Related papers: Nonlinear constructive observer design for direct …
This paper introduces a new linear parameterization to the problem of visual inertial simultaneous localization and mapping (VI-SLAM) -- without any approximation -- for the case only using information from a single monocular camera and an…
We study the homology groups of the complement of a complexified real line arrangement with coefficients in complex rank-one local systems. Using Borel--Moore homology, we establish an algorithm computing their dimensions via the real…
Monocular 3D Object Detection represents a challenging Computer Vision task due to the nature of the input used, which is a single 2D image, lacking in any depth cues and placing the depth estimation problem as an ill-posed one. Existing…
Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…
A hybrid observer is described for estimating the state of an $m>0$ channel, $n$-dimensional, continuous-time, distributed linear system of the form $\dot{x} = Ax,\;y_i = C_ix,\;i\in\{1,2,\ldots, m\}$. The system's state $x$ is…
Image segmentation aims at identifying regions of interest within an image, by grouping pixels according to their properties. This task resembles the statistical one of clustering, yet many standard clustering methods fail to meet the basic…
This paper introduces a new nonlinear observer for state estimation of linear time invariant systems. The proposed observer contains a (nonlinear) cubic term in its error dynamics. "For the final version of this article, please refer to the…
The structure representation of data distribution plays an important role in understanding the underlying mechanism of generating data. In this paper, we propose nearest prime simplicial complex approaches (NSC) by utilizing persistent…
Visual localization on standard-definition (SD) maps has emerged as a promising low-cost and scalable solution for autonomous driving. However, existing regression-based approaches often overlook inherent geometric priors, resulting in…
0-dimensional persistent homology is known, from a computational point of view, as the easy case. Indeed, given a list of $n$ edges in non-decreasing order of filtration value, one only needs a union-find data structure to keep track of the…
In this paper, we present a multi-object 6D detection and tracking pipeline for potentially similar and non-textured objects. The combination of a convolutional neural network for object classification and rough pose estimation with a local…
Additive models play an essential role in studying non-linear relationships. Despite many recent advances in estimation, there is a lack of methods and theories for inference in high-dimensional additive models, including confidence…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the…
Two novel robust nonlinear stochastic full pose (i.e, attitude and position) estimators on the Special Euclidean Group SE(3) are proposed using the available uncertain measurements. The resulting estimators utilize the basic structure of…
This paper introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not require pre-binning or any other…
Feature extraction in noisy image datasets presents many challenges in model reliability. In this paper, we use the discrete Fourier transform in conjunction with persistent homology analysis to extract specific frequencies that correspond…
We extend the approach in [Ann. Statist. 38 (2010) 2499-2524] for identifying locally optimal designs for nonlinear models. Conceptually the extension is relatively simple, but the consequences in terms of applications are profound. As we…
Successful navigation of a rigid-body traveling with six degrees of freedom (6 DoF) requires accurate estimation of attitude , position, and linear velocity. The true navigation dynamics are highly nonlinear and are modeled on the matrix…
Real-time rendering with global illumination is crucial to afford the user realistic experience in virtual environments. We present a learning-based estimator to predict diffuse indirect illumination in screen space, which then is combined…