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This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics ingredients based on the Koopman operator theory. In the offline step of the proposed framework, DMD constructs a low-rank linear surrogate model for the high dimensional quantities of interest (QoIs) derived from the (nonlinear) complex high fidelity models (HFMs) of unknown forms. Then in the online step, the resulting local reduced order bases (ROBs) and parametric reduced order models (PROMs) at the training parameter sample points are interpolated to construct a new PROM with the corresponding ROB for a new set of target/test parameter values. The interpolations need to be done on the appropriate manifolds within consistent sets of generalized coordinates. The proposed framework is illustrated by numerical examples for both linear and nonlinear problems. In particular, its advantages in computational costs and accuracy are demonstrated by the comparisons with projection-based proper orthogonal decomposition (POD)-PROM and Kriging.

Consistent motion estimation is fundamental for all mobile autonomous systems. While this sounds like an easy task, often, it is not the case because of changing environmental conditions affecting odometry obtained from vision, Lidar, or the wheels themselves. Unsusceptible to challenging lighting and weather conditions, radar sensors are an obvious alternative. Usually, automotive radars return a sparse point cloud, representing the surroundings. Utilizing this information to motion estimation is challenging due to unstable and phantom measurements, which result in a high rate of outliers. We introduce a credible and robust probabilistic approach to estimate the ego-motion based on these challenging radar measurements; intended to be used within a loosely-coupled sensor fusion framework. Compared to existing solutions, evaluated on the popular nuScenes dataset and others, we show that our proposed algorithm is more credible while not depending on explicit correspondence calculation.

Many recent state-of-the-art (SOTA) optical flow models use finite-step recurrent update operations to emulate traditional algorithms by encouraging iterative refinements toward a stable flow estimation. However, these RNNs impose large computation and memory overheads, and are not directly trained to model such stable estimation. They can converge poorly and thereby suffer from performance degradation. To combat these drawbacks, we propose deep equilibrium (DEQ) flow estimators, an approach that directly solves for the flow as the infinite-level fixed point of an implicit layer (using any black-box solver), and differentiates through this fixed point analytically (thus requiring $O(1)$ training memory). This implicit-depth approach is not predicated on any specific model, and thus can be applied to a wide range of SOTA flow estimation model designs. The use of these DEQ flow estimators allows us to compute the flow faster using, e.g., fixed-point reuse and inexact gradients, consumes $4\sim6\times$ times less training memory than the recurrent counterpart, and achieves better results with the same computation budget. In addition, we propose a novel, sparse fixed-point correction scheme to stabilize our DEQ flow estimators, which addresses a longstanding challenge for DEQ models in general. We test our approach in various realistic settings and show that it improves SOTA methods on Sintel and KITTI datasets with substantially better computational and memory efficiency.

Monocular SLAM in deformable scenes will open the way to multiple medical applications like computer-assisted navigation in endoscopy, automatic drug delivery or autonomous robotic surgery. In this paper we propose a novel method to simultaneously track the camera pose and the 3D scene deformation, without any assumption about environment topology or shape. The method uses an illumination-invariant photometric method to track image features and estimates camera motion and deformation combining reprojection error with spatial and temporal regularization of deformations. Our results in simulated colonoscopies show the method's accuracy and robustness in complex scenes under increasing levels of deformation. Our qualitative results in human colonoscopies from Endomapper dataset show that the method is able to successfully cope with the challenges of real endoscopies: deformations, low texture and strong illumination changes. We also compare with previous tracking methods in simpler scenarios from Hamlyn dataset where we obtain competitive performance, without needing any topological assumption.

Stereoscopy exposits a natural perception of distance in a scene, and its manifestation in 3D world understanding is an intuitive phenomenon. However, an innate rigid calibration of binocular vision sensors is crucial for accurate depth estimation. Alternatively, a monocular camera alleviates the limitation at the expense of accuracy in estimating depth, and the challenge exacerbates in harsh environmental conditions. Moreover, an optical sensor often fails to acquire vital signals in harsh environments, and radar is used instead, which gives coarse but more accurate signals. This work explores the utility of coarse signals from radar when fused with fine-grained data from a monocular camera for depth estimation in harsh environmental conditions. A variant of feature pyramid network (FPN) extensively operates on fine-grained image features at multiple scales with a fewer number of parameters. FPN feature maps are fused with sparse radar features extracted with a Convolutional neural network. The concatenated hierarchical features are used to predict the depth with ordinal regression. We performed experiments on the nuScenes dataset, and the proposed architecture stays on top in quantitative evaluations with reduced parameters and faster inference. The depth estimation results suggest that the proposed techniques can be used as an alternative to stereo depth estimation in critical applications in robotics and self-driving cars. The source code will be available in the following: \url{//github.com/MI-Hussain/RVMDE}.

