Rotation-Invariant Descriptors

Global localization with scanning millimeter-wave radar remains challenging because place-recognition descriptors often discard spatial structure needed for accurate pose retrieval. We present ReRadar, a radar global localization pipeline that extracts rotation-equivariant intermediate features using steerable convolutional neural networks, forms rotation-invariant descriptors through group pooling and NetVLAD aggregation, and combines descriptor retrieval with landmark-based matching to estimate the robot's three-degree-of-freedom (3-DoF) pose. Across fixed database-query evaluations, ReRadar with target-dataset adaptation achieves 99.37% Recall@1 on OORD Bellmouth, 91.44% Recall@1 with 80.99% F1_max on Mulran DCC01, and 99.38% Recall@1 on falling-snow Boreas sequence. Without target-dataset data, the cross-dataset model reaches 98.07% Recall@1 on OORD, performing comparably to the evaluated state-of-the-art methods.

We present DXPR, a depth-based cross-modal place recognition (CMPR) framework that uses vision foundation models (VFMs) to match monocular camera queries against a LiDAR map without modality-specific encoders. This enables robots and autonomous vehicles to robustly localize using only cameras within pre-built LiDAR maps, even under severe seasonal, weather, and illumination changes. The key idea is to convert both camera images and LiDAR scans into a unified depth image representation so that a single VFM backbone with an aggregation head can learn modality-invariant global descriptors. To make pairwise metric learning faithful to scene geometry, we introduce a geometry-aware overlap miner: after cross-modal scale alignment of camera and LiDAR depth, we forward-warp measurements between views to compute a pixel-level overlap score. This score relabels ambiguous pairs and adaptively modulates the positive margin in a multi-similarity loss to avoid overfitting on weakly overlapping views. Extensive experiments on KITTI odometry and Boreas demonstrate strong performance and robustness across seasons, weather, and day/night. On KITTI, DXPR achieves near-perfect Recall@1 on most sequences and outperforms prior CMPR baselines. On Boreas, DXPR achieves intra-sequence performance on par with a strong single-modal baseline (DINOv2-SALAD), while showing clear improvements in the more challenging inter-sequence setting. Compared with RangeBEV, our method consistently performs better in both intra- and inter-sequence evaluations, demonstrating robustness under diverse seasonal and illumination changes.

Multi-oriented text is ubiquitous in real-world scenes and remains a major challenge for scene text recognition (STR). Existing rotation-aware methods explicitly estimate text orientation. However, due to the lack of theoretical guarantees, they are prone to error accumulation, increased computational cost, and strong reliance on data. In this work, we incorporate rotation invariance into the STR framework to address these limitations. Specifically, we adopt an encoder-decoder architecture, embedding rotation equivariance in the encoder and rotation invariance in the decoder to construct a fully rotation-invariant network. On the decoder side, we first identify and prove the rotation-invariant property of the cross-attention mechanism and use it to formulate a rotation-invariant text decoder that maps visual features to output text in a rotation-invariant manner. On the encoder side, we propose a rotation-equivariant local-global extraction network that integrates deep equivariant convolutions with self-attention, enabling rotation-equivariant feature extraction while modeling inter-character dependencies and preserving fine-grained visual details. By integrating the encoder and decoder, we obtain an end-to-end Rotation-Invariant Scene Text Recognition network (RISTER). RISTER provides rotation invariance with theoretical guarantees, enhancing robustness on multi-oriented samples without introducing additional inference computation or relying on data-driven orientation correction. Experiments show that RISTER achieves state-of-the-art performance on both standard and multi-oriented benchmarks, surpassing the second-best model by 4.0 percent in accuracy on the general multi-oriented dataset.

Multimodal learning of images and tabular data is often impaired by ineffective representations, resulting in redundancy, dispersion, and generalization problems. To tackle this challenge, we introduce Graph-Enhanced Descriptor Sequencing (GEDS), a structured feature sequencing algorithm grounded in principles from the Column Permutation Problem (CPP). GEDS refines statistical descriptors of the features through similarity graph-based computations, systematically determining an effective feature sequencing. We incorporate GEDS within an order-aware efficient transformer framework, utilizing order-aware memory tokens that explicitly adhere to the derived feature sequencing via a dedicated loss function. Experimental results across multimodal benchmarks demonstrate that iStructTab effectively minimizes feature dispersion, improving predictive performance and robustness, and highlighting the significance of structured feature sequencing in multimodal learning.

