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We introduce Power Bundle Adjustment as an expansion type algorithm for solving large-scale bundle adjustment problems. It is based on the power series expansion of the inverse Schur complement and constitutes a new family of solvers that we call inverse expansion methods. We theoretically justify the use of power series and we prove the convergence of our approach. Using the real-world BAL dataset we show that the proposed solver challenges the state-of-the-art iterative methods and significantly accelerates the solution of the normal equation, even for reaching a very high accuracy. This easy-to-implement solver can also complement a recently presented distributed bundle adjustment framework. We demonstrate that employing the proposed Power Bundle Adjustment as a sub-problem solver significantly improves speed and accuracy of the distributed optimization.

Conditional normalizing flows can generate diverse image samples for solving inverse problems. Most normalizing flows for inverse problems in imaging employ the conditional affine coupling layer that can generate diverse images quickly. However, unintended severe artifacts are occasionally observed in the output of them. In this work, we address this critical issue by investigating the origins of these artifacts and proposing the conditions to avoid them. First of all, we empirically and theoretically reveal that these problems are caused by ``exploding variance'' in the conditional affine coupling layer for certain out-of-distribution (OOD) conditional inputs. Then, we further validated that the probability of causing erroneous artifacts in pixels is highly correlated with a Mahalanobis distance-based OOD score for inverse problems in imaging. Lastly, based on our investigations, we propose a remark to avoid exploding variance and then based on it, we suggest a simple remedy that substitutes the affine coupling layers with the modified rational quadratic spline coupling layers in normalizing flows, to encourage the robustness of generated image samples. Our experimental results demonstrated that our suggested methods effectively suppressed critical artifacts occurring in normalizing flows for super-resolution space generation and low-light image enhancement without compromising performance.

Attention-based arbitrary style transfer studies have shown promising performance in synthesizing vivid local style details. They typically use the all-to-all attention mechanism: each position of content features is fully matched to all positions of style features. However, all-to-all attention tends to generate distorted style patterns and has quadratic complexity. It virtually limits both the effectiveness and efficiency of arbitrary style transfer. In this paper, we rethink what kind of attention mechanism is more appropriate for arbitrary style transfer. Our answer is a novel all-to-key attention mechanism: each position of content features is matched to key positions of style features. Specifically, it integrates two newly proposed attention forms: distributed and progressive attention. Distributed attention assigns attention to multiple key positions; Progressive attention pays attention from coarse to fine. All-to-key attention promotes the matching of diverse and reasonable style patterns and has linear complexity. The resultant module, dubbed StyA2K, has fine properties in rendering reasonable style textures and maintaining consistent local structure. Qualitative and quantitative experiments demonstrate that our method achieves superior results than state-of-the-art approaches.

An implicit variable-step BDF2 scheme is established for solving the space fractional Cahn-Hilliard equation, involving the fractional Laplacian, derived from a gradient flow in the negative order Sobolev space $H^{-\alpha}$, $\alpha\in(0,1)$. The Fourier pseudo-spectral method is applied for the spatial approximation. The proposed scheme inherits the energy dissipation law in the form of the modified discrete energy under the sufficient restriction of the time-step ratios. The convergence of the fully discrete scheme is rigorously provided utilizing the newly proved discrete embedding type convolution inequality dealing with the fractional Laplacian. Besides, the mass conservation and the unique solvability are also theoretically guaranteed. Numerical experiments are carried out to show the accuracy and the energy dissipation both for various interface widths. In particular, the multiple-time-scale evolution of the solution is captured by an adaptive time-stepping strategy in the short-to-long time simulation.

