Camera calibration is a crucial component in the realm of sports analytics, as it serves as the foundation to extract 3D information out of the broadcast images. Despite the significance of camera calibration research in sports analytics, progress is impeded by outdated benchmarking criteria. Indeed, the annotation data and evaluation metrics provided by most currently available benchmarks strongly favor and incite the development of sports field registration methods, i.e. methods estimating homographies that map the sports field plane to the image plane. However, such homography-based methods are doomed to overlook the broader capabilities of camera calibration in bridging the 3D world to the image. In particular, real-world non-planar sports field elements (such as goals, corner flags, baskets, ...) and image distortion caused by broadcast camera lenses are out of the scope of sports field registration methods. To overcome these limitations, we designed a new benchmarking protocol, named ProCC, based on two principles: (1) the protocol should be agnostic to the camera model chosen for a camera calibration method, and (2) the protocol should fairly evaluate camera calibration methods using the reprojection of arbitrary yet accurately known 3D objects. Indirectly, we also provide insights into the metric used in SoccerNet-calibration, which solely relies on image annotation data of viewed 3D objects as ground truth, thus implementing our protocol. With experiments on the World Cup 2014, CARWC, and SoccerNet datasets, we show that our benchmarking protocol provides fairer evaluations of camera calibration methods. By defining our requirements for proper benchmarking, we hope to pave the way for a new stage in camera calibration for sports applications with high accuracy standards.

A Universal Protocol to Benchmark Camera Calibration for Sports

Towards a new paradigm in intelligence-driven computational fluid dynamics simulations

In order to bridge the fundamental commonalities between imaging models of camera lenses with different principles and structures, allowing for an accurate description of imaging characteristics across a wide range of field-of-view (FOV), we have proposed a generic camera calibration method on the basis of the projection model optimization strategy. First, in order to cover the current mainstream projection models, piecewise functions for geometric projection models and a polynomial function for the fitting projection model are designed. Then, the corresponding camera multistation self-calibration bundle adjustment (BA) module is developed for various projection models. Further, by integrating the self-calibration BA algorithm into the northern goshawk optimization architecture, iterative optimization is performed on the projection model adjustment parameters, camera interior parameters, camera exterior parameters, and lens distortion parameters until the target reprojection (RP) error reaches the global minimum. The experimental results indicate that the calibration RP root mean square error in this method is 1/20 pixel for a 68° FOV camera, 1/13 pixel for an 84° FOV camera, 1/9 pixel for a 115° FOV camera, 1/9 pixel for a 135° FOV camera, and 1/6 pixel for a 180° FOV camera. This calibration method offers fast and versatile optimization for various projection model types, encompassing a wide range of projection functions. It can efficiently determine the optimal projection model and all imaging parameters for multiple cameras during the calibration process. 

A Camera Optimal Projection Model Identification and Calibration Method Based on the NGO-BA Architecture

Letter to the editor regarding "Three-dimensional videography using omnidirectional cameras: An approach inspired by the direct linear transformation method".

MTGNet: multi-label mesh quality evaluation using topology-guided graph neural network

Mesh quality is a major factor affecting the structure of computational fluid dynamics (CFD) calculations. Traditional mesh quality evaluation is based on the geometric factors of the mesh cells and does not effectively take into account the defects caused by the integrity of the mesh. Ensuring the generated meshes are of sufficient quality for numerical simulation requires considerable intervention by CFD professionals. In this paper, a Transformer-based network for automatic mesh quality evaluation (Gridformer), which translates the mesh quality evaluation into an image classification problem, is proposed. By comparing different mesh features, we selected the three features that highly influence mesh quality, providing reliability and interpretability for feature extraction work. To validate the effectiveness of Gridformer, we conduct experiments on the NACA-Market dataset. The experimental results demonstrate that Gridformer can automatically identify mesh integrity quality defects and has advantages in computational efficiency and prediction accuracy compared to widely used neural networks. Furthermore, a complete workflow for automatic generation of high-quality meshes based on Gridformer was established to facilitate automated mesh generation. This workflow can produce a high-quality mesh with a low-quality mesh input through automatic evaluation and optimization cycles. The preliminary implementation of automated mesh generation proves the versatility of Gridformer.

/pdf/evaluating-airfoil-mesh-quality-with-transformer-20hu1s58.pdf

Evaluating Airfoil Mesh Quality with Transformer

Low-cost camera calibration is vital in air and underwater photogrammetric applications. However, various lens distortions and the underwater environment influence are difficult to be covered by a universal distortion compensation model, and the residual distortions may still remain after conventional calibration. In this paper, we propose a combined physical and mathematical camera calibration method for low-cost cameras, which can adapt to both in-air and underwater environments. The commonly used physical distortion models are integrated to describe the image distortions. The combination is a high-order polynomial, which can be considered as basis functions to successively approximate the image deformation from the point of view of mathematical approximation. The calibration process is repeated until certain criteria are met and the distortions are reduced to a minimum. At the end, several sets of distortion parameters and stable camera interior orientation (IO) parameters act as the final camera calibration results. The Canon and GoPro in-air calibration experiments show that GoPro owns distortions seven times larger than Canon. Most Canon distortions have been described with the Australis model, while most decentering distortions for GoPro still exist. Using the proposed method, all the Canon and GoPro distortions are decreased to close to 0 after four calibrations. Meanwhile, the stable camera IO parameters are obtained. The GoPro Hero 5 Black underwater calibration indicates that four sets of distortion parameters and stable camera IO parameters are obtained after four calibrations. The camera calibration results show a difference between the underwater environment and air owing to the refractive and asymmetric environment effects. In summary, the proposed method improves the accuracy compared with the conventional method, which could be a flexible way to calibrate low-cost cameras for high accurate in-air and underwater measurement and 3D modeling applications.

/pdf/a-combined-physical-and-mathematical-calibration-method-for-srscc0f0.pdf

A Combined Physical and Mathematical Calibration Method for Low-Cost Cameras in the Air and Underwater Environment

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Evaluating Airfoil Mesh Quality with Transformer

A Combined Physical and Mathematical Calibration Method for Low-Cost Cameras in the Air and Underwater Environment