We introduce Fengbo, a pipeline entirely in Clifford Algebra to solve 3D partial differential equations (PDEs) specifically for computational fluid dynamics (CFD). Fengbo is an architecture composed of only 3D convolutional and Fourier Neural Operator (FNO) layers, all working in 3D Clifford Algebra. It models the PDE solution problem as an interpretable mapping from the geometry to the physics of the problem. Despite having just few layers, Fengbo achieves competitive accuracy, superior to 5 out of 6 proposed models reported in \cite{li2024geometry} for the $\emph{ShapeNet Car}$ dataset, and it does so with only 42 million trainable parameters, at a reduced computational complexity compared to graph-based methods, and estimating jointly pressure \emph{and} velocity fields. In addition, the output of each layer in Fengbo can be clearly visualised as objects and physical quantities in 3D space, making it a whitebox model. By leveraging Clifford Algebra and establishing a direct mapping from the geometry to the physics of the PDEs, Fengbo provides an efficient, geometry- and physics-aware approach to solving complex PDEs.

We propose LiteReality, a novel pipeline that converts RGB-D scans of indoor environments into compact, realistic, and interactive 3D virtual replicas. LiteReality not only reconstructs scenes that visually resemble reality but also supports key features essential for graphics pipelines—such as object individuality, articulation, high-quality physically based rendering materials. At its core, LiteReality first performs scene understanding and parses the results into a coherent 3D layout and objects, with the help of a structured scene graph. It then reconstructs the scene by retrieving the most visually similar 3D artist-crafted models from a curated asset database. Later, the Material Painting module enhances the realism of retrieved objects by recovering high-quality, spatially varying materials. Finally, the reconstructed scene is integrated into a simulation engine with basic physical properties applied to enable interactive behavior. The resulting scenes are compact, editable, and fully compatible with standard graphics pipelines, making them suitable for applications in AR/VR, gaming, robotics, and digital twins. In addition, LiteReality introduces a training-free object retrieval module that achieves state-of-the-art similarity performance, as benchmarked on the Scan2CAD dataset, along with a robust Material Painting module capable of transferring appearances from images of any style to 3D assets—even in the presence of severe misalignment, occlusion, and poor lighting. We demonstrate the effectiveness of LiteReality on both real-life scans and public datasets.

Heart rate is an important indicator of newborn health status. Conventional wired heart rate monitoring is affected by motion, can limit parental bonding and is prone to damage the fragile newborn skin. Video-based heart rate monitoring in adults has shown potential for the assessment of cardiac functions in optimal acquisition conditions. However, automated methods adapted for neonates, trained with limited sample sizes and capable of handling occlusions and variable illumination, still need to be explored. This work proposes a new deep-learning pipeline for video-based neonatal heart rate measurement, integrating color and infrared signals from mul-tiple neonatal body regions. We train deep learning models for pose estimation and heart rate detection in a pilot cohort of five neonates recorded in the clinic for up to 60 minutes. Our methods show generalization in a leave-one-out cross-validation scheme; the newborn pose estimation model presents high performance (average precision=0.85±0.07), while the heart rate detection model achieves a mean absolute error of 3.83±1.22 beats per minute compared to the electrocardiogram heart rate. Automated video-based heart rate measurement could provide a non-contact, low-cost complement to current HR monitoring technologies in the clinic or outpatient settings.

We introduce CGAPoseNet+GCAN, which enhances CGAPoseNet, an architecture for camera pose regression, with a Geometric Clifford Algebra Network (GCAN). With the addition of the GCAN we obtain a geometry-aware pipeline for camera pose regression from RGB images only. CGAPoseNet employs Clifford Geometric Algebra to unify quaternions and translation vectors into a single mathematical object, the motor, which can be used to uniquely describe camera poses. CGAPoseNet can obtain comparable results to other approaches without the need of expensive tuning of the loss function or additional information about the scene, such as 3D point clouds, which might not always be available. CGAPoseNet, however, like several approaches in the literature, only learns to predict motor coefficients, and it is unaware of the mathematical space in which predictions sit in and of their geometrical meaning. By leveraging recent advances in Geometric Deep Learning, we modify CGAPoseNet with a GCAN: proposals of possible motor coefficients associated with a camera frame are obtained from the InceptionV3 backbone, and the GCAN downsamples them to a single motor through a sequence of layers that work in ${{\mathcal{G}}_{4,0}}$0. The network is hence geometry-aware, has multivector-valued inputs, weights and biases and preserves the grade of the objects that it receives in input. CGAPoseNet+GCAN has almost 4 million fewer trainable parameters, it reduces the average rotation error by 41% and the average translation error by 8.8% compared to CGAPoseNet. Similarly, it reduces rotation and translation errors by 32.6% and 19.9%, respectively, compared to the best performing PoseNet strategy. CGAPoseNet+GCAN reaches the state-of-the-art results on 13 commonly employed datasets. To the best of our knowledge, it is the first experiment in GCANs applied to the problem of camera pose regression.

