Related papers: Shape Analysis on Lie Groups with Applications in …
The Shape Calculus is a bio-inspired calculus for describing 3D shapes moving in a space. A shape forms a 3D process when combined with a behaviour. Behaviours are specified with a timed CCS-like process algebra using a notion of channel…
Learning curves model a classifier's test error as a function of the number of training samples. Prior works show that learning curves can be used to select model parameters and extrapolate performance. We investigate how to use learning…
Graphs are ubiquitous in encoding relational information of real-world objects in many domains. Graph generation, whose purpose is to generate new graphs from a distribution similar to the observed graphs, has received increasing attention…
We introduce a novel class of rotation invariants of two dimensional curves based on iterated integrals. The invariants we present are in some sense complete and we describe an algorithm to calculate them, giving explicit computations up to…
The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also…
This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…
We introduce an approach based on moving frames for polygon recognition and symmetry detection. We present detailed algorithms for recognition of polygons modulo the special Euclidean, Euclidean, equi-affine, skewed-affine and similarity…
We consider practical aspects of reconstructing planar curves with prescribed Euclidean or affine curvatures. These curvatures are invariant under the special Euclidean group and the equi-affine groups, respectively, and play an important…
We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…
Cracks on a painting is not a defect but an inimitable signature of an artwork which can be used for origin examination, aging monitoring, damage identification, and even forgery detection. This work presents the development of a new…
In interactive object segmentation a user collaborates with a computer vision model to segment an object. Recent works employ convolutional neural networks for this task: Given an image and a set of corrections made by the user as input,…
Texture classification is an active topic in image processing which plays an important role in many applications such as image retrieval, inspection systems, face recognition, medical image processing, etc. There are many approaches…
With the widespread use of sophisticated machine learning models in sensitive applications, understanding their decision-making has become an essential task. Models trained on tabular data have witnessed significant progress in explanations…
Reconstructing the 3D geometry, pose, and motion of animals is a long-standing problem, which has a wide range of applications, from biology, livestock management, and animal conservation and welfare to content creation in digital…
We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of…
This publication serves as an overview of clique topology -- a novel matrix analysis technique used to extract structural features from neural activity data that contains hidden nonlinearities. We highlight work done by Gusti et al. which…
A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
The square root velocity transformation provides a convenient and numerically efficient approach to functional and shape data analysis of curves. We study fundamental geometric properties of curves under this transformation. Moreover,…
Collective motion in animal groups, such as swarms of insects, flocks of birds, and schools of fish, are some of the most visually striking examples of emergent behavior. Empirical analysis of these behaviors in experiment or computational…