Symmetry-Aware Orientation Estimation via Outer-Product Rotation Targets in YOLO26
- 1Faculty of Electrical Engineering and Computer Science, University of Maribor, Koroška cesta 46, SI-2000 Maribor, Slovenia
Abstract
Regressing the 3D orientation of a symmetric object with a signed rotation representation is ill posed: the rotations that render an indistinguishable image form an equivalence class, so physically identical poses receive inconsistent labels. This is a common case in robotic manipulation, bin picking, and part feeding, where machined parts are routinely symmetric about an axis or a mirror plane. We extend the YOLO26 segmentation architecture with a rotation-regression branch whose target, building on Saxena et al., gives each sign-ambiguous axis its own outer product rather than a signed vector, and each directed axis a signed vector, so physically equivalent poses map to the same target of 6, 9, or 12 values instead of 9 to 39. The training data comes from a MuJoCo-based synthetic rendering pipeline with an on-the-fly composition loader that combines randomly posed, rotated part instances into each training image. We evaluate the outer-product representation against direct, signed regression on four part categories spanning axial and mirror-plane symmetry, testing both on held-out synthetic images and on 21 real, annotated MVTec ITODD instances, and additionally compare this grayscale-only system with the published SARR networks, including their depth-input variant, on the same real parts using the BOP ARB metric.
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BibTeX
@article{pahic2026symmetryaware,
title = {{Symmetry-Aware Orientation Estimation via Outer-Product Rotation Targets in YOLO26}},
author = {Rok Pahič and Aleš Hace},
journal = {Mathematics},
year = {2026},
month = nov,
doi = {10.3390/math14214014},
url = {https://www.mdpi.com/2227-7390/14/21/4014},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Symmetry-Aware Orientation Estimation via Outer-Product Rotation Targets in YOLO26
AU - Rok Pahič
AU - Aleš Hace
PY - 2026
DA - 2026/11/03
JO - Mathematics
DO - 10.3390/math14214014
UR - https://www.mdpi.com/2227-7390/14/21/4014
AB - Regressing the 3D orientation of a symmetric object with a signed rotation representation is ill posed: the rotations that render an indistinguishable image form an equivalence class, so physically identical poses receive inconsistent labels. This is a common case in robotic manipulation, bin picking, and part feeding, where machined parts are routinely symmetric about an axis or a mirror plane. We extend the YOLO26 segmentation architecture with a rotation-regression branch whose target, building on Saxena et al., gives each sign-ambiguous axis its own outer product rather than a signed vector, and each directed axis a signed vector, so physically equivalent poses map to the same target of 6, 9, or 12 values instead of 9 to 39. The training data comes from a MuJoCo-based synthetic rendering pipeline with an on-the-fly composition loader that combines randomly posed, rotated part instances into each training image. We evaluate the outer-product representation against direct, signed regression on four part categories spanning axial and mirror-plane symmetry, testing both on held-out synthetic images and on 21 real, annotated MVTec ITODD instances, and additionally compare this grayscale-only system with the published SARR networks, including their depth-input variant, on the same real parts using the BOP ARB metric.
SN - 2227-7390
ER -