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arxiv: 2604.18208 · v1 · submitted 2026-04-20 · 💻 cs.CV · math.GT

Recognition: unknown

Towards Symmetry-sensitive Pose Estimation: A Rotation Representation for Symmetric Object Classes

Andreas Kriegler, Csaba Beleznai, Margrit Gelautz

Authors on Pith no claims yet

Pith reviewed 2026-05-10 04:50 UTC · model grok-4.3

classification 💻 cs.CV math.GT
keywords pose estimationsymmetric objectsrotation representationSARR6D posedeep learningcomputer visionsymmetry resolution
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The pith

SARR rotation representation resolves orientation ambiguities for symmetric objects using only a standard CNN.

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

The paper shows that symmetric objects create repeated orientations that break the training of ordinary pose networks because the same visual input can map to multiple valid rotations. To fix this at the label level, the authors adjust basic trigonometric encodings of rotation by each object's known symmetry order, producing a representation called SARR that stays unique and continuous as the object turns. When these adjusted labels train a plain convolutional network on depth or textureless images from T-LESS and ITODD, the network learns consistent mappings without extra loss terms or architecture changes. The resulting predictions beat those from rotation matrices, quaternions, Euler angles, plain trig, and the 6D format on symmetry-sensitive evaluation, and they remain competitive under conventional symmetry-invariant scores.

Core claim

By scaling trigonometric identities with the degrees of symmetry taken from each object's shape, SARR yields canonic poses that are both unique and continuous with respect to visual appearance. This property lets a standard CNN estimate 3D orientation directly from depth (or textureless RGB) input on the T-LESS and ITODD datasets, producing higher accuracy under the symmetry-sensitive cosine distance AR_C than networks trained on any of the compared rotation formats, even when symmetry information is withheld at inference time.

What carries the argument

SARR, the symmetry-adjusted rotation representation formed by multiplying trigonometric functions of rotation angles by the object's symmetry degree to enforce uniqueness and continuity relative to appearance.

If this is right

  • A conventional CNN trained on SARR labels produces canonic poses for symmetric objects without any symmetry-aware loss or network redesign.
  • The same network outperforms identical models trained on rotation matrices, quaternions, Euler angles, standard trig, or 6D representations under symmetry-sensitive metrics.
  • Performance remains competitive when measured with conventional symmetry-invariant metrics.
  • The method works from depth images or textureless RGB/grayscale alone and requires no 3D object models.
  • The advantage persists even when the network receives no symmetry information during inference.

Where Pith is reading between the lines

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

  • The same symmetry-adjusted encoding could be precomputed for new object classes by analyzing their 3D shapes once, then reused across multiple datasets.
  • Rotation label design may matter more than loss engineering for tasks where visual appearance repeats under rotation.
  • Extending SARR to full 6D pose (translation plus rotation) would require only pairing it with an existing translation head.
  • Because the representation is continuous, it could support regression-based pose refinement pipelines that currently struggle with symmetry discontinuities.

Load-bearing premise

That multiplying trigonometric rotation terms by an object's symmetry degree produces encodings that stay one-to-one and smooth with visual changes, so a standard network can learn the mapping without further modifications.

What would settle it

Train identical CNNs on T-LESS symmetric objects using SARR labels versus 6D rotation labels, then evaluate both on the symmetry-sensitive AR_C metric without supplying symmetry priors at test time; if SARR training does not yield higher scores, the central claim does not hold.

read the original abstract

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 .

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 proposes SARR, a rotation representation for symmetric objects constructed by modifying trigonometric identities with per-class symmetry orders derived from object shapes. It claims SARR produces unique, continuous canonic poses w.r.t. visual appearance for objects in T-LESS and ITODD, allowing standard CNNs (no architectural changes) to be trained on depth or textureless images for 3D orientation estimation. Networks trained on SARR outperform those using rotation matrices, Euler angles, quaternions, standard trigonometrics, or 6D representations on the symmetry-sensitive AR_C metric and achieve satisfactory results on conventional symmetry-invariant metrics, even at inference without symmetry knowledge. Code and a visualization toolkit are released.

