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Trajectories that capture object movement have numerous applications, in which similarity computation between trajectories often plays a key role. Traditionally, the similarity between two trajectories is quantified by means of heuristic…
Comparison between multidimensional persistent Betti numbers is often based on the multidimensional matching distance. While this metric is rather simple to define and compute by considering a suitable family of filtering functions…
This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both…
We present the Procrustes measure, a novel measure based on Procrustes rotation that enables quantitative comparison of the output of manifold-based embedding algorithms (such as LLE (Roweis and Saul, 2000) and Isomap (Tenenbaum et al,…
Reachability queries ask whether there exists a path from the source vertex to the target vertex on a graph. Recently, several powerful reachability queries, such as Label-Constrained Reachability (LCR) queries and Regular Path Queries…
The conventional definition of a depth function is vector-based. In this paper, a novel projection depth (PD) technique directly based on tensors, such as matrices, is instead proposed. Tensor projection depth (TPD) is still an ideal depth…
Depth from defocus and defocus deblurring from a single image are two challenging problems that are derived from the finite depth of field in conventional cameras. Coded aperture imaging is one of the techniques that is used for improving…
In absence of a lens to form an image, incoherent or partially coherent light scattering off an obstructive or reflective object forms a broad intensity distribution in the far field with only feeble spatial features. We show here that…
Passive millimeter-wave (PMMW) is a significant potential technique for human security screening. Several popular object detection networks have been used for PMMW images. However, restricted by the low resolution and high noise of PMMW…
A discrete conformality for polyhedral metrics on surfaces is introduced in this paper which generalizes earlier work on the subject. It is shown that each polyhedral metric on a surface is discrete conformal to a constant curvature…
Point cloud registration is a central theme in computer vision, with alignment algorithms continuously improving for greater robustness. Commonly used methods evaluate Euclidean distances between point clouds and minimize an objective…
A microfluidic device is constructed from PDMS with a single channel having a short section that is a thin flexible membrane, in order to investigate the complex fluid-structure interaction that arises between a flowing fluid and a…
The most recent trend in estimating the 6D pose of rigid objects has been to train deep networks to either directly regress the pose from the image or to predict the 2D locations of 3D keypoints, from which the pose can be obtained using a…
Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…
Image editing and compositing have become ubiquitous in entertainment, from digital art to AR and VR experiences. To produce beautiful composites, the camera needs to be geometrically calibrated, which can be tedious and requires a physical…
In this paper, we introduce a definition of discrete conformality for triangulated surfaces with flat cone metrics and describe an algorithm for solving the problem of prescribing curvature, that is to deform the metric discrete conformally…
We introduce a highly performant 3D object detector for point clouds using the DETR framework. The prior attempts all end up with suboptimal results because they fail to learn accurate inductive biases from the limited scale of training…
Ground-penetrating radar (GPR) has been an effective technology for locating metal bars in civil engineering structures. However, the accurate sizing of subsurface metal bars of small diameters remains a challenging problem for the existing…
Depth measures quantify central tendency in the analysis of statistical and geometric data. Selecting a depth measure that is simple and efficiently computable is often important, e.g., when calculating depth for multiple query points or…
We investigate the modified trace distance measure of coherence recently introduced in [Phys. Rev. A 94, 060302(R) (2016)]. We show that for any single-qubit state, the modified trace norm of coherence is equal to the $l_{1}$-norm of…