In digital dentistry and oral surgery, the registration of jawbone CT and intraoral scanner (IOS) data is essential for integrating internal bone structure with high-resolution dental surface geometry. However, this registration is challenging because the two modalities share only a limited region in common, and their true correspondence is generally unknown. This uncertainty has prevented rigorous quantitative evaluation of registration accuracy. In this study, we propose a pseudoIOS evaluation framework in which a point cloud emulating an intraoral scan is generated from CT data within the same coordinate frame, so that the transformation between them is known by construction and can serve as a true ground truth. Using this framework, we propose a coarse-to-fine registration method that combines a domain-generalizable local descriptor (GeDi) for initialization-independent global alignment with the iterative closest point (ICP) algorithm for local refinement, and also evaluate the influence of metal artifacts on registration. In experiments on seven cases, ICP alone frequently converged to local minima from a perturbed initial position, whereas GeDi$+$ICP maintained submillimeter mean absolute error (MAE) across all evaluated jaw and artifact conditions (0.55-0.69 mm). A three-way repeated-measures analysis confirmed that GeDi$+$ICP was significantly more accurate than GeDi alone. Metal artifacts had a statistically detectable overall effect, but their absolute impact on GeDi$+$ICP was small.

Chemical structures appear in patents and the scientific literature as images. For programmatic usage, such as indexing in databases or constructing machine learning model training sets, they must be transformed into line notations. The two common forms of this task are translating an image of a single molecule (optical chemical structure recognition - OCSR) and translating a Markush structure that represents a family of molecules. While prior work in the former case is quite mature, Markush structure parsing remains a challenging task. In this work, we treat both tasks as an image-to-text translation problem. We then propose OCSRGlyph, a state-of-the-art OCSR model, improving performance over prior methods by carefully considering stereochemistry. For the Markush task, we introduce MarkushGlyph, a vision-language model that reads the entire Markush structure as an image. This contrasts with prior systems, which often use multiple stages to separately process visual and text input content. Finally, we introduce a new metric for determining the accuracy of Markush structure translations, handling failure modes present in prior metrics.

Reflection symmetry detection remains challenging due to interference from asymmetric regions and arbitrary orientations of symmetric patterns. Asymmetric regions introduce background clutter that disrupts symmetric pattern matching, whereas conventional convolutional neural networks lack rotation equivariance, leading to inconsistent feature representations under rotational transformations. To address these issues, we propose an Asymmetric Region Denoising (ARD) module and a Rotation Equivariant Feature Similarity Matching (REFSM) module. The ARD module suppresses asymmetric interference to refine symmetric patterns, while the REFSM module enhances rotation equivariance through feature similarity matching between original and rotated images. Specifically, our dual-input REFSM framework leverages rotation loss to maximize consistency between the score maps of original and rotated images, thereby enabling precise prediction of rotation-equivariant symmetry axes. Furthermore, we introduce GMSYM, a new benchmark dataset that categorizes images into diverse scenarios and incorporates various interferences to address the limitations of existing reflection symmetry detection benchmarks. Extensive experiments on four standard datasets (DENDI, NYU, LDRS, SDRW) and our proposed GMSYM dataset demonstrate that our method achieves state-of-the-art performance in both accuracy and robustness.

Accurate refinement of Rational Polynomial Camera (RPC) models is essential for high-quality satellite image geolocation. In ground control point (GCP)-free multi-view pipelines, this refinement is commonly performed through bundle adjustment from automatically extracted image correspondences. However, conventional RPC bundle adjustment pipelines rely on handcrafted feature matching, which becomes unreliable in multi-date collections affected by seasonal, illumination, and land-cover changes. We propose an appearance-aware RPC refinement pipeline that combines learned local feature matching for season-invariant correspondences with global image descriptors for selecting visually compatible image pairs. This reduces redundant and error-prone matching while preserving the connectivity of the matching graph. Experiments on seasonally diverse WorldView-3 images show that our pipeline improves GCP-free relative RPC refinement over open-source baselines, achieving lower geometric consistency errors while substantially reducing matching time on collections with 39-42 views. By making RPC refinement more robust to diachronic appearance variation, our approach enables more effective use of multi-date satellite imagery.

