Related papers: Polygon Recognition and Symmetry Detection
The complex-step derivative approximation is a numerical differentiation technique that can achieve analytical accuracy, to machine precision, with a single function evaluation. In this letter, the complex-step derivative approximation is…
Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…
Symmetry is one of the significant visual properties inside an image plane, to identify the geometrically balanced structures through real-world objects. Existing symmetry detection methods rely on descriptors of the local image features…
The method of moving frames (rep\`ere mobile) was used by Elie Cartan as a way of organizing the identification of differential invariants and solving equivalence problems. In this expository paper, we discuss how moving frames are used to…
By combining the ideas of Cartan's equivalence method and the method of the equivariant moving frame for pseudo-groups, we develop an efficient method for solving equivalence problems arising from horizontal Lie pseudo-group actions. The…
The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved…
This article presents an automated method to quantify and detect symmetry elements in 2D patterns by means of image processing. Escher's woodcuts, a widely recognized didactic tool for crystallographic education of students, were used to…
Determining visibility in planar polygons and arrangements is an important subroutine for many algorithms in computational geometry. In this paper, we report on new implementations, and corresponding experimental evaluations, for two…
Collision detection plays an important role in simulation, control, and learning for robotic systems. However, no existing method is differentiable with respect to the configurations of the objects, greatly limiting the sort of algorithms…
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…
We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral…
We present a systematic study of symmetries, invariants and moduli spaces of classes of coframes. We introduce a classifying Lie algebroid to give a complete description of the solution to Cartan's realization problem that applies to both…
Boundary detection is essential for a variety of computer vision tasks such as segmentation and recognition. In this paper we propose a unified formulation and a novel algorithm that are applicable to the detection of different types of…
Lie derivatives of various geometrical and physical quantities define symmetries and conformal symmetries in general relativity. Thus we obtain motions, collineations, conformal motions and conformal collineations. These symmetries are used…
An automatic road sign detection system localizes road signs from within images captured by an on-board camera of a vehicle, and support the driver to properly ride the vehicle. Most existing algorithms include a preprocessing step, feature…
This paper proves explicit formulas for the number of dissections of a convex regular polygon modulo the action of the cyclic and dihedral groups. The formulas are obtained by making use of the Cauchy-Frobenius Lemma as well as bijections…
Previous face forgery detection methods mainly focus on appearance features, which may be easily attacked by sophisticated manipulation. Considering the majority of current face manipulation methods generate fake faces based on a single…
Based on cluster de-synchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and…
Over the past few years, symmetric positive definite (SPD) matrices have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing SPD matrices, the…
This thesis is devoted to algorithmic aspects of the implementation of Cartan's moving frame method to the problem of the equivalence of submanifolds under a Lie group action. We adopt a general definition of a moving frame as an…