Magnetic resonance imaging serves as an essential tool for clinical diagnosis. However, it suffers from a long acquisition time. The utilization of deep learning, especially the deep generative models, offers aggressive acceleration and better reconstruction in magnetic resonance imaging. Nevertheless, learning the data distribution as prior knowledge and reconstructing the image from limited data remains challenging. In this work, we propose a novel Hankel-k-space generative model (HKGM), which can generate samples from a training set of as little as one k-space data. At the prior learning stage, we first construct a large Hankel matrix from k-space data, then extract multiple structured k-space patches from the large Hankel matrix to capture the internal distribution among different patches. Extracting patches from a Hankel matrix enables the generative model to be learned from redundant and low-rank data space. At the iterative reconstruction stage, it is observed that the desired solution obeys the learned prior knowledge. The intermediate reconstruction solution is updated by taking it as the input of the generative model. The updated result is then alternatively operated by imposing low-rank penalty on its Hankel matrix and data consistency con-strain on the measurement data. Experimental results confirmed that the internal statistics of patches within a single k-space data carry enough information for learning a powerful generative model and provide state-of-the-art reconstruction.

Based on the continuum model for granular media developed in Dunatunga et al. we propose a mesh-free generalized finite difference method for the simulation of granular flows. The model is given by an elasto-viscoplastic model with a yield criterion using the $\mu(I)$ rheology from Jop et al. The numerical procedure is based on a mesh-free particle method with a least squares approximation of the derivatives in the balance equations combined with the numerical algorithm developed in Dunatunga et al. to compute the plastic stresses. The method is numerically tested and verified for several numerical experiments including granular column collapse and rigid body motion in granular materials. For comparison a nonlinear microscopic model from Lacaze et al. is implemented and results are compared to the those obtained from the continuum model for granular column collapse and rigid body coupling to granular flow.

In-home gait analysis is important for providing early diagnosis and adaptive treatments for individuals with gait disorders. Existing systems include wearables and pressure mats, but they have limited scalability. Recent studies have developed vision-based systems to enable scalable, accurate in-home gait analysis, but it faces privacy concerns due to the exposure of people's appearances. Our prior work developed footstep-induced structural vibration sensing for gait monitoring, which is device-free, wide-ranged, and perceived as more privacy-friendly. Although it has succeeded in temporal gait event extraction, it shows limited performance for spatial gait parameter estimation due to imprecise footstep localization. In particular, the localization error mainly comes from the estimation error of the wave arrival time at the vibration sensors and its error propagation to wave velocity estimations. Therefore, we present GaitVibe+, a vibration-based footstep localization method fused with temporarily installed cameras for in-home gait analysis. Our method has two stages: fusion and operating. In the fusion stage, both cameras and vibration sensors are installed to record only a few trials of the subject's footstep data, through which we characterize the uncertainty in wave arrival time and model the wave velocity profiles for the given structure. In the operating stage, we remove the camera to preserve privacy at home. The footstep localization is conducted by estimating the time difference of arrival (TDoA) over multiple vibration sensors, whose accuracy is improved through the reduced uncertainty and velocity modeling during the fusion stage. We evaluate GaitVibe+ through a real-world experiment with 50 walking trials. With only 3 trials of multi-modal fusion, our approach has an average localization error of 0.22 meters, which reduces the spatial gait parameter error from 111% to 27%.

Estimating human pose and shape from monocular images is a long-standing problem in computer vision. Since the release of statistical body models, 3D human mesh recovery has been drawing broader attention. With the same goal of obtaining well-aligned and physically plausible mesh results, two paradigms have been developed to overcome challenges in the 2D-to-3D lifting process: i) an optimization-based paradigm, where different data terms and regularization terms are exploited as optimization objectives; and ii) a regression-based paradigm, where deep learning techniques are embraced to solve the problem in an end-to-end fashion. Meanwhile, continuous efforts are devoted to improving the quality of 3D mesh labels for a wide range of datasets. Though remarkable progress has been achieved in the past decade, the task is still challenging due to flexible body motions, diverse appearances, complex environments, and insufficient in-the-wild annotations. To the best of our knowledge, this is the first survey to focus on the task of monocular 3D human mesh recovery. We start with the introduction of body models and then elaborate recovery frameworks and training objectives by providing in-depth analyses of their strengths and weaknesses. We also summarize datasets, evaluation metrics, and benchmark results. Open issues and future directions are discussed in the end, hoping to motivate researchers and facilitate their research in this area. A regularly updated project page can be found at //github.com/tinatiansjz/hmr-survey.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.