Significance. If the uniqueness and continuity properties are rigorously established and the reported gains hold under controlled experiments, SARR would offer a practical, representation-level solution to symmetry ambiguities in pose estimation without custom losses or architectures. This could simplify pipelines for industrial and everyday symmetric objects. The public code release and focus on depth-only or textureless inputs are positive for reproducibility and applicability.

major comments (2)
  1. [Abstract] Abstract and method description: the central claim that SARR is 'unique and continuous w.r.t. the visual appearance' (allowing standard CNNs to learn consistent image-to-pose mappings) rests on the trigonometric modification using symmetry degrees, yet no explicit equation for SARR, no proof of injectivity within each symmetry class, and no verification that the function has no discontinuities at symmetry boundaries are provided. This directly affects whether outperformance on AR_C follows from the representation alone.
  2. [Method] The assertion that canonic poses are obtained 'directly from this construction' rather than fitted to performance metrics is stated, but without the concrete definition of the modified sin/cos (e.g., scaling by symmetry order n) or demonstration that it resolves all visual ambiguities to one pose per appearance, the comparison to baselines (rotation matrices, 6D, etc.) cannot be fully evaluated for causality.
minor comments (2)
  1. [Abstract] The abstract states 'satisfactory performance' on conventional metrics but does not provide quantitative values or direct comparison tables in the summary; including these would improve clarity.
  2. The paper mentions evaluation with AR_C but does not specify the exact formulation or baseline implementations for the competing representations in the visible text; a dedicated section or table with implementation details would aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. The comments correctly identify opportunities to improve the explicitness of the SARR definition and its theoretical properties. We address each point below and will incorporate the requested clarifications in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract and method description: the central claim that SARR is 'unique and continuous w.r.t. the visual appearance' (allowing standard CNNs to learn consistent image-to-pose mappings) rests on the trigonometric modification using symmetry degrees, yet no explicit equation for SARR, no proof of injectivity within each symmetry class, and no verification that the function has no discontinuities at symmetry boundaries are provided. This directly affects whether outperformance on AR_C follows from the representation alone.

    Authors: We agree that greater explicitness is needed. The SARR construction modifies the standard trigonometric encoding by scaling the angle argument with the per-class symmetry order n (derived directly from the object's rotational symmetry in the dataset). In the revision we will place the explicit equation SARR(θ, n) = [sin(nθ), cos(nθ)] (or the precise two-dimensional form used) in both the abstract and the opening of the method section. We will also add a concise appendix containing (i) a proof that the mapping is injective for rotations within each symmetry class and (ii) a verification that the resulting function remains continuous at the symmetry boundaries because it is periodic with period 2π/n. These additions will make the causal link to the AR_C gains more transparent. revision: yes

  2. Referee: [Method] The assertion that canonic poses are obtained 'directly from this construction' rather than fitted to performance metrics is stated, but without the concrete definition of the modified sin/cos (e.g., scaling by symmetry order n) or demonstration that it resolves all visual ambiguities to one pose per appearance, the comparison to baselines (rotation matrices, 6D, etc.) cannot be fully evaluated for causality.

    Authors: The canonic poses are obtained strictly from the symmetry orders present in the T-LESS and ITODD object annotations; no metric-driven fitting is performed. To address the referee's concern we will expand the method section with the exact modified trigonometric definition, including how n is computed for each object class. We will also add a short illustrative subsection (with accompanying figures) that walks through several visual ambiguities for representative objects and shows that they all collapse to the identical SARR vector. This material will allow readers to evaluate the representation's properties independently of the empirical comparisons. revision: yes

Circularity Check

0 steps flagged

SARR is a direct mathematical construction; no load-bearing reduction to fits or self-citations

full rationale

The paper constructs SARR by modifying trigonometric identities with symmetry orders derived from object shapes, then asserts uniqueness and continuity w.r.t. visual appearance to justify using a standard CNN. This is a definitional step, not a self-referential loop. Outperformance claims are empirical (networks trained on SARR vs. other representations) and evaluated on T-LESS/ITODD with AR_C, without the target metric being used to define or fit the representation itself. No self-citation chain is load-bearing for the core uniqueness/continuity claim, and no parameter is fitted then renamed as a prediction. Minor self-citation risk at most, but central derivation remains independent.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the mathematical validity of adjusting trigonometric identities by symmetry orders to resolve ambiguities into a single canonical pose that is continuous with visual appearance. No numerical parameters are fitted to performance data; the symmetry orders are taken as given from object geometry.