Point cloud registration critically depends on local features that are both distinctive and robust to arbitrary 3D rotations. Existing learning-based methods typically approximate rotation invariance via fragile local reference frames or extensive data augmentation, providing only empirical invariance and often degrading under unseen rotational transformations. In this paper, we propose SHReg, a strictly rotation-equivariant point cloud registration framework grounded in the representation theory of $SO(3)$. By representing local geometric features as irreducible representations of $SO(3)$, SHReg guarantees exact equivariance under arbitrary rotations without relying on local reference frames. Built upon a spherical-harmonics-based equivariant backbone, SHReg jointly learns rotation-invariant descriptors for robust correspondence matching and rotation-equivariant features that preserve fine-grained orientation information. The preserved equivariant structure enables each correspondence to directly hypothesize a rigid transformation, reducing reliance on large-scale hypothesis sampling in conventional RANSAC-based pipelines and leading to improved robustness under challenging rotational variations. Extensive experiments on 3DMatch, 3DLoMatch, and KITTI demonstrate that SHReg consistently outperforms state-of-the-art methods in registration accuracy, particularly under large rotational perturbations.

Protein fold classification can be approached via sequence-based representations or structural descriptors, but direct comparisons between lightweight handcrafted descriptors and pretrained protein language model embeddings remain limited. We investigate discrete Ricci curvature on Calpha contact graphs as a lightweight structural descriptor for fold classification. Each protein domain is represented by a 22-dimensional fixed-length feature derived from summary statistics and quantiles of Ollivier-Ricci and Forman-Ricci edge curvature distributions. We evaluate on CATH top-10 Topology classification and on the ASTRAL 40%-identity SCOPe top-10 Fold benchmark, comparing against geometry, contact-graph statistics, persistent homology, and mean-pooled ESM-2 (150M) baselines. On both datasets, lightweight structural descriptors substantially outperform mean-pooled ESM-2 embeddings, with a larger performance gap on the ASTRAL 40% SCOPe benchmark. Ricci alone uses 22 dimensions, or 3.4% of the ESM-2 baseline dimensionality, and already outperforms mean-pooled ESM-2 on both datasets. Combining Ricci with persistent homology yields the strongest performance, achieving macro-F1 of 0.71 on CATH and 0.68 on SCOPe with a 112-dimensional feature vector. These results identify a regime where lightweight interpretable graph descriptors offer a practical alternative to pretrained protein language model embeddings.

Category-level object pose estimation is a crucial yet challenging task in both academia and industry, and has achieved remarkable success by leveraging keypoint-based correspondence paradigms. However, most existing methods increasingly rely on stronger feature learning while overlooking whether the established correspondences are geometrically stable across diverse perturbations. This often results in fragile pose recovery under intra-class shape variations and occlusions. To tackle this challenge, we develop a novel Triangle-Invariant Geometric Consistency Learning for Category-Level Object Pose Estimation (TriCons-Pose) to anchor stable keypoints and aggregate pose-invariant cues, yielding reliable canonical mapping and accurate pose estimation. Specifically, a Structure-Consistent Keypoint Detector (SCKD) is designed to identify robust keypoints by enforcing cross-view structural consistency via normalized pairwise distance matching. Moreover, we propose a Pose-Invariant Geometric Aggregator (PIGA) to augment keypoint representations by injecting triangle-based pose-invariant descriptors into a local-to-global attention mechanism. The proposed framework is optimized using standard objective functions while incorporating an additional geometry consistency loss. Extensive experiments on REAL275, CAMERA25, and HouseCat6D datasets demonstrate the effectiveness of the proposed approach.

Quantifying how mirror-symmetric an image is about a given axis (symmetry scoring) underpins applications from visual aesthetics to medical imaging, yet proposed scoring methods have never been compared on a common, statistically grounded protocol. We benchmark 13 scoring methods (nine collected from literature, four introduced here) spanning from classical features to frozen deep features, across four single-axis and five multi-axis datasets under a reflection-exact protocol with a chance-anchored, significance-tested discrimination skill. Deep backbones perform best on single-axis and harder multi-axis protocols. However, a classical histogram-of-oriented-gradients (HOG) descriptor trails the best frozen-network readout by a small (but significant) margin, is not statistically separable from the runner-up (a CNN-filter measure), and runs ~300x faster on CPU. Our results show that discrimination concentrates in mid-scale oriented features, where deep backbones peak at a low or mid stage, and HOG peaks at a mid cell size. Among existing methods, frozen deep features thus offer little over a tuned classical descriptor for measuring symmetry; whether task-trained deep scorers can do better remains open. We release the scorers and harness in imgsym, an open toolkit for image symmetry detection and measurement.

