segment- ing and modeling range data,”IEEE Trans. Pattern Anal. Mach. Intell., vol. 19, no. 11, pp. 1289–1295, 1997. 3

    work page 1997

  24. [24]

    Iterative superquadric recomposition of 3d objects from multiple views,

    S. Alaniz, M. Mancini, and Z. Akata, “Iterative superquadric recomposition of 3d objects from multiple views,” inProc. IEEE Conf. Comput. Vis. Pattern Recog., pp. 18013–18023, 2023. 3

    work page 2023

  25. [25]

    Volumetric representation of human body parts using superquadrics,

    R. Hachiuma and H. Saito, “Volumetric representation of human body parts using superquadrics,” inIEEE Int. Symp. Mixed. Aug- mented. Real. Adjunct., pp. 187–188, 2019. 3

    work page 2019

  26. [26]

    Primitive-based shape abstraction via nonparametric bayesian inference,

    Y. Wu, W. Liu, S. Ruan, and G. S. Chirikjian, “Primitive-based shape abstraction via nonparametric bayesian inference,” inProc. Eur. Conf. Comput. Vis., pp. 479–495, 2022. 3, 13, 14 IEEE TRANSACTIONS ON PATTERN ANAL YSIS AND MACHINE INTELLIGENCE 17

    work page 2022

  27. [27]

    Global and local deformations of solid primitives,

    A. H. Barr, “Global and local deformations of solid primitives,” ACM Trans. Graph., vol. 18, no. 3, pp. 21–30, 1984. 3, 4

    work page 1984

  28. [28]

    Fuzzy clustering with a fuzzy covariance matrix,

    D. E. Gustafson and W. C. Kessel, “Fuzzy clustering with a fuzzy covariance matrix,” inIEEE Conf. Decis. Control., pp. 761–766, 1979. 4

    work page 1979

  29. [29]

    l 2,p-norm and mahalanobis distance based robust fuzzy c-means,

    Q. Chen, F. Nie, W. Yu, and X. Li, “l 2,p-norm and mahalanobis distance based robust fuzzy c-means,”IEEE Trans Fuzzy Syst, 2023. 4

    work page 2023

  30. [30]

    Miyamoto, H

    S. Miyamoto, H. Ichihashi, K. Honda, and H. Ichihashi,Algorithms for fuzzy clustering, vol. 10. 2008. 4

    work page 2008

  31. [31]

    Non-linear minimax optimiza- tion as a sequence of least p th optimization with finite values of p,

    C. Charalambous and J. Bandler, “Non-linear minimax optimiza- tion as a sequence of least p th optimization with finite values of p,”Int. J. Syst. Sci., vol. 7, no. 4, pp. 377–391, 1976. 5

    work page 1976

  32. [32]

    Statistical approaches to feature-based object recognition,

    W. M. Wells III, “Statistical approaches to feature-based object recognition,”Int. J. Comput. Vis., vol. 21, no. 1, pp. 63–98, 1997. 6

    work page 1997

  33. [33]

    An interior trust region approach for nonlinear minimization subject to bounds,

    T. F. Coleman and Y. Li, “An interior trust region approach for nonlinear minimization subject to bounds,”SIAM J. Optimiz., vol. 6, no. 2, pp. 418–445, 1996. 6

    work page 1996

  34. [34]

    The levenberg-marquardt algorithm: implementation and theory,

    J. J. Mor ´e, “The levenberg-marquardt algorithm: implementation and theory,” inNumer. Anal. : Proc. Bienn. Conf. 1977, pp. 105–116,

    work page 1977

  35. [35]

    Joint alignment of multiple point sets with batch and incremental expectation-maximization,

    G. D. Evangelidis and R. Horaud, “Joint alignment of multiple point sets with batch and incremental expectation-maximization,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 40, no. 6, pp. 1397–1410,

    work page

  36. [36]

    Convergence properties of a class of minimiza- tion algorithms,

    M. J. D. Powell, “Convergence properties of a class of minimiza- tion algorithms,” inNonlinear Program. 2, pp. 1–27, 1975. 7

    work page 1975

  37. [37]

    A family of trust- region-based algorithms for unconstrained minimization with strong global convergence properties,

    G. A. Shultz, R. B. Schnabel, and R. H. Byrd, “A family of trust- region-based algorithms for unconstrained minimization with strong global convergence properties,”SIAM J. Numer. Anal., vol. 22, no. 1, pp. 47–67, 1985. 7

    work page 1985

  38. [38]

    3d human body pose estimation by superquadrics.,

    I. Afanasyev, M. Lunardelli, N. Biasi, L. Baglivo, M. Tavernini, F. Setti, M. De Cecco,et al., “3d human body pose estimation by superquadrics.,” inInt. Conf. Comput. Vis. Theory App., pp. 294–302,

    work page

  39. [39]

    The kit object models database: An object model database for object recognition, lo- calization and manipulation in service robotics,