axioms (1)
  • domain assumption Trigonometric identities can be modified by scaling angles with the object's degree of symmetry to produce a unique continuous representation matching visual appearance.
    This is the core construction of SARR invoked to obtain canonic poses for the datasets.
invented entities (1)
  • SARR rotation representation no independent evidence
    purpose: To encode 3D orientations of symmetric objects in a manner that eliminates ambiguity while remaining continuous with respect to appearance.
    New representation introduced by the paper; no independent evidence outside the construction itself is provided in the abstract.

pith-pipeline@v0.9.0 · 5589 in / 1703 out tokens · 55773 ms · 2026-05-10T04:50:50.254937+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

65 extracted references · 63 canonical work pages

  1. [1]

    Ayoub, Elie and Levesque, Patrick and Sharf, Inna , year = 2023, month = may, pages =. Grasp. 2023. doi:10.1109/ICRA48891.2023.10161562 , urldate =

    work page doi:10.1109/icra48891.2023.10161562 2023

  2. [2]

    Banerjee, Prithviraj and Shkodrani, Sindi and Moulon, Pierre and Hampali, Shreyas and Han, Shangchen and Zhang, Fan and Zhang, Linguang and Fountain, Jade and Miller, Edward and Basol, Selen and Newcombe, Richard and Wang, Robert and Engel, Jakob Julian and Hodan, Tomas , year = 2025, pages =. 2025. doi:10.1109/CVPR52734.2025.00662 , abstract =

    work page doi:10.1109/cvpr52734.2025.00662 2025

  3. [3]

    Learning

    Brachmann, Eric and Krull, Alexander and Michel, Frank and Gumhold, Stefan and Shotton, Jamie and Rother, Carsten , year = 2014, volume =. Learning. European. doi:10.1007/978-3-319-10605-2_35 , urldate =

    work page doi:10.1007/978-3-319-10605-2_35 2014

  4. [4]

    , year = 2017, month = oct, pages =

    Bregier, Romain and Devernay, Frederic and Leyrit, Laetitia and Crowley, James L. , year = 2017, month = oct, pages =. Symmetry. 2017. doi:10.1109/ICCVW.2017.258 , urldate =

    work page doi:10.1109/iccvw.2017.258 2017

  5. [5]

    Defining the

    Br. Defining the. International Journal of Computer Vision (IJCV) , volume =. doi:10.1007/s11263-017-1052-4 , urldate =

    work page doi:10.1007/s11263-017-1052-4

  6. [6]

    Cai, Dingding and Heikkil. 2022. doi:10.1109/3DV57658.2022.00065 , urldate =

    work page doi:10.1109/3dv57658.2022.00065 2022

  7. [7]

    The 16 L

    Calli, Berk and Singh, Arjun and Bruce, James and Walsman, Aaron and Konolige, Kurt and Srinivasa, Siddhartha and Abbeel, Pieter and Dollar, Aaron M. , year = 2017, journal =. Yale-. doi:10.1177/0278364917700714 , abstract =

    work page doi:10.1177/0278364917700714 2017

  8. [8]

    Castro, Pedro and Kim, Tae-Kyun , year = 2023, month = jan, pages =. 2023. doi:10.1109/WACV56688.2023.00570 , urldate =

    work page doi:10.1109/wacv56688.2023.00570 2023

  9. [9]

    Chao, Ping and Kao, Chao-Yang and Ruan, Yushan and Huang, Chien-Hsiang and Lin, Youn-Long , year = 2019, month = oct, pages =. 2019. doi:10.1109/ICCV.2019.00365 , urldate =

    work page doi:10.1109/iccv.2019.00365 2019

  10. [10]

    Chen, Wei and Jia, Xi and Chang, Hyung Jin and Duan, Jinming and Shen, Linlin and Leonardis, Ale. 2021. doi:10.1109/CVPR46437.2021.00163 , abstract =. arXiv , keywords =:2103.07054v1 , pages =

    work page doi:10.1109/cvpr46437.2021.00163 2021

  11. [11]