At Amazon Prime Video, we face the critical operational challenge of managing code deployments during live events and rapid feature releases without causing service outages. Current change control approaches use blanket deployment freezes that block all changes regardless of risk, creating significant developer toil. While prior research has explored risky change predictors, these rely on developer-specific metadata or extensive historical data, raising privacy concerns and limiting applicability to new projects. We introduce a framework centered on diff-aware features, characteristics derived directly from code modifications. Our key contribution is the systematic identification of which quantitative metrics (code-level and change-level metrics) and qualitative indicators (coding style violations, change type classification) are necessary for risk prediction. We employ LLMs as multi-language feature extractors, demonstrating their effectiveness for code analysis beyond generation tasks and eliminating the need for language-specific tooling. We evaluated our framework on two datasets: Prime Video's production environment and the public ApacheJIT dataset. Our best-performing model achieves an average recall of 0.83 and F1 score of 0.81 across both datasets for detecting risky code changes. Notably, ablation analysis reveals that change-level volume metrics (e.g., lines added/deleted) are noisy predictors, while structural code complexity provides a substantially stronger risk signal. These results demonstrate that thoughtful feature curation enables effective change risk assessment across different programming languages and organizational contexts while avoiding privacy concerns.

Positional encoding is a fundamental component of Transformer architectures, as it injects information about the spatial or sequential arrangement of inputs. Among recent alternatives to standard absolute and sinusoidal encodings, similarity-based positional encoding (simPE) has emerged as a flexible framework for representing positional structure through pairwise relations. simPE was originally designed for medical imaging applications, where geometric robustness is especially relevant: small rotations naturally arise during image acquisition, induced by imaging instruments, patient positioning, or slight acquisition misalignments. Despite its empirical promise, the theoretical behavior of simPE under geometric perturbations has not been fully characterized. In this paper, we study the robustness of simPE with respect to rotations, combining formal theoretical analysis with experimental validation. We first show that simPE is generally not rotation-invariant. We then prove that, under mild Lipschitz assumptions on the elementary components, simPE is stable under rotational perturbations and derive explicit perturbation bounds in Frobenius norm. We validate these findings experimentally on four controlled datasets--a synthetic Arrow dataset, a synthetic Shapes dataset (four geometric shape categories), a synthetic Digits dataset, and a benchmark image classification dataset (FashionMNIST)--in which training and validation images are kept in a fixed canonical orientation while test images are subjected to increasing rotation angles. Across all datasets, simPE consistently outperforms standard learned positional encoding in terms of accuracy, F1 score, precision, and recall under rotation, particularly in the small-to-moderate angle regime, corroborating the theoretical stability guarantees.

Fingerprint recognition is still dominated by task-specific pipelines, where enhancement, structural parsing, alignment, and matching are optimized in isolation. Although effective in narrow settings, this design limits representation reuse across sensors, qualities, and downstream applications. We therefore present UoU, short for ``a \textbf{U}niversal fingerprint foundation model based \textbf{o}n large-scale \textbf{U}nsupervised learning,'' which reframes fingerprint feature extraction as a domain-specific foundation-model problem. UoU is organized around a multi-level representation hierarchy spanning image restoration, structural fields, semantic tokens, point-level biometric entities, and compact global descriptors. Its training recipe combines a supervised cold start on precise annotations, large-scale weakly supervised refinement, and large-scale unsupervised consolidation, with the latter two stages iterated during large-scale training so that weak supervision broadens semantic coverage while unsupervised learning stabilizes correspondences, invariances, and representation geometry. Rather than treating fingerprint imagery as generic texture, UoU exploits domain-specific symmetries and intermediate structure, including orientation flow, periodic ridge patterns, sparse biometric entities, and spatial equivariance. The framework is intentionally architecture-agnostic: while the present study includes an initial transformer-based structured-prediction instantiation, the broader design supports multi-task learning, scalable model configurations, and downstream specialization for matching, alignment, enhancement, registration, and related fingerprint applications. This paper presents the technical motivation, system design, and validation protocol of UoU, and part of the baseline implementation is publicly available at https://github.com/XiongjunGuan/UoU.