Variable Speed Limit (VSL) is a commonly applied active traffic management measure for urban motorways. In recent years, model-based and model-free approaches have been extensively adopted to solve VSL optimization problems. However, the success of model-based VSL relies heavily on the nature of the environmental model adopted (e.g., traffic flow model). Implicit environment models may result in inappropriate control actions. Although model-free approaches are able to directly map raw measurements to control actions without a need for an environment model, they usually require large amounts of training data. In order to address these issues, we propose an Imagination-Augmented Agent (I2A) for VSL control. The I2A consists an imagination path and a model-free path, which work together to generate appropriate control actions. The simulation results show that the proposed I2A agent outperforms other tested Reinforcement Learning (RL) agents in terms of Total Time Spent and bottleneck volume.

Graph Self-Supervised Learning (GSSL) provides a robust pathway for acquiring embeddings without expert labelling, a capability that carries profound implications for molecular graphs due to the staggering number of potential molecules and the high cost of obtaining labels. However, GSSL methods are designed not for optimisation within a specific domain but rather for transferability across a variety of downstream tasks. This broad applicability complicates their evaluation. Addressing this challenge, we present "Molecular Graph Representation Evaluation" (MOLGRAPHEVAL), generating detailed profiles of molecular graph embeddings with interpretable and diversified attributes. MOLGRAPHEVAL offers a suite of probing tasks grouped into three categories: (i) generic graph, (ii) molecular substructure, and (iii) embedding space properties. By leveraging MOLGRAPHEVAL to benchmark existing GSSL methods against both current downstream datasets and our suite of tasks, we uncover significant inconsistencies between inferences drawn solely from existing datasets and those derived from more nuanced probing. These findings suggest that current evaluation methodologies fail to capture the entirety of the landscape.

Traffic prediction, as a core component of intelligent transportation systems (ITS), has been investigated thoroughly in the literature. Nevertheless, timely accurate traffic prediction still remains an open challenge due to the nonlinearities and complex patterns of traffic flows. In addition, most of the existing traffic prediction methods focus on grid-based computing problems (e.g., crowd in-out flow prediction) and point-based computing problems (e.g., traffic detector data prediction), ignoring the segment-based traffic prediction tasks. In this study, we propose an attention-based spatiotemporal graph attention network (AST-GAT) for segment-level traffic speed prediction. In particular, a multi-head graph attention block is designed to capture the spatial dependencies among road segments. Then, a component fusion block is built for speed, volume, and weather information integration. Finally, an attention-based Long short-term memory (LSTM) block is constructed for temporal dependency learning as well as segment-based speed prediction. Experiments on a real-world dataset from Highways England demonstrate that the proposed AST-GAT model outperforms the state-of-the-art baselines, providing an efficient tool for segment-based traffic prediction and therefore filling the gap between point-based and grid-based predictions.

We describe a simple pre-training approach for point clouds. It works in three steps: 1. Mask all points occluded in a camera view; 2. Learn an encoder-decoder model to reconstruct the occluded points; 3. Use the encoder weights as initialisation for downstream point cloud tasks. We find that even when we pre-train on a single dataset (ModelNet40), this method improves accuracy across different datasets and encoders, on a wide range of downstream tasks. Specifically, we show that our method outperforms previous pre-training methods in object classification, and both part-based and semantic segmentation tasks. We study the pre-trained features and find that they lead to wide downstream minima, have high transformation invariance, and have activations that are highly correlated with part labels. Code and data are available at: https://github.com/hansen7/OcCo

Abstract Inverse kinematics (IK) is the use of kinematic equations to determine the joint parameters of a manipulator so that the end effector moves to a desired position; IK can be applied in many areas, including robotics, engineering, computer graphics and video games. In this survey, we present a comprehensive review of the IK problem and the solutions developed over the years from the computer graphics point of view. The paper starts with the definition of forward and IK, their mathematical formulations and explains how to distinguish the unsolvable cases, indicating when a solution is available. The IK literature in this report is divided into four main categories: the analytical , the numerical , the data‐driven and the hybrid methods. A timeline illustrating key methods is presented, explaining how the IK approaches have progressed over the years. The most popular IK methods are discussed with regard to their performance, computational cost and the smoothness of their resulting postures, while we suggest which IK family of solvers is best suited for particular problems. Finally, we indicate the limitations of the current IK methodologies and propose future research directions.

