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The fisheye camera, with its unique wide field of view and other characteristics, has found extensive applications in various fields. However, the fisheye camera suffers from significant distortion compared to pinhole cameras, resulting in distorted images of captured objects. Fish-eye camera distortion is a common issue in digital image processing, requiring effective correction techniques to enhance image quality. This review provides a comprehensive overview of various methods used for fish-eye camera distortion correction. The article explores the polynomial distortion model, which utilizes polynomial functions to model and correct radial distortions. Additionally, alternative approaches such as panorama mapping, grid mapping, direct methods, and deep learning-based methods are discussed. The review highlights the advantages, limitations, and recent advancements of each method, enabling readers to make informed decisions based on their specific needs.

Vertical Sato-Tate states that the Frobenius trace of a randomly chosen elliptic curve over $\mathbb F_p$ tends to a semicircular distribution as $p\rightarrow \infty$. We go beyond this statement by considering the number of elliptic curves $N_{t,p}'$ with a given trace $t$ over $\mathbb F_p$ and characterizing the 2-dimensional distribution of $(t,N_{t,p}')$. In particular, this gives the distribution of the size of isogeny classes of elliptic curves over $\mathbb F_p$. Furthermore, we show a notion of stronger convergence for vertical Sato-Tate which states that the number of elliptic curves with Frobenius trace in an interval of length $p^\epsilon$ converges to the expected amount. The key step in the proof is to truncate Gekeler's infinite product formula, which relies crucially on an effective Chebotarev's density theorem that was recently developed by Pierce, Turnage-Butterbaugh and Wood., Comment: 27 pages, 4 figures. Minor edits for clarity

Stanley's inequalities for partially ordered sets establish important log-concavity relations for sequences of linear extensions counts. Their extremals however, i.e., the equality cases of these inequalities, were until now poorly understood with even conjectures lacking. In this work, we solve this problem by providing a complete characterization of the extremals of Stanley's inequalities. Our proof is based on building a new ``dictionary" between the combinatorics of partially ordered sets and the geometry of convex polytopes, which captures their extremal structures., Comment: 53 pages, 7 figures

Quantum coherence has wide-ranging applications from quantum thermodynamics to quantum metrology, quantum channel discrimination and even quantum biology. Thus, detecting and quantifying coherence are two fundamental problems in quantum resource theory. Here, we introduce feasible methods to detect and estimate the coherence by constructing coherence witnesses for any finite-dimensional states. Our coherence witnesses detect coherent states by testing whether the expectation value of the witness is negative or not. Two typical coherence witnesses are proposed and discussed based on our witness-constructing method, which are also used to estimate the robustness of coherence, $l_1$-norm and $l_2$-norm of coherence measures. Furthermore, we compare one of our coherence witness with a previously introduced witness, by proving that our witness is strictly stronger than that previous witness. We also present an application of coherence in a quantum metrology task, in which we estimate an unknown parameter by measuring our coherence witness., Comment: 7 pages, 2 figures

Cardiac coronary angiography is a major technology to assist doctors during cardiac interventional surgeries. Under the exposure of X-ray radiation, doctors inject contrast agents through catheters to determine the position and status of coronary vessels in real time. To get a coronary angiography video with a high frame rate, the doctor needs to increase the exposure frequency and intensity of the X-ray. This will inevitably increase the X-ray harm to both patients and surgeons. In this work, we innovatively utilize a deep-learning based video interpolation algorithm to interpolate coronary angiography videos. Moreover, we establish a new coronary angiography image dataset ,which contains 95,039 triplets images to retrain the video interpolation network model. Using the retrained network we synthesize high frame rate coronary angiography video from the low frame rate coronary angiography video. The average peak signal to noise ratio(PSNR) of those synthesized video frames reaches 34dB. Extensive experiment results demonstrate the feasibility of using the video frame interpolation algorithm to synthesize continuous and clear high frame rate coronary angiography video. With the help of this technology, doctors can significantly reduce exposure frequency and intensity of the X-ray during coronary angiography.

Thin-film lithium niobate on insulator (LNOI) has emerged as a superior integrated-photonics platform for linear, nonlinear, and electro-optics. Here we combine quasi-phase-matching, dispersion engineering, and tight mode confinement to realize nonlinear parametric processes with both high efficiency and wide wavelength tunability. On a millimeter-long, Z-cut LNOI waveguide, we demonstrate ultra-efficient ($1900\pm500 \% $W$^{-1}$cm$^{-2}$) and highly tunable (-1.71 nm/K) second-harmonic generation from 1530 to 1583 nm by type-0 quasi-phase-matching. Our technique is applicable to optical harmonic generation, quantum light sources, frequency conversion, and many other photonic information processing across visible to mid-IR spectral bands.

Coronary angiography is an indispensable assistive technique for cardiac interventional surgery. Segmentation and extraction of blood vessels from coronary angiography videos are very essential prerequisites for physicians to locate, assess and diagnose the plaques and stenosis in blood vessels. This article proposes a new video segmentation framework that can extract the clearest and most comprehensive coronary angiography images from a video sequence, thereby helping physicians to better observe the condition of blood vessels. This framework combines a 3D convolutional layer to extract spatial--temporal information from a video sequence and a 2D CE--Net to accomplish the segmentation task of an image sequence. The input is a few continuous frames of angiographic video, and the output is a mask of segmentation result. From the results of segmentation and extraction, we can get good segmentation results despite the poor quality of coronary angiography video sequences.

The reconstruction of three-dimensional models of coronary arteries is of great significance for the localization, evaluation and diagnosis of stenosis and plaque in the arteries, as well as for the assisted navigation of interventional surgery. In the clinical practice, physicians use a few angles of coronary angiography to capture arterial images, so it is of great practical value to perform 3D reconstruction directly from coronary angiography images. However, this is a very difficult computer vision task due to the complex shape of coronary blood vessels, as well as the lack of data set and key point labeling. With the rise of deep learning, more and more work is being done to reconstruct 3D models of human organs from medical images using deep neural networks. We propose an adversarial and generative way to reconstruct three dimensional coronary artery models, from two different views of angiographic images of coronary arteries. With 3D fully supervised learning and 2D weakly supervised learning schemes, we obtained reconstruction accuracies that outperform state-of-art techniques.

The dynamic dispatch (DD) of battery energy storage systems (BESSs) in microgrids integrated with volatile energy resources is essentially a multiperiod stochastic optimization problem (MSOP). Because the life span of a BESS is significantly affected by its charging and discharging behaviors, its lifecycle degradation costs should be incorporated into the DD model of BESSs, which makes it non-convex. In general, this MSOP is intractable. To solve this problem, we propose a reinforcement learning (RL) solution augmented with Monte-Carlo tree search (MCTS) and domain knowledge expressed as dispatching rules. In this solution, the Q-learning with function approximation is employed as the basic learning architecture that allows multistep bootstrapping and continuous policy learning. To improve the computation efficiency of randomized multistep simulations, we employed the MCTS to estimate the expected maximum action values. Moreover, we embedded a few dispatching rules in RL as probabilistic logics to reduce infeasible action explorations, which can improve the quality of the data-driven solution. Numerical test results show the proposed algorithm outperforms other baseline RL algorithms in all cases tested.