    A. Kasper, Z. Xue, and R. Dillmann, “The kit object models database: An object model database for object recognition, lo- calization and manipulation in service robotics,”Int. J. Rob. Res., vol. 31, no. 8, pp. 927–934, 2012. 9

    work page 2012

  40. [40]

    The MATLAB dataset. [Online]. Available

    “The MATLAB dataset. [Online]. Available.” https://ww2.mathworks.cn/help/vision/ref/pcfitcylinder.html,

    work page

  41. [41]

    Mlesac: A new robust estimator with application to estimating image geometry,

    P . H. Torr and A. Zisserman, “Mlesac: A new robust estimator with application to estimating image geometry,”Comput. Vis. Image. Und., vol. 78, no. 1, pp. 138–156, 2000. 12

    work page 2000

  42. [42]

    ShapeNet: An Information-Rich 3D Model Repository

    A. X. Chang, T. Funkhouser, L. Guibas, P . Hanrahan, Q. Huang, Z. Li, S. Savarese, M. Savva, S. Song, H. Su,et al., “Shapenet: An information-rich 3d model repository,”arXiv preprint arXiv:1512.03012, 2015. 13

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  43. [43]

    A Large Dataset of Object Scans

    S. Choi, Q.-Y. Zhou, S. Miller, and V . Koltun, “A large dataset of object scans,”arXiv preprint arXiv:1602.02481, 2016. 12

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  44. [44]

    Recognition-by-components: a theory of human image understanding.,

    I. Biederman, “Recognition-by-components: a theory of human image understanding.,”Psychol. Rev., vol. 94, no. 2, p. 115, 1987. 13

    work page 1987

  45. [45]

    Edelman,Representation and recognition in vision

    S. Edelman,Representation and recognition in vision. 1999. 13

    work page 1999

  46. [46]

    Core systems in human cognition,

    K. D. Kinzler and E. S. Spelke, “Core systems in human cognition,” Prog. Brain Res., vol. 164, pp. 257–264, 2007. 13

    work page 2007

  47. [47]

    arXiv preprint arXiv:2504.00992 , year=

    E. Fedele, B. Sun, L. Guibas, M. Pollefeys, and F. Engelmann, “Su- perdec: 3d scene decomposition with superquadric primitives,” arXiv preprint arXiv:2504.00992, 2025. 13

    work page arXiv 2025

  48. [48]

    Unsupervised learning for cuboid shape abstraction via joint segmentation from point clouds,

    K. Yang and X. Chen, “Unsupervised learning for cuboid shape abstraction via joint segmentation from point clouds,”ACM Trans. Graph., vol. 40, no. 4, pp. 1–11, 2021. 13

    work page 2021

  49. [49]

    Continuous collision detection for two moving elliptic disks,

    Y.-K. Choi, W. Wang, Y. Liu, and M.-S. Kim, “Continuous collision detection for two moving elliptic disks,”IEEE Trans. Robot., vol. 22, no. 2, pp. 213–224, 2006. 14

    work page 2006

  50. [50]

    Velocity obstacle based local collision avoidance for a holonomic elliptic robot,

    B. H. Lee, J. D. Jeon, and J. H. Oh, “Velocity obstacle based local collision avoidance for a holonomic elliptic robot,”Auton. Robot., vol. 41, no. 6, pp. 1347–1363, 2017. 14

    work page 2017

  51. [51]

    FAUST: Dataset and evaluation for 3D mesh registration,

    F. Bogo, J. Romero, M. Loper, and M. J. Black, “FAUST: Dataset and evaluation for 3D mesh registration,” inProc. IEEE Conf. Comput. Vis. Pattern Recog., 2014. 14

    work page 2014

  52. [52]

    The Grabcad 3D Modeling Repository. [Online]. Available

    T. P . Cahill, “The Grabcad 3D Modeling Repository. [Online]. Available.” https://grabcad.com/library/blood-vessel-1, 2025. 14

    work page 2025

  53. [53]

    Robust 3-D modeling of vasculature imagery using superellipsoids,

    J. A. Tyrrell, E. di Tomaso, D. Fuja, R. Tong, K. Kozak, R. K. Jain, and B. Roysam, “Robust 3-D modeling of vasculature imagery using superellipsoids,”IEEE Trans. Med. Imaging., vol. 26, no. 2, pp. 223–237, 2007. 14

    work page 2007

  54. [54]

    Hastie, R

    T. Hastie, R. Tibshirani, J. H. Friedman, and J. H. Friedman,The elements of statistical learning: data mining, inference, and prediction, vol. 2. 2009. 15 IEEE TRANSACTIONS ON PATTERN ANAL YSIS AND MACHINE INTELLIGENCE 18 SUPPLEMENTARYMATERIAL Abstract—In this supplementary material, we provide additional content to support our paper. Concretely, the fol...

    work page 2009