Related papers: Shape Analysis on Lie Groups with Applications in …

Shape recognition is the main challenging problem in computer vision. Different approaches and tools are used to solve this problem. Most existing approaches to object recognition are based on pixels. Pixel-based methods are dependent on…

Graphs and graph transformation systems are a frequently used modelling technique for a wide range of different domains, cover- ing areas as diverse as refactorings, network topologies or reconfigurable software. Being a formal method,…

We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localised basis functions of different shapes, which we…

Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…

Shearlet systems have so far been only considered as a means to analyze $L^2$-functions defined on $\R^2$, which exhibit curvilinear singularities. However, in applications such as image processing or numerical solvers of partial…

Shapelet-based algorithms are widely used for time series classification because of their ease of interpretation, but they are currently outperformed by recent state-of-the-art approaches. We present a new formulation of time series…

Statistical shape analysis is a very useful tool in a wide range of medical and biological applications. However, it typically relies on the ability to produce a relatively small number of features that can capture the relevant variability…

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the…

An effective way to model the complex real world is to view the world as a composition of basic components of objects and transformations. Although humans through development understand the compositionality of the real world, it is…

Exploiting the relationships between attributes is a key challenge for improving multiple facial attribute recognition. In this work, we are concerned with two types of correlations that are spatial and non-spatial relationships. For the…

Good parametrisations of affine transformations are essential to interpolation, deformation, and analysis of shape, motion, and animation. It has been one of the central research topics in computer graphics. However, there is no single…

We suggest a new algorithm to estimate representations of compact Lie groups from finite samples of their orbits. Different from other reported techniques, our method allows the retrieval of the precise representation type as a direct sum…

Generative AI is reshaping art, gaming, and most notably animation. Recent breakthroughs in foundation and diffusion models have reduced the time and cost of producing animated content. Characters are central animation components, involving…

A novel algorithm for creating a mathematical model of curved shapes is introduced. The core of the algorithm is based on building a graph representation of the contoured image, which occupies less storage space than produced by raster…

Statistical Shape Models of faces and various body parts are heavily used in medical image analysis, computer vision and visualization. Whilst the field is well explored with many existing tools, all of them aim at experts, which limits…

In the field of spatial computing, one of the most essential tasks is the pose estimation of 3D objects. While rigid transformations of arbitrary 3D objects are relatively hard to detect due to varying environment introducing factors like…

We describe and analyze algorithms for shape-constrained symbolic regression, which allows the inclusion of prior knowledge about the shape of the regression function. This is relevant in many areas of engineering -- in particular whenever…

We survey recent work on the geometry and dynamics of transverse subgroups of semi-simple Lie groups.

The identification of the interfacial molecules in fluid-fluid equilibrium is a long-standing problem in the area of simulation. We here propose a new point of view, making use of concepts taken from the field of computational geometry,…

Algebraic geometry for groups and Lie algebraic has been recently defined and studied by many authors on the purpose to study set defined by algebraic equations on abstract groups and Lie algebras. The purpose of this paper is to present a…