Urban green-space extraction from ultra-high-resolution (UHR) imagery is commonly performed patch by patch, which limits semantic reuse among spatially separated but visually similar vegetation patterns. Directly injecting the Normalized Difference Vegetation Index (NDVI) into red-green-blue (RGB) backbones can also blur the roles of visual appearance learning and physical vegetation confidence. We propose GMBFormer, a SegFormer-based framework that replaces adjacency-driven feature propagation with selective, similarity-driven prototype retrieval. Only RGB channels enter the backbone and decoder, while NDVI is decoupled as a physics-informed gate that admits high-confidence vegetation descriptors into a compact global memory bank through momentum updates. During training and inference, the current patch queries stored prototypes through memory-mediated cross-attention, and the retrieved response is integrated with bounded overhead. Experiments use a self-constructed Chengdu UHR dataset with 7,700 labeled 512 x 512 patches and two reduced-label settings derived from the public International Society for Photogrammetry and Remote Sensing (ISPRS) Potsdam dataset. Under the same training and evaluation protocol, GMBFormer obtains mean intersection over union (mIoU)/mean Dice (mDice) scores of 89.25%/94.31%, 92.17%/95.92%, and 83.72%/90.86%, respectively, improving the controlled SegFormer-B4 baseline in each setting. Ablation studies indicate that decoupled NDVI admission, memory retrieval, capacity, and momentum jointly shape the final performance.

Reliable watermarking of panoramic imagery is fundamentally challenged by arbitrary 3D rotations. As panoramas are defined on the sphere, they naturally transform under the action of $SO(3)$, rendering conventional planar representations and augmentation-based robustness strategies inadequate and devoid of theoretical guarantees. To address this, we formulate panoramas as spherical signals and leverage $SO(3)$ representation theory to derive provably rotation-invariant descriptors. While spherical harmonic coefficients transform equivariantly under rotations, the natural invariant constructions are typically limited to zeroth-order statistics which eliminate directional information and severely constrain embedding capacity. In this work, we introduce a principled third-order invariant construction by coupling higher-order $SO(3)$ irreducible representations via tensor products and projecting onto the trivial representation. This yields a spherical invariant bispectrum that preserves phase information while remaining strictly rotation-invariant. Leveraging this property, we embed watermarks into higher-order spherical harmonic coefficients and recover them from invariant bispectral scalars, enabling reliable extraction under arbitrary 3D rotations. We provide a theoretical proof of $SO(3)$ invariance for it and demonstrate experimentally its near-perfect robustness to continuous rotations while maintaining high visual fidelity.

We present S2P-Net (Spectral-Spatial Polar Network), a compact deep learning architecture that achieves mathematically guaranteed rotation invariance without data augmentation. In this Paper, we also made a comparison to other neural network architectures (CNN`s). Have a look at the results and feel free to contact me for any questions. This is my first paper:) Made by Hackbert

Progress on graph foundation models is hindered by benchmark practices that conflate the contributions of node features and graph structure, making it hard to tell whether a model actually learns from connectivity, or whether it even needs to. We propose addressing this using graph invariants, i.e., permutation-invariant, task-agnostic structural descriptors that serve as a diagnostic framework for graph benchmarks. We show that (i) invariants are more expressive than standard GNNs, (ii) invariants characterize structural heterogeneity within and across benchmark datasets, (iii) invariants predict multi-task performance, and (iv) simple invariant-based models are competitive with, and sometimes exceed, transformer and message-passing baselines across 26 datasets. Our results suggest that expressivity is not the main driver of predictive performance, and that on tasks where structure matters, a non-trainable structural proxy often matches trained message-passing models. We thus posit that invariant baselines should become a standard for evaluating whether structure is required for a task and whether a model picks up on it, serving as a stepping stone towards graph foundation models.

Person re-identification (ReID) systems that match individuals across images or video frames are essential in many real-world applications. However, existing methods are often influenced by attributes such as gender, pose, and body mass index (BMI), which vary in unconstrained settings and raise concerns related to fairness and generalization. To address this, we extend the notion of expressivity, defined as the mutual information between learned features and specific attributes, using a secondary neural network to quantify how strongly attributes are encoded. Applying this framework to three transformer-based ReID models on a large-scale visible-spectrum dataset, we find that BMI consistently shows the highest expressivity in deeper layers. Attributes in the final representation are ranked as BMI > Pitch > Gender > Yaw, and expressivity evolves across layers and training epochs, with pose peaking in intermediate layers and BMI strengthening with depth. We further extend the analysis to cross-spectral person identification across infrared modalities including short-wave, medium-wave, and long-wave infrared. In this setting, pitch becomes comparable to BMI and attribute trends increase monotonically across depth, suggesting increased reliance on structural cues when bridging modality gaps. Overall, the results show that transformer-based ReID embeddings encode a hierarchy of implicit attributes, with morphometric information persistently embedded and pose contributing more strongly under cross-spectral conditions.

