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The lightweight Multi-state Constraint Kalman Filter (MSCKF) has been well-known for its high efficiency, in which the delayed update has been usually adopted since its proposal. This work investigates the immediate update strategy of MSCKF based on timely reconstructed 3D feature points and measurement constraints. The differences between the delayed update and the immediate update are theoretically analyzed in detail. It is found that the immediate update helps construct more observation constraints and employ more filtering updates than the delayed update, which improves the linearization point of the measurement model and therefore enhances the estimation accuracy. Numerical simulations and experiments show that the immediate update strategy significantly enhances MSCKF even with a small amount of feature observations., Comment: 8 pages, 5 figures

Seismic imaging from sparsely acquired data faces challenges such as low image quality, discontinuities, and migration swing artifacts. Existing convolutional neural network (CNN)-based methods struggle with complex feature distributions and cannot effectively assess uncertainty, making it hard to evaluate the reliability of their processed results. To address these issues, we propose a new method using a generative diffusion model (GDM). Here, in the training phase, we use the imaging results from sparse data as conditional input, combined with noisy versions of dense data imaging results, for the network to predict the added noise. After training, the network can predict the imaging results for test images from sparse data acquisition, using the generative process with conditional control. This GDM not only improves image quality and removes artifacts caused by sparse data, but also naturally evaluates uncertainty by leveraging the probabilistic nature of the GDM. To overcome the decline in generation quality and the memory burden of large-scale images, we develop a patch fusion strategy that effectively addresses these issues. Synthetic and field data examples demonstrate that our method significantly enhances imaging quality and provides effective uncertainty quantification.

In this paper we derive new second-order optimality conditions for a very general set-constrained optimization problem where the underlying set may be nononvex. We consider local optimality in specific directions (i.e., optimal in a directional neighborhood) in pursuit of developing these new optimality conditions. First-order necessary conditions for local optimality in given directions are provided by virtue of the corresponding directional normal cones. Utilizing the classical and/or the lower generalized support function, we obtain new second-order necessary and sufficient conditions for local optimality of general nonconvex constrained optimization problem in given directions via both the corresponding asymptotic second-order tangent cone and outer second-order tangent set. Our results do not require convexity and/or nonemptyness of the outer second-order tangent set. This is an important improvement to other results in the literature since the outer second-order tangent set can be nonconvex and empty even when the set is convex.

The traditional GNSS-aided inertial navigation system (INS) usually exploits the extended Kalman filter (EKF) for state estimation, and the initial attitude accuracy is key to the filtering performance. To spare the reliance on the initial attitude, this work generalizes the previously proposed trident quaternion within the framework of Clifford algebra to represent the extended pose, IMU biases and lever arms on the Lie group. Consequently, a quasi-group-affine system is established for the low-cost INS/GNSS integrated navigation system, and the right-error Clifford algebra-based EKF (Clifford-RQEKF) is accordingly developed. The iterated filtering approach is further applied to significantly improve the performances of the Clifford-RQEKF and the previously proposed trident quaternion-based EKFs. Numerical simulations and experiments show that all iterated filtering approaches fulfill the fast and global convergence without the prior attitude information, whereas the iterated Clifford-RQEKF performs much better than the others under especially large IMU biases.

We present the BioImage$.$IO Chatbot, an AI assistant powered by Large Language Models and supported by a community-driven knowledge base and toolset. This chatbot is designed to cater to a wide range of user needs through a flexible extension mechanism that spans from information retrieval to AI-enhanced analysis and microscopy control. Embracing open-source principles, the chatbot is designed to evolve through community contributions. By simplifying navigation through the intricate bioimaging landscape, the BioImage$.$IO Chatbot empowers life sciences to progress by leveraging the collective expertise and innovation of its users., Comment: 15 pages, 2 figures

We present JDLL, an agile Java library that offers a comprehensive toolset/API to unify the development of high-end applications of DL for bioimage analysis and to streamline their installation and maintenance. JDLL provides all the functions required to consume DL models seamlessly, without being burdened by the configuration of the Python-based DL frameworks, within Java bioimage informatics platforms. Moreover, it allows the deployment of pre-trained models in the Bioimage Model Zoo (BMZ) by shipping the logic to connect to the BMZ website, download and run a selected model inference., Comment: New version with new figure and updated links

Through digital imaging, microscopy has evolved from primarily being a means for visual observation of life at the micro- and nano-scale, to a quantitative tool with ever-increasing resolution and throughput. Artificial intelligence, deep neural networks, and machine learning are all niche terms describing computational methods that have gained a pivotal role in microscopy-based research over the past decade. This Roadmap is written collectively by prominent researchers and encompasses selected aspects of how machine learning is applied to microscopy image data, with the aim of gaining scientific knowledge by improved image quality, automated detection, segmentation, classification and tracking of objects, and efficient merging of information from multiple imaging modalities. We aim to give the reader an overview of the key developments and an understanding of possibilities and limitations of machine learning for microscopy. It will be of interest to a wide cross-disciplinary audience in the physical sciences and life sciences.

Strapdown inertial navigation research involves the parameterization and computation of the attitude, velocity and position of a rigid body in a chosen reference frame. The community has long devoted to finding the most concise and efficient representation for the strapdown inertial navigation system (INS). The current work is motivated by simplifying the existing dual quaternion representation of the kinematic model. This paper proposes a compact and elegant representation of the body's attitude, velocity and position, with the aid of a devised trident quaternion tool in which the position is accounted for by adding a second imaginary part to the dual quaternion. Eventually, the kinematics of strapdown INS are cohesively unified in one concise differential equation, which bears the same form as the classical attitude quaternion equation. In addition, the computation of this trident quaternion-based kinematic equation is implemented with the recently proposed functional iterative integration approach. Numerical results verify the analysis and show that incorporating the new representation into the functional iterative integration scheme achieves high inertial navigation computation accuracy as well., Comment: 10 pages, 5 figures

This work deals with error models for trident quaternion framework proposed in the companion paper (Part I) and further uses them to investigate the odometer-aided static/in-motion inertial navigation attitude alignment for land vehicles. By linearizing the trident quaternion kinematic equation, the left and right trident quaternion error models are obtained, which are found to be equivalent to those derived from profound group affine. The two error models are used to design their corresponding extended Kalman filters (EKF), namely, the left-quaternion EKF (LQEKF) and the right-quaternion EKF (RQEKF). Simulations and field tests are conducted to evaluate their actual performances. Owing to the high estimation consistency, the L/RQEKF converge much faster in the static alignment than the traditional error model-based EKF, even under arbitrary large heading initialization. For the in-motion alignment, the L/RQEKF possess much larger convergence region than the traditional EKF does, although they still require the aid of attitude initialization so as to avoid large initial attitude errors., Comment: 17 pages, 13 figures