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Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…
In the Metric Dimension problem, one asks for a minimum-size set $R$ of vertices such that for any pair of vertices of the graph, there is a vertex from $R$ whose two distances to the vertices of the pair are distinct. This problem has…
Accurate and robust modelling of large deformation three dimensional contact interaction is an important area of engineering, but it is also challenging from a computational mechanics perspective. This is particularly the case when there is…
Many methods exist to model and track deformable one-dimensional objects (e.g., cables, ropes, and threads) across a stream of video frames. However, these methods depend on the existence of some initial conditions. To the best of our…
Reconstruction-based anomaly detection models achieve their purpose by suppressing the generalization ability for anomaly. However, diverse normal patterns are consequently not well reconstructed as well. Although some efforts have been…
When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of…
Perspective distortion (PD) causes unprecedented changes in shape, size, orientation, angles, and other spatial relationships of visual concepts in images. Precisely estimating camera intrinsic and extrinsic parameters is a challenging task…
Metric embeddings traditionally study how to map $n$ items to a target metric space such that distance lengths are not heavily distorted; but what if we only care to preserve the relative order of the distances (and not their length)? In…
This paper uses clustering algorithms to introduce a shape framework for deformable objects. Until now, the shape detection of the deformable objects has faced several challenges: 1) unable to form a unified framework for multiple shapes;…
Detection Transformers (DETR) have recently set new benchmarks in object detection. However, their performance in detecting rotated objects lags behind established oriented object detectors. Our analysis identifies a key observation: the…
Tracking by detection is a common approach to solving the Multiple Object Tracking problem. In this paper we show how learning a deep similarity metric can improve three key aspects of pedestrian tracking on a multiple object tracking…
DETR has been recently proposed to eliminate the need for many hand-designed components in object detection while demonstrating good performance. However, it suffers from slow convergence and limited feature spatial resolution, due to the…
We consider defining the embedding of a triangle mesh into $R^3$, up to translation, rotation, and scale, by its vector of dihedral angles. Theoretically, we show that locally, almost everywhere, the map from realizable vectors of dihedrals…
In this paper, we introduce and study the Parallel Polyhedral Projection Method (3PM) and the Approximate Parallel Polyhedral Projection Method (A3PM) for finding a point in the intersection of finitely many closed convex sets. Each…
Reconstructing the three-dimensional (3D) geometry of object surfaces is essential for robot perception, yet vision-based approaches are generally unreliable under low illumination or occlusion. This limitation motivates the design of a…
Estimating accurate 3D locations of objects from monocular images is a challenging problem because of lacking depth. Previous work shows that utilizing the object's keypoint projection constraints to estimate multiple depth candidates…
We consider the problem of determining the length of the shortest paths between points on the surfaces of tetrahedra and cubes. Our approach parallels the concept of Alexandrov's star unfolding but focuses on specific polyhedra and uses…
Measuring the similarity of images is a fundamental problem to computer vision for which no universal solution exists. While simple metrics such as the pixel-wise L2-norm have been shown to have significant flaws, they remain popular. One…
This article presents a new distance for measuring shape dissimilarity between objects. Recent publications introduced the use of eigenvalues of the Laplace operator as compact shape descriptors. Here, we revisit the eigenvalues to define a…
We show that computing the interleaving distance between two multi-graded persistence modules is NP-hard. More precisely, we show that deciding whether two modules are $1$-interleaved is NP-complete, already for bigraded, interval…