This paper proposes a numerical method based on the Adomian decomposition approach for the time discretization, applied to Euler equations. A recursive property is demonstrated that allows to formulate the method in an appropriate and efficient way. To obtain a fully numerical scheme, the space discretization is achieved using the classical DG techniques. The efficiency of the obtained numerical scheme is demonstrated through numerical tests by comparison to exact solution and the popular Runge-Kutta DG method results.

Locating 3D objects from a single RGB image via Perspective-n-Points (PnP) is a long-standing problem in computer vision. Driven by end-to-end deep learning, recent studies suggest interpreting PnP as a differentiable layer, so that 2D-3D point correspondences can be partly learned by backpropagating the gradient w.r.t. object pose. Yet, learning the entire set of unrestricted 2D-3D points from scratch fails to converge with existing approaches, since the deterministic pose is inherently non-differentiable. In this paper, we propose the EPro-PnP, a probabilistic PnP layer for general end-to-end pose estimation, which outputs a distribution of pose on the SE(3) manifold, essentially bringing categorical Softmax to the continuous domain. The 2D-3D coordinates and corresponding weights are treated as intermediate variables learned by minimizing the KL divergence between the predicted and target pose distribution. The underlying principle unifies the existing approaches and resembles the attention mechanism. EPro-PnP significantly outperforms competitive baselines, closing the gap between PnP-based method and the task-specific leaders on the LineMOD 6DoF pose estimation and nuScenes 3D object detection benchmarks.

In this paper we propose a novel sparse optical flow (SOF)-based line feature tracking method for the camera pose estimation problem. This method is inspired by the point-based SOF algorithm and developed based on an observation that two adjacent images in time-varying image sequences satisfy brightness invariant. Based on this observation, we re-define the goal of line feature tracking: track two endpoints of a line feature instead of the entire line based on gray value matching instead of descriptor matching. To achieve this goal, an efficient two endpoint tracking (TET) method is presented: first, describe a given line feature with its two endpoints; next, track the two endpoints based on SOF to obtain two new tracked endpoints by minimizing a pixel-level grayscale residual function; finally, connect the two tracked endpoints to generate a new line feature. The correspondence is established between the given and the new line feature. Compared with current descriptor-based methods, our TET method needs not to compute descriptors and detect line features repeatedly. Naturally, it has an obvious advantage over computation. Experiments in several public benchmark datasets show our method yields highly competitive accuracy with an obvious advantage over speed.

Imposing consistency through proxy tasks has been shown to enhance data-driven learning and enable self-supervision in various tasks. This paper introduces novel and effective consistency strategies for optical flow estimation, a problem where labels from real-world data are very challenging to derive. More specifically, we propose occlusion consistency and zero forcing in the forms of self-supervised learning and transformation consistency in the form of semi-supervised learning. We apply these consistency techniques in a way that the network model learns to describe pixel-level motions better while requiring no additional annotations. We demonstrate that our consistency strategies applied to a strong baseline network model using the original datasets and labels provide further improvements, attaining the state-of-the-art results on the KITTI-2015 scene flow benchmark in the non-stereo category. Our method achieves the best foreground accuracy (4.33% in Fl-all) over both the stereo and non-stereo categories, even though using only monocular image inputs.

Substantial efforts have been devoted more recently to presenting various methods for object detection in optical remote sensing images. However, the current survey of datasets and deep learning based methods for object detection in optical remote sensing images is not adequate. Moreover, most of the existing datasets have some shortcomings, for example, the numbers of images and object categories are small scale, and the image diversity and variations are insufficient. These limitations greatly affect the development of deep learning based object detection methods. In the paper, we provide a comprehensive review of the recent deep learning based object detection progress in both the computer vision and earth observation communities. Then, we propose a large-scale, publicly available benchmark for object DetectIon in Optical Remote sensing images, which we name as DIOR. The dataset contains 23463 images and 192472 instances, covering 20 object classes. The proposed DIOR dataset 1) is large-scale on the object categories, on the object instance number, and on the total image number; 2) has a large range of object size variations, not only in terms of spatial resolutions, but also in the aspect of inter- and intra-class size variability across objects; 3) holds big variations as the images are obtained with different imaging conditions, weathers, seasons, and image quality; and 4) has high inter-class similarity and intra-class diversity. The proposed benchmark can help the researchers to develop and validate their data-driven methods. Finally, we evaluate several state-of-the-art approaches on our DIOR dataset to establish a baseline for future research.