One of the most exciting applications of vision models involve pixel-level reasoning. Despite the abundance of vision foundation models, we still lack representations that effectively embed spatio-temporal properties of visual scenes at the pixel level. Existing frameworks either train on image-based pretext tasks, which do not account for dynamic elements, or on video sequences for action-level reasoning, which does not scale to dense pixel-level prediction. We present a framework that learns pixel-accurate feature descriptors from videos, LILA. The core element of our training framework is linear in-context learning. LILA leverages spatio-temporal cue maps -- depth and motion -- estimated with off-the-shelf networks. Despite the noisy nature of those cues, LILA trains effectively on uncurated video datasets, embedding semantic and geometric properties in a temporally consistent manner. We demonstrate compelling empirical benefits of the learned representation across a diverse suite of vision tasks: video object segmentation, surface normal estimation and semantic segmentation.

Architectural floor plans are widely available priors which contain not only geometry but also the semantic information of the environment, yet existing localization methods largely ignore this semantic information. To address this, we present COMPASS, an algorithm that exploits both geometric and semantic priors from floor plans to estimate the pose of a robot equipped with dual fisheye cameras. Inspired by scan context descriptor from LiDAR-based place recognition, we design a multi-channel radial descriptor that encodes the geometric layout surrounding a position. From the floor plan, rays are cast in 360 azimuth bins and the results are encoded into five channels: normalized range, structural hit type (wall, window, or opening), range gradient, inverse range, and local range variance. From the image side, the same descriptor structure is populated by detecting structural elements in the fisheye imagery. As a first step toward full cross-modal matching, we present a window detection algorithm for fisheye images that uses a line segment detector to identify window frames via vertical edge clustering and brightness verification. Detected windows are projected to azimuthal bearings through the fisheye camera model, producing the hit-type channel of the visual descriptor. As a proof of concept, we generate both descriptors at a single known pose from the Hilti-Trimble SLAM Challenge 2026 dataset and demonstrate that the wall-window pattern extracted from the first frame of each camera closely matches the floor plan descriptor, validating the feasibility of cross-modal structural matching.

Spatiotemporal Local Binary Pattern (STLBP) is a widely used dynamic texture descriptor, but it suffers from extremely high dimensionality. To tackle this, STLBP features are often extracted on three orthogonal planes, which sacrifice inter-plane correlation. In this work, we propose a Locality-Preserving Pixel-Difference Hashing (LP$^{2}$DH) framework that jointly encodes pixel differences in the full spatiotemporal neighbourhood. LP$^{2}$DH transforms Pixel-Difference Vectors (PDVs) into compact binary codes with maximal discriminative power. Furthermore, we incorporate a locality-preserving embedding to maintain the PDVs' local structure before and after hashing. Then, a curvilinear search strategy is utilized to jointly optimize the hashing matrix and binary codes via gradient descent on the Stiefel manifold. After hashing, dictionary learning is applied to encode the binary vectors into codewords, and the resulting histogram is utilized as the final feature representation. The proposed LP$^{2}$DH achieves state-of-the-art performance on three major dynamic texture recognition benchmarks: 99.80% against DT-GoogleNet's 98.93% on UCLA, 98.52% against HoGF$^{3D}$'s 97.63% on DynTex++, and 96.19% compared to STS's 95.00% on YUPENN. The source code is available at: https://github.com/drx770/LP2DH.