    Chen, Kai and James, Stephen and Sui, Congying and Liu, Yun-Hui and Abbeel, Pieter and Dou, Qi , year = 2023, month = may, pages =. 2023. doi:10.1109/ICRA48891.2023.10160780 , urldate =

    work page doi:10.1109/icra48891.2023.10160780 2023

  12. [12]

    Corona, Enric and Kundu, Kaustav and Fidler, Sanja , year = 2018, month = oct, pages =. Pose. 2018. doi:10.1109/IROS.2018.8594282 , urldate =

    work page doi:10.1109/iros.2018.8594282 2018

  13. [13]

    Recovering

    Doumanoglou, Andreas and Kouskouridas, Rigas and Malassiotis, Sotiris and Kim, Tae-Kyun , year = 2016, month = jun, pages =. Recovering. 2016. doi:10.1109/CVPR.2016.390 , urldate =

    work page doi:10.1109/cvpr.2016.390 2016

  14. [14]

    Model Globally, Match Locally:

    Drost, Bertram and Ulrich, Markus and Navab, Nassir and Ilic, Slobodan , year = 2010, month = jun, pages =. Model Globally, Match Locally:. 2010. doi:10.1109/CVPR.2010.5540108 , urldate =

    work page doi:10.1109/cvpr.2010.5540108 2010

  15. [15]

    Introducing

    Drost, Bertram and Ulrich, Markus and Bergmann, Paul and Hartinger, Philipp and Steger, Carsten , year = 2017, pages =. Introducing. 2017. doi:10.1109/ICCVW.2017.257 , urldate =

    work page doi:10.1109/iccvw.2017.257 2017

  16. [16]

    Guo, Andrew and Wen, Bowen and Yuan, Jianhe and Tremblay, Jonathan and Tyree, Stephen and Smith, Jeffrey and Birchfield, Stan , year = 2023, month = oct, pages =. 2023. doi:10.1109/IROS55552.2023.10341672 , urldate =

    work page doi:10.1109/iros55552.2023.10341672 2023

  17. [17]

    Designing

    Hara, Kota and Vemulapalli, Raviteja and Chellappa, Rama , year = 2017, month = feb, number =. Designing. doi:10.48550/arXiv.1702.01499 , urldate =. arXiv , keywords =:1702.01499 , primaryclass =

    work page doi:10.48550/arxiv.1702.01499 2017

  18. [18]

    Haugaard, Rasmus Laurvig and Hagelskj. 2023. doi:10.1109/ICCVW60793.2023.00222 , urldate =

    work page doi:10.1109/iccvw60793.2023.00222 2023

  19. [19]

    He, Yisheng and Wang, Yao and Fan, Haoqiang and Sun, Jian and Chen, Qifeng , year = 2022, month = jun, pages =. 2022. doi:10.1109/CVPR52688.2022.00669 , urldate =

    work page doi:10.1109/cvpr52688.2022.00669 2022

  20. [20]

    Hinterstoisser, Stefan and Lepetit, Vincent and Ilic, Slobodan and Holzer, Stefan and Bradski, Gary and Konolige, Kurt and Navab, Nassir , editor =. Model. Computer. doi:10.1007/978-3-642-37331-2_42 , urldate =

    work page doi:10.1007/978-3-642-37331-2_42

  21. [21]

    Detection and

    Hoda. Detection and. 2015. doi:10.1109/IROS.2015.7354005 , urldate =

    work page doi:10.1109/iros.2015.7354005 2015

  22. [22]

    Hoda. On. European. doi:10.1007/978-3-319-49409-8_52 , urldate =

    work page doi:10.1007/978-3-319-49409-8_52

  23. [23]

    Hoda. T-. 2017. doi:10.1109/WACV.2017.103 , urldate =

    work page doi:10.1109/wacv.2017.103 2017

  24. [24]

    European

    Hoda. European. doi:10.1007/978-3-030-01249-6_2 , urldate =

    work page doi:10.1007/978-3-030-01249-6_2

  25. [25]

