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Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…

This manuscript provides a collection of new methods for the automated detection of non-overlapping ellipses from edge points. The methods introduce new developments in: (i) robust Monte Carlo-based ellipse fitting to 2-dimensional (2D)…

We present an adaptive regularization algorithm that can be effectively applied to the optimization problem in deep learning framework. Our regularization algorithm aims to take into account the fitness of data to the current state of model…

Cloud-related parameterizations remain a leading source of uncertainty in climate projections. Although machine learning holds promise for Earth system models (ESMs), many data-driven parameterizations lack interpretability, physical…

We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…

This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any…

In this work we develop a novel approach using deep neural networks to reconstruct the conductivity distribution in elliptic problems from one measurement of the solution over the whole domain. The approach is based on a mixed reformulation…

This technical report investigates the potential of Convolutional Neural Networks to post-process images from primary atomization. Three tasks are investigated. First, the detection and segmentation of liquid droplets in degraded optical…

Convolutional neural network (CNN) based architectures, such as Mask R-CNN, constitute the state of the art in object detection and segmentation. Recently, these methods have been extended for model-based segmentation where the network…

The parameter selection is crucial to regularization based image restoration methods. Generally speaking, a spatially fixed parameter for regularization item in the whole image does not perform well for both edge and smooth areas. A larger…

Path planning has long been one of the major research areas in robotics, with PRM and RRT being two of the most effective classes of planners. Though generally very efficient, these sampling-based planners can become computationally…

Model fitting is frequently used to determine the shape of galaxies and the point spread function, for examples, in weak lensing analyses or morphology studies aiming at probing the evolution of galaxies. However, the number of parameters…

High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…

Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…

Collision avoidance in the presence of dynamic obstacles in unknown environments is one of the most critical challenges for unmanned systems. In this paper, we present a method that identifies obstacles in terms of ellipsoids to estimate…

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…

The parameter fit from a model grid is limited by our capability to reduce the number of models, taking into account the number of parameters and the non linear variation of the models with the parameters. The Local MultiLinear Regression…

In object segmentation by active contours, the initial contour is often required. Conventionally, the initial contour is provided by the user. This paper extends the conventional active contour model by incorporating feature matching in the…

The diameter, radius and eccentricities are natural graph parameters. While these problems have been studied extensively, there are no known dynamic algorithms for them beyond the ones that follow from trivial recomputation after each…

In this paper, we propose a method for initial camera pose estimation from just a single image which is robust to viewing conditions and does not require a detailed model of the scene. This method meets the growing need of easy deployment…