相关论文: Polygon Recognition and Symmetry Detection

Pose estimation, tracking, and action recognition of articulated objects from depth images are important and challenging problems, which are normally considered separately. In this paper, a unified paradigm based on Lie group theory is…

We introduce a machine-learning approach (denoted Symmetry Seeker Neural Network) capable of automatically discovering discrete symmetry groups in physical systems. This method identifies the finite set of parameter transformations that…

We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of…

Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equation. We apply this principle by finding dilatations and…

In complex plasmas, the behavior of freely floating micrometer sized particles is studied. The particles can be directly visualized and recorded by digital video cameras. To analyze the dynamics of single particles, reliable algorithms are…

Geometric features, robust to noise, of curves in Euclidean space are of great interest for various applications such as machine learning and image analysis. We apply the Fels-Olver's moving frame method (for geometric features) paired with…

It is at times important to detect human presence automatically in secure environments. This needs a shape recognition algorithm that is robust, fast and has low error rates. The algorithm needs to process camera images quickly to detect…

We focus on the analysis of planar shapes and solid objects having thin features and propose a new mathematical model to characterize them. Based on our model, that we call an epsilon-shape, we show how thin parts can be effectively and…

Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated…

We present a method for guaranteed collision detection with toleranced motions. The basic idea is to consider the motion as a curve in the 12-dimensional space of affine displacements, endowed with an object-oriented Euclidean metric, and…

We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry adapted coordinates system where the given SDE has notable invariant properties. An approximation scheme preserving the…

We develop a self-contained theory of log-Euclidean Lie groups: smooth manifolds diffeomorphic to finite-dimensional vector spaces, equipped with the pullback of a constant Euclidean metric. This framework encompasses symmetric…

This paper presents a model-driven approach to detect image line segments. The approach incrementally detects segments on the gradient image using a linear Kalman filter that estimates the supporting line parameters and their associated…

Deep learning was recently successfully used in deriving symmetry transformations that preserve important physics quantities. Being completely agnostic, these techniques postpone the identification of the discovered symmetries to a later…

We propose a new algorithm for real-time detection and tracking of elliptic patterns suitable for real-world robotics applications. The method fits ellipses to each contour in the image frame and rejects ellipses that do not yield a good…

Automated symmetry detection is still a difficult task in 2021. However, it has applications in computer vision, and it also plays an important part in understanding art. This paper focuses on aiding the latter by comparing different…

Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation…

In the field of face recognition, a model learns to distinguish millions of face images with fewer dimensional embedding features, and such vast information may not be properly encoded in the conventional model with a single branch. We…

This paper presents a real-time solution for collision detection between objects based on the physics properties. Traditional approaches on collision detection often rely on the geometric relationships that computing the intersections…

Recently there has been renewed interest in signed distance bound representations due to their unique properties for 3D shape modelling. This is especially the case for deep learning-based bounds. However, it is beneficial to work with…