KASALv2: Fully Automatic 3D Rotational Symmetry Classification and Axis Localization

Mengxin Zhang; Yulin Wang; Chen Luo; Yongzhe Li; Yijun Zhou

cs.CVOct 7, 2026

KASALv2: Fully Automatic 3D Rotational Symmetry Classification and Axis Localization

Authors: Mengxin Zhang, Yulin Wang, Chen Luo, Yongzhe Li, Yijun Zhou

Organizations: School of Mechanical Engineering, Southeast University Nanjing, China

Abstract

Rotational symmetry is an important prior in 6D pose estimation, improving pose accuracy and supporting symmetry-aware evaluation. However, current symmetry annotations for 3D objects remain largely manual or semi-automatic, often requiring predefined types or orders, which limits scalability. This work introduces a fully automatic, reference-free framework for symmetry-type classification, rotational-order identification, and full-axis localization across all eight canonical 3D rotational symmetry types. The method localizes a dominant high-order axis, infers its rotational order through self-consistency analysis, and reconstructs the complete symmetry structure under a hierarchy-guided formulation. A texture-aware extension further models appearance-induced reductions in rotational order while preserving axis orientations. Experiments on idealized and real-world datasets demonstrate strong accuracy and generalization, achieving 94.75% accuracy on 438 symmetric objects in GSO. Training FoundationPose with these priors improves accuracy by up to 0.9% across five BOP datasets, showing that automatically estimated rotational priors improve downstream 6D pose estimation. Code is available at https://github.com/WangYuLin-SEU/KASAL.

Figures & tables

Figure 1 : Comparative landscape of rotational symmetry analysis methods categorized by geometric reference dependency and task capability. The proposed method supports all eight canonical types without geometric references and handles texture-induced symmetries.

Figure 2 : The pipeline integrates a Geometric Degeneration Hierarchy (GDH) and an operational framework. The GDH establishes the hierarchical taxonomy of 3D rotational symmetry, while the operational framework implements it. Given a 3D object of unknown symmetry, the system first localizes a dominant high-order axis and infers its rotational order through self-consistency optimization. Based on this order, candidate symmetry types are derived and verified by checking whether a secondary axis satisfies the corresponding geometric constraints. This hierarchical verification yields type classification and reconstruction of all canonical axes under the identified geometric relations. Finally, the texture-symmetry module refines the classification by modeling appearance-induced degradation, covering reduced, invariant, and discretized texture cases.

Figure 3 : Aggregated alignment-loss distribution on the unit sphere. Low-loss regions (orange) cluster around the true high-order axis, illustrating the self-consistent nature of high-order symmetries.

Figure 4 : Effect of the spherical-cap radius

r

on sampling performance. Dashed curves indicate fitted trends for total accuracy (blue) and normalized alignment error

e_{\text{ADI}}/d

(orange). The optimal configuration appears near

r=10^{\circ}

Method	Dataset		Category Statistics			Dataset-Level Performance
	Name	Object Type	Count	Errors	$acc_{T}$	$acc_{t}$	$acc_{o}$	$acc_{T}$	time	$e_{\mathrm{ADI}}/d$ (ours / Wang et al. [ 26 ] )
BOP (original)	BOP [ 27 ]	${C}_{\infty}$	7	0	100.00%	80.00%	100.00%	80.00%	—	—
		${D}_{\infty}$	3	0	100.00%
		$C_{n}$	35	9	74.29%
		$D_{n}$	5	1	80.00%
KASALv2(ours)	BOP [ 27 ]	${C}_{\infty}$	7	0	100.00%	92.00%	91.30%	84.00%	1.61	0.00256/0.00290

Table 2 : Comprehensive evaluation of symmetry classification and axis localization across datasets. DSRSTO tex : texture subset.

Dataset	w/ KASALv2 mean (range)	w/o KASALv2 mean (range)	Diff.
LM-O	71.9 (71.7–72.0)	71.6 (71.5–71.8)	+0.3
IC-BIN	64.7 (64.4–65.3)	63.8 (63.2–64.4)	+0.9
YCB-V	87.7 (87.6–87.9)	87.6 (87.5–87.8)	+0.1
ITODD	65.8 (65.1–66.4)	65.0 (64.9–65.2)	+0.8
T-LESS	59.3 (58.6–60.1)	58.8 (58.3–59.3)	+0.5

Table 3 : FoundationPose with and without KASALv2 symmetry priors on five BOP datasets. Results are reported as mean (range) over five checkpoints from the same training run (seed 0).

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Category-Level Object Pose Estimation Symmetry Geometric Deep Learning Objects Cosine Similarity

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Symmetric objects are common in daily life and industry, yet their inherent orientation ambiguities that impede the training of deep learning networks for pose estimation are rarely discussed in the literature. To cope with these ambiguities, existing solutions typically require the design of specific loss functions and network architectures or resort to symmetry-invariant evaluation metrics. In contrast, we focus on the numeric representation of the rotation itself, modifying trigonometric identities with the degrees of symmetry derived from the objects' shapes. We use our representation, SARR, to obtain canonic (symmetry-resolved) poses for the symmetric objects in two popular 6D pose estimation datasets, T-LESS and ITODD, where SARR is unique and continuous w.r.t. the visual appearance. This allows us to use a standard CNN for 3D orientation estimation whose performance is evaluated with the symmetry-sensitive cosine distance

\text{AR}_{\text{C}}

. Our networks outperform the state of the art using

\text{AR}_{\text{C}}

and achieve satisfactory performance when using conventional symmetry-invariant measures. Our method does not require any 3D models but only depth, or, as part of an additional experiment, texture-less RGB/grayscale images as input. We also show that networks trained on SARR outperform the same networks trained on rotation matrices, Euler angles, quaternions, standard trigonometrics or the recently popular 6d representation -- even in inference scenarios where no prior knowledge of the objects' symmetry properties is available. Code and a visualization toolkit are available at https://github.com/akriegler/SARR .

Abstract

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