Abstract Forward and Backward Reaching Inverse Kinematics (FABRIK) is a recent iterative inverse kinematics solver that became very popular because of its simplicity, convergence speed and control performance, especially in models with multiple end effectors. In this paper, we extend and/or adjust FABRIK to be used in problems with leaf joints and closed‐loop chains and to control a fixed inter‐joint distance in a kinetic chain with unsteady data. In addition, we provide optimisation solutions when the target is unreachable and a proof of convergence when a solution is available. We also present various techniques for constraining anthropometric and robotic joint models using FABRIK and provide clarifications and solutions to many questions raised since the first publication of FABRIK. Finally, a human‐like model that has been structured hierarchically and sequentially using FABRIK is presented, utilising most of the suggested joint models; it can efficiently trace targets in real time, without oscillations or discontinuities, verifying the effectiveness of FABRIK. Copyright © 2015 John Wiley & Sons, Ltd.

This paper introduces a pantomimic gesture interface, which classifies human hand gestures using unmanned aerial vehicle (UAV) behavior recordings as training data. We argue that pantomimic gestures are more intuitive than iconic gestures and show that a pantomimic gesture recognition strategy using micro-UAV behavior recordings can be more robust than one trained directly using hand gestures. Hand gestures are isolated by applying a maximum information criterion, with features extracted using principal component analysis and compared using a nearest neighbor classifier. These features are biased in that they are better suited to classifying certain behaviors. We show how a Bayesian update step accounting for the geometry of training features compensates for this, resulting in fairer classification results, and introduce a weighted voting system to aid in sequence labeling.

Relative (comparative) attributes are promising for thematic ranking of visual entities, which also aids in recognition tasks. However, attribute rank learning often requires a substantial amount of relational supervision, which is highly tedious, and apparently impractical for real-world applications. In this paper, we introduce the Semantic Transform, which under minimal supervision, adaptively finds a semantic feature space along with a class ordering that is related in the best possible way. Such a semantic space is found for every attribute category. To relate the classes under weak supervision, the class ordering needs to be refined according to a cost function in an iterative procedure. This problem is ideally NP-hard, and we thus propose a constrained search tree formulation for the same. Driven by the adaptive semantic feature space representation, our model achieves the best results to date for all of the tasks of relative, absolute and zero-shot classification on two popular datasets.

Current methods for formation of detected chess-board vertices into a grid structure tend to be weak in situations with a warped grid, and false and missing vertex-features. In this paper we present a highly robust, yet efficient, scheme suitable for inference of regular 2D square mesh structure from vertices recorded both during projection of a chess-board pattern onto 3D objects, and in the more simple case of camera calibration. Examples of the method's performance in a lung function measuring application, observing chess-boards projected on to patients' chests, are given. The method presented is resilient to significant surface deformation, and tolerates inexact vertex-feature detection. This robustness results from the scheme's novel exploitation of feature orientation information.

In this study, the authors describe two-dimensional direction finding and signal polarisation estimation from a cylindrical conformal array consisting of directional and polarised antenna elements. Firstly, a simple and general transformation procedure, based on the mathematical framework of geometric algebra, is presented for arbitrary conformal arrays with polarised and directional antennas. Subsequently, the authors utilise the symmetry of cylindrical arrays to estimate signal parameters via rotational invariance techniques. The authors show how to iteratively estimate the azimuth and elevation angles of the incident signal, as well as its polarisation. To illustrate the versatility of this method, the results of simulations on a 3×4 cylindrical conformal array are shown and discussed.

Structured Light Plethysmography (SLP) is a novel non-invasive method that uses structured light to perform pulmonary function testing that does not require physical contact with a patient. The technique produces an estimate of chest wall volume changes over time. A patient is observed continuously by two cameras and a known pattern of light (i.e. structured light) is projected onto the chest using an off-the-shelf projector. Corner features from the projected light pattern are extracted, tracked and brought into correspondence for both camera views over successive frames. A novel self calibration algorithm recovers the intrinsic and extrinsic camera parameters from these point correspondences. This information is used to reconstruct a surface approximation of the chest wall and several novel ideas for 'cleaning up' the reconstruction are used. The resulting volume and derived statistics (e.g. FVC, FEV) agree very well with data taken with a spirometer. © 2010. The copyright of this document resides with its authors.

Since the pioneering work of Gibson in 1950, Shape-From-Texture has been considered by researchers as a hard problem, mainly due to restrictive assumptions which often limit its applicability. We assume a very general stochastic homogeneity and perspective camera model, for both deterministic and stochastic textures. A multi-scale distortion is efficiently estimated with a previously presented method based on Fourier analysis and Gabor filters. The novel 3D reconstruction method that we propose applies to general shapes, and includes non-developable and extensive surfaces. Our algorithm is accurate, robust and compares favorably to the present state of the art of Shape-From-Texture. Results show its application to non-invasively study shape changes with laid-on textures, while rendering and re-texturing of cloth is suggested for future work.