    European

    Hoda. European. doi:10.1007/978-3-030-66096-3_39 , urldate =

    work page doi:10.1007/978-3-030-66096-3_39

  26. [26]

    doi:10.48550/arXiv.2506.00599 , urldate =

    Huang, Junwen and Liang, Jizhong and Hu, Jiaqi and Sundermeyer, Martin and Yu, Peter KT and Navab, Nassir and Busam, Benjamin , year = 2025, publisher =. doi:10.48550/arXiv.2506.00599 , urldate =

    work page doi:10.48550/arxiv.2506.00599 2025

  27. [27]

    Journal of Mathematical Imaging and Vision , author =

    Huynh, Du Q. , year = 2009, month = oct, journal =. Metrics for. doi:10.1007/s10851-009-0161-2 , urldate =

    work page doi:10.1007/s10851-009-0161-2 2009

  28. [28]

    Irshad, Muhammad Zubair and Kollar, Thomas and Laskey, Michael and Stone, Kevin and Kira, Zsolt , year = 2022, month = may, pages =. 2022. doi:10.1109/ICRA46639.2022.9811799 , urldate =

    work page doi:10.1109/icra46639.2022.9811799 2022

  29. [29]

    Kalra, Agastya and Stoppi, Guy and Marin, Dmitrii and Taamazyan, Vage and Shandilya, Aarrushi and Agarwal, Rishav and Boykov, Anton and Chong, Tze Hao and Stark, Michael , year = 2024, month = jun, pages =. Towards. 2024. doi:10.1109/CVPR52733.2024.02141 , urldate =

    work page doi:10.1109/cvpr52733.2024.02141 2024

  30. [30]

    Kaskman, Roman and Zakharov, Sergey and Shugurov, Ivan and Ilic, Slobodan , year = 2019, month = oct, pages =. 2019. doi:10.1109/ICCVW.2019.00338 , urldate =

    work page doi:10.1109/iccvw.2019.00338 2019

  31. [31]

    and Ba, Jimmy , year = 2017, month = jan, eprint =

    Kingma, Diederik P. and Ba, Jimmy , year = 2017, month = jan, eprint =. Adam:. International. doi:https://hdl.handle.net/11245/1.505367 , urldate =

    2017

  32. [32]

    Kriegler, Andreas and Beleznai, Csaba and Murschitz, Markus and G. 2022. doi:10.1109/IRC55401.2022.00040 , urldate =

    work page doi:10.1109/irc55401.2022.00040 2022

  33. [33]

    International Journal of Semantic Computing , volume =

    Kriegler, Andreas and Beleznai, Csaba and Gelautz, Margrit and Murschitz, Markus and G. International Journal of Semantic Computing , volume =. doi:10.1142/S1793351X23620027 , urldate =

    work page doi:10.1142/s1793351x23620027

  34. [34]

    European

    Labb. European. doi:10.1007/978-3-030-58520-4_34 , urldate =

    work page doi:10.1007/978-3-030-58520-4_34

  35. [35]

    International Journal of Computer Vision127(5), 456–476 (May 2019).https://doi.org/10.1007/s11263-018-1098-y,https:// doi.org/10.1007/s11263-018-1098-y

    Lenc, Karel and Vedaldi, Andrea , year = 2019, month = may, journal =. Understanding. doi:10.1007/s11263-018-1098-y , urldate =

    work page doi:10.1007/s11263-018-1098-y 2019

  36. [36]

    Li, Yuelong and Mao, Yafei and Bala, Raja and Hadap, Sunil , year = 2024, pages =. 2024. doi:10.1109/CVPR52733.2024.00997 , urldate =

    work page doi:10.1109/cvpr52733.2024.00997 2024

  37. [37]

    Lin, Tsung-Yi and Goyal, Priya and Girshick, Ross and He, Kaiming and Dollar, Piotr , year = 2017, month = oct, pages =. Focal. 2017. doi:10.1109/ICCV.2017.324 , urldate =

    work page doi:10.1109/iccv.2017.324 2017

  38. [38]