In this paper, we present a network structure for classifying metadata of cuneiform tablets. The problem is of practical importance, as the size of the existing corpus far exceeds the number of experts available to analyze it. But the task is made difficult by the combination of limited annotated datasets and the high-resolution point-cloud representation of each tablet. To address this, we develop a convolution-inspired architecture that gradually down-scales the point cloud while integrating local neighbor information. The final down-scaled point cloud is then processed by computing neighbors in the feature space to include global information. Our method is compared with the state-of-the-art transformer-based network Point-BERT, and consistently obtains the best performance. Source code and data available at github.com/fhagelskjaer/cuneiform3d

Panoramic dense-prediction models, spanning semantic segmentation and depth estimation, are typically trained under a strict gravity-aligned assumption. Real-world captures, however, routinely violate it: handheld devices jitter and aerial platforms change attitude, so the camera is rarely upright. Under such 3D reorientation, standard spherical Transformers overfit global latitude cues and collapse. We introduce SO3UFormer, an architecture that learns intrinsic spherical features largely decoupled from the underlying coordinate frame, through three geometric components: (1) removing absolute latitude encoding, which breaks the dependence on the gravity axis; (2) quadrature-consistent spherical attention, which corrects for non-uniform sampling density; and (3) a gauge-aware relative positional bias built from local tangent-plane angles rather than global axes. A logit-space \emph{SO(3)}-consistency regularizer, used only during training, further suppresses residual discretization effects. To benchmark robustness, we introduce Pose35, a variant of Stanford2D3D perturbed by random rotations within $\pm 35^\circ$, and evaluate under a full, arbitrary \emph{SO(3)} stress test. There, the baseline SphereUFormer collapses from 67.53 \emph{mIoU} on Pose35 to 25.26 under the full \emph{SO(3)} test, whereas SO3UFormer reaches 72.03 on Pose35 and retains 70.67 under the same test. Similarly, on a second real-world dataset (Matterport3D) for segmentation and on panoramic depth estimation, SO3UFormer remains essentially rotation-invariant while the gravity-anchored baseline again loses most of its accuracy. Code and models are available at https://github.com/zhuqinfeng1999/SO3UFormer.

Online handwritten character recognition leverages stroke order and dynamic features, which generally provide higher accuracy and robustness compared with offline recognition. However, in practical applications, rotational deformations can disrupt the spatial layout of strokes, substantially reducing recognition accuracy. Extracting rotation-invariant features therefore remains a challenging open problem. In this work, we employ the Sliding Window Path Signature (SW-PS) to capture local structural features of characters, and introduce the lightweight Linear Recurrent Units (LRU) as the classifier. The LRU combine the fast incremental processing capability of recurrent neural networks (RNN) with the efficient parallel training of state space models (SSM), while reliably modelling dynamic stroke characteristics. We conducted recognition experiments with random rotation angle up to $\pm 180^{\circ}$ on three subsets of the CASIA-OLHWDB1.1 dataset: digits, English upper letters, and Chinese radicals. The accuracies achieved after ensemble learning were $99.62\%$, $96.67\%$, and $94.33\%$, respectively. Experimental results demonstrate that the proposed SW-PS+LRU framework consistently surpasses competing models in both convergence speed and test accuracy.

PCA can be used for rotation invariant features, describing a shape with its $p_{ab}=E[(x_i-E[x_a])(x_b-E[x_b])]$ covariance matrix approximating shape by ellipsoid, allowing for rotation invariants like its traces of powers. However, real shapes are usually much more complicated, hence there is proposed its extension to e.g. $p_{abc}=E[(x_a-E[x_a])(x_b-E[x_b])(x_c-E[x_c])]$ order-3 or higher tensors describing central moments, or polynomial times Gaussian allowing decodable shape descriptors of arbitrarily high accuracy, and their analogous rotation invariants. Its practical applications could be rotation-invariant features to include shape modulo rotation e.g. for molecular shape descriptors, or for up to rotation object recognition in 2D images/3D scans maybe also for 3D scene understanding, or shape similarity metric allowing inexpensive comparison of objects modulo rotation avoiding costly optimization over rotations.

Few-shot fine-grained image classification (FSFGIC) aims to classify similar images with limited labeled examples. This work highlights the critical yet underutilized role of phase information in capturing structural relationships within an image. This study introduces a novel plug-and-play amplitude-phase integration (API) module that effectively combines local and global frequency amplitude and phase information for obtaining more comprehensive feature descriptors. Additionally, a dedicated network, named PSF-Net, is proposed that adaptively fuses phase-based spatial and frequency information for FSFGIS. The designed PSF-Net can be easily integrated into standard episodic training architectures for end-to-end training from scratch. Extensive experiments on five public datasets demonstrate that the method outperforms existing state-of-the-art benchmarks.