Shape from texture has received much attention in the past few decades. We propose a computationally efficient method to extract 3D planar surface orientation from the spectral variations of a visual texture. Under the assumption of homogeneity, the texture is represented by the novel method of identifying ridges of its Fourier transform. Local spatial frequencies are then computed using a minimal set of selected Gabor filters. Under perspective projection, frequencies are backprojected and orientation is computed so as to minimize the variance of the frequencies' backprojections. A comparative study with two existing methods, and experimentation on simulated and real texture images is given.

The aim of optical motion capture is to sequentially estimate the true state X of the subject (generally an articulated body) at any time instant t/sub k/ from a set of data D/sub k/, captured by N calibrated cameras each of resolution U/spl times/V pixels. Our aim is to achieve this without the need for markers. This is to enhance both utility and portability for the motion capture system and to render it suitable for surveillance issues. Even though several stochastic techniques to address this issue exist, we aim to solve this problem in a deterministic way, for future real-time performance. We adopt a Bayesian framework under which we employ a 3D articulated model M and a rendering function /spl Lambda/ to describe the data. Unlike other existing approaches [R. Urtasun et al. (2004), J. Deutscher et al. (2000)], we solely use silhouette matching to obtain a measure of how well the model describes the data.

Abstract Model-based optical motion capture systems require knowledge of the position of the markers relative to the underlying skeleton, the lengths of the skeleton's limbs, and which limb each marker is attached to. These model parameters are typically assumed and entered into the system manually, although techniques exist for calculating some of them, such as the position of the markers relative to the skeleton's joints. We present a fully automatic procedure for determining these model parameters. It tracks the 2D positions of the markers on the cameras' image planes and determines which markers lie on each limb before calculating the position of the underlying skeleton. The only assumption is that the skeleton consists of rigid limbs connected with ball joints. The proposed system is demonstrated on a number of real data examples and is shown to calculate good estimates of the model parameters in each.

A new method for estimating the pose of a person in a marker-based visual motion capture system is presented. In such systems, certain markers are not detected at each time frame due to occlusion by the subject. It is proposed to estimate the person's pose subject to the constraint that non-detected markers remain occluded and that detected markers remain visible. In this paper, the complete posterior PDF for the person's pose is developed using the constraints mentioned above, as is a least squares solution for determining its maximum. It is shown that the new technique is able to correctly estimate a variety of poses in which many marker occlusions occur and in which typical motion capture systems fail.

www-sigproc.cam.ac.uk/vision This paper describes a scheme for modelling and tracking the motion of ar-ticulated bodies using a number of video cameras. The aim is to obtain com-plete and accurate information on the three-dimensional location and motion of the bodies over time. Applications include medicine, sports analysis and motion capture for animation. Feature extraction is avoided by placing markers at the joints of the body so that model selection, marker-to-measured-point association, occlusion and the choice of tracking filter are the important issues. While the scheme is gen-eral for any number of cameras, emphasis is placed on systems with a small number of cameras where occlusions are a major problem. The system is an amalgamation of new ideas and existing techniques drawn from a variety of disciplines such as machine vision, geometric algebra and radar tracking the-ory, which have been extended and developed for the marked joints/multiple camera problem. The proposed schemes for modelling and tracking would be easily adapted to markerless motion capture. The paper concludes with examples of the system successfully tracking limb motion using three cameras. 1

A central task of computer vision is to automatically recognize objects in real-world scenes. The parameters defining image and object spaces can vary due to lighting conditions, camera calibration and viewing positions. It is therefore desirable to look for geometric properties of the object which remain invariant under such changes. In this paper we present geometric algebra as a complete framework for the theory and computation of projective invariants formed from points and lines in computer vision. We will look at the formation of 3D projective invariants from multiple images, show how they can be formed from image coordinates and estimated tensors (F, fundamental matrix and T, trilinear tensor) and give results on simulated and real data.

The Creep–and–Merge (CAM) segmentation system (described in [3, 2]) is a novel architecture for region-based segmentation; it is designed to be efficient, insensitive to noise, scale and image geometry, capable of applying the widest range of statistical models, and to contain no adjustable parameters. This paper describes the continuing development of higher–level processing models utilising this system: we present a geometric (“true”) corner detector with good performance, and give qualitative and quantitative comparisons with other leading systems. 1

We present geometric algebra as a new framework for the theory and computation of invariants and multiple-view constraints in computer vision. We discuss the formation of 3D projective invariants and a wholly geometric formulation of constraints from a number of images.

We present geometric algebra as system for analysing the geometry of multiple-view images. The power of this approach is illustrated by giving purely geometric derivations of the constraints, for point and line correspondences in n-views and via a discussion of projective structure.

We present geometric algebra, as a new, framework for the theory and computation of invariants in computer vision and compare it with the currently popular Grassmann-Cayley algebra. We also discuss the formation, of 3D projective invariants in terms of image coordinates.