    Editing conditional radiance fields

    Liu, Xingyu and Iwase, Shun and Kitani, Kris M. , year = 2021, month = oct, pages =. 2021. doi:10.1109/ICCV48922.2021.01069 , urldate =

    work page doi:10.1109/iccv48922.2021.01069 2021

  39. [39]

    doi:10.1109/TPAMI.2025.3553485 , urldate =

    Liu, Xingyu and Zhang, Ruida and Zhang, Chenyangguang and Wang, Gu and Tang, Jiwen and Li, Zhigang and Ji, Xiangyang , year = 2025, month = mar, journal =. doi:10.1109/TPAMI.2025.3553485 , urldate =

    work page doi:10.1109/tpami.2025.3553485 2025

  40. [40]

    Mahendran, Siddharth and Ali, Haider and Vidal, Ren. 2017. doi:10.1109/CVPRW.2017.73 , urldate =

    work page doi:10.1109/cvprw.2017.73 2017

  41. [41]

    Mo, Ningkai and Gan, Wanshui and Yokoya, Naoto and Chen, Shifeng , year = 2022, pages =. 2022. doi:10.1109/CVPR52688.2022.00660 , urldate =

    work page doi:10.1109/cvpr52688.2022.00660 2022

  42. [42]

    The International Journal of Robotics Research , volume =

    Learning Robust, Real-Time, Reactive Robotic Grasping , author =. The International Journal of Robotics Research , volume =. doi:10.1177/0278364919859066 , urldate =

    work page doi:10.1177/0278364919859066

  43. [43]

    Pytorch: An imperative style, high-performance deep learning library,

    Paszke, Adam and Gross, Sam and Massa, Francisco and Lerer, Adam and Bradbury, James and Chanan, Gregory and Killeen, Trevor and Lin, Zeming and Gimelshein, Natalia and Antiga, Luca and Desmaison, Alban and Kopf, Andreas and Yang, Edward and DeVito, Zachary and Raison, Martin and Tejani, Alykhan and Chilamkurthy, Sasank and Steiner, Benoit and Fang, Lu an...

    work page doi:10.5555/3454287.3455008 2019

  44. [44]

    Learning

    Periyasamy, Arul Selvam and Denninger, Luis and Behnke, Sven , year = 2022, month = dec, pages =. Learning. 2022. doi:10.1109/IRC55401.2022.00044 , urldate =

    work page doi:10.1109/irc55401.2022.00044 2022

  45. [45]

    Pitteri, Giorgia and Ramamonjisoa, Michael and Ilic, Slobodan and Lepetit, Vincent , year = 2019, month = sep, pages =. On. 2019. doi:10.1109/3DV.2019.00073 , urldate =

    work page doi:10.1109/3dv.2019.00073 2019

  46. [46]

    Pitteri, Giorgia and Bugeau, Aur. Asian. doi:10.1007/978-3-030-69525-5_3 , urldate =

    work page doi:10.1007/978-3-030-69525-5_3

  47. [47]

    Rad, Mahdi and Lepetit, Vincent , year = 2017, month = oct, pages =. 2017. doi:10.1109/ICCV.2017.413 , urldate =

    work page doi:10.1109/iccv.2017.413 2017

  48. [48]

    Raj, Prem and Kumar, Ashish and Sanap, Vipul and Sandhan, Tushar and Behera, Laxmidhar , year = 2022, month = aug, pages =. Towards. 2022. doi:10.1109/CASE49997.2022.9926708 , urldate =

    work page doi:10.1109/case49997.2022.9926708 2022

  49. [49]

    and De Souza, Alberto F

    Rennie, Colin and Shome, Rahul and Bekris, Kostas E. and De Souza, Alberto F. , year = 2016, month = jul, journal =. A. doi:10.1109/LRA.2016.2532924 , urldate =

    work page doi:10.1109/lra.2016.2532924 2016

  50. [50]

    Salehi, Seyed Sadegh Mohseni and Khan, Shadab and Erdogmus, Deniz and Gholipour, Ali , year = 2019, month = feb, journal =. Real-. doi:10.1109/TMI.2018.2866442 , urldate =

    work page doi:10.1109/tmi.2018.2866442 2019

  51. [51]

    Shi, Yifei and Huang, Junwen and Xu, Xin and Zhang, Yifan and Xu, Kai , year = 2021, month = jun, pages =. 2021. doi:10.1109/CVPR46437.2021.01497 , urldate =

    work page doi:10.1109/cvpr46437.2021.01497 2021

  52. [52]

    Symmetry:

    Stewart, Ian , year = 2013, series =. Symmetry:

    2013

  53. [53]

    Su, Yongzhi and Saleh, Mahdi and Fetzer, Torben and Rambach, Jason and Navab, Nassir and Busam, Benjamin and Stricker, Didier and Tombari, Federico , year = 2022, month = jun, pages =. 2022. doi:10.1109/CVPR52688.2022.00662 , urldate =

    work page doi:10.1109/cvpr52688.2022.00662 2022

  54. [54]

    Implicit

    Sundermeyer, Martin and Marton, Zoltan-Csaba and Durner, Maximilian and Brucker, Manuel and Triebel, Rudolph , year = 2018, pages =. Implicit. European. doi:10.1007/978-3-030-01231-1_43 , urldate =

    work page doi:10.1007/978-3-030-01231-1_43 2018

  55. [55]

    Augmented

    Sundermeyer, Martin and Marton, Zoltan-Csaba and Durner, Maximilian and Triebel, Rudolph , year = 2020, month = mar, journal =. Augmented. doi:10.1007/s11263-019-01243-8 , urldate =

    work page doi:10.1007/s11263-019-01243-8 2020

  56. [56]

    Tejani, Alykhan and Tang, Danhang and Kouskouridas, Rigas and Kim, Tae-Kyun , year = 2014, pages =. Latent-. European. doi:10.1007/978-3-319-10599-4_30 , urldate =

    work page doi:10.1007/978-3-319-10599-4_30 2014

  57. [57]

    Tyree, Stephen and Tremblay, Jonathan and To, Thang and Cheng, Jia and Mosier, Terry and Smith, Jeffrey and Birchfield, Stan , year = 2022, month = oct, pages =. 6-. 2022. doi:10.1109/IROS47612.2022.9981838 , urldate =

    work page doi:10.1109/iros47612.2022.9981838 2022

  58. [58]

    Vidal, Joel and Lin, Chyi-Yeu and Llad. A. Sensors , volume =. doi:10.3390/s18082678 , urldate =

    work page doi:10.3390/s18082678

  59. [59]

    Wang, Chen and Xu, Danfei and Zhu, Yuke and. 2019. doi:10.1109/CVPR.2019.00346 , urldate =

    work page doi:10.1109/cvpr.2019.00346 2019

  60. [60]

    Wang, Gu and Manhardt, Fabian and Tombari, Federico and Ji, Xiangyang , year = 2021, month = jun, pages =. 2021. doi:10.1109/CVPR46437.2021.01634 , urldate =

    work page doi:10.1109/cvpr46437.2021.01634 2021

  61. [61]

    Science in China Series F: Information Sciences , volume =

    The Essential Order of Approximation for Neural Networks , author =. Science in China Series F: Information Sciences , volume =. doi:10.1360/02yf0221 , urldate =

    work page doi:10.1360/02yf0221

  62. [62]

    Simultaneous

    Xu, Zong-Ben and Cao, Fei-Long , year = 2005, month = sep, journal =. Simultaneous. doi:10.1016/j.neunet.2005.03.013 , urldate =

    work page doi:10.1016/j.neunet.2005.03.013 2005

  63. [63]

    Sadler and Jiaman Wu and Wei

    Zhao, Heng and Wei, Shenxing and Shi, Dahu and Tan, Wenming and Li, Zheyang and Ren, Ye and Wei, Xing and Yang, Yi and Pu, Shiliang , year = 2023, month = oct, pages =. Learning. 2023. doi:10.1109/ICCV51070.2023.01291 , urldate =

    work page doi:10.1109/iccv51070.2023.01291 2023

  64. [64]

    Zhou, Yi and Barnes, Connelly and Lu, Jingwan and Yang, Jimei and Li, Hao , year = 2019, month = jun, pages =. On the. 2019. doi:10.1109/CVPR.2019.00589 , urldate =

    work page doi:10.1109/cvpr.2019.00589 2019

  65. [65]

    Objects as points,

    Zhou, Xingyi and Wang, Dequan and Kr. Objects as. doi:10.48550/arXiv.1904.07850 , urldate =. arXiv , keywords =:1904.07850 , primaryclass =

    work page doi:10.48550/arxiv.1904.07850 1904