Related papers: Signatures in Shape Analysis: an Efficient Approac…
We survey the 19th century development of the signature of a quadratic form, and the applications in the 20th and 21st century to the topology of manifolds and dynamical systems. Version 2 is an expanded and corrected version of Version 1,…
Graph neural networks (GNNs) have evolved into one of the most popular deep learning architectures. However, GNNs suffer from over-smoothing node information and, therefore, struggle to solve tasks where global graph properties are…
Signature kernels, inner products of path signatures, underpin several machine learning algorithms for multivariate time series analysis. For bounded variation paths, signature kernels were recently shown to solve a Goursat PDE. However,…
Automated Driving Functions (ADFs) need to comply with spatial properties of varied complexity while driving on public roads. Since such situations are safety-critical in nature, it is necessary to continuously check ADFs for compliance…
We propose a signal analysis tool based on the sign (or the phase) of complex wavelet coefficients, which we call a signature. The signature is defined as the fine-scale limit of the signs of a signal's complex wavelet coefficients. We show…
The Structure from Motion (SfM) challenge in computer vision is the process of recovering the 3D structure of a scene from a series of projective measurements that are calculated from a collection of 2D images, taken from different…
Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the…
The signature of a $p$-weakly geometric rough path summarises a path up to a generalised notion of reparameterisation. The quotient space of equivalence classes on which the signature is constant yields unparameterised path space. The study…
The signature transform is a 'universal nonlinearity' on the space of continuous vector-valued paths, and has received attention for use in machine learning on time series. However, real-world temporal data is typically observed at discrete…
Road signs detection and recognition in natural scenes is one of the most important tasksin the design of Intelligent Transport Systems (ITS). However, illumination changes remain a major problem. In this paper, an efficient ap-proach of…
A reparametrization (of a continuous path) is given by a surjective weakly increasing self-map of the unit interval. We show that the monoid of reparametrizations (with respect to compositions) can be understood via ``stop-maps'' that allow…
Many features have been proposed in on-line signature verification. Generally, these features rely on the position of the on-line signature samples and their dynamic properties, as recorded by a tablet. This paper proposes a novel feature…
The sequence of moments of a vector-valued random variable can characterize its law. We study the analogous problem for path-valued random variables, that is stochastic processes, by using so-called robust signature moments. This allows us…
We present a sample-based motion planning algorithm specialised to a class of underactuated systems using path parameterisation. The structure this class presents under a path parameterisation enables the trivial computation of dynamic…
Fingerprint verification is an important bio-metric technique for personal identification. Most of the automatic verification systems are based on matching of fingerprint minutiae. Extraction of minutiae is an essential process which…
The evolution of 3D visual content calls for innovative methods for modelling shapes based on their intended usage, function and role in a complex scenario. Even if different attempts have been done in this direction, shape modelling still…
Different fonts have different impressions, such as elegant, scary, and cool. This paper tackles part-based shape-impression analysis based on the Transformer architecture, which is able to handle the correlation among local parts by its…
The motivation for using qualitative shape descriptions is as follows: qualitative shape descriptions can implicitly act as a schema for measuring the similarity of shapes, which has the potential to be cognitively adequate. Then, shapes…
AR/VR applications and robots need to know when the scene has changed. An example is when objects are moved, added, or removed from the scene. We propose a 3D object discovery method that is based only on scene changes. Our method does not…
Alignment or registration of functions is a fundamental problem in statistical analysis of functions and shapes. While there are several approaches available, a more recent approach based on Fisher-Rao metric and square-root velocity…