Related papers: Inverting the signature of a path
We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in…
We propose an approach to 3D reconstruction via inverse procedural modeling and investigate two variants of this approach. The first option consists in the fitting set of input parameters using a genetic algorithm. We demonstrate the…
Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem…
Two long-standing problems in the construction of coherent state path integrals, the unwarranted assumption of path continuity and the ambiguous definition of the Hamiltonian symbol, are rigorously solved. To this end the fully controlled…
We propose a path-based approach to program repair for imperative programs. Our repair framework takes as input a faulty program, a logic specification that is refuted, and a hint where the fault may be located. An iterative abstraction…
Decomposition of tomographic reconstructions has many different practical application. We propose two new reconstruction methods that combines the task of tomographic reconstruction with object decomposition. We demonstrate these…
The normalization in the path integral approach to quantum field theory, in contrast with statistical field theory, can contain physical information. The main claim of this paper is that the inner product on the space of field…
To address the problem of 3D point matching where the poses of two point sets are unknown, we adapt a recently proposed path following based method to use similarity transformation instead of the original affine transformation. The reduced…
For sufficiently tame paths in $\mathbb{R}^n$, Euclidean length provides a canonical parametrization of a path by length. In this paper we provide such a parametrization for all continuous paths. This parametrization is based on an…
The problem addressed here can be concisely formulated as follows: given a stable surface orientation with a known reconstruction and given a direction in the plane of this surface, find the atomic structure of the steps oriented along that…
Iterated-integral signatures and log signatures are vectors calculated from a path that characterise its shape. They come from the theory of differential equations driven by rough paths, and also have applications in statistics and machine…
Multi-view 3D surface reconstruction using neural implicit representations has made notable progress by modeling the geometry and view-dependent radiance fields within a unified framework. However, their effectiveness in reconstructing…
Biometric authentication by means of handwritten signatures is a challenging pattern recognition task, which aims to infer a writer model from only a handful of genuine signatures. In order to make it more difficult for a forger to attack…
Digital circles not only play an important role in various technological settings, but also provide a lively playground for more fundamental number-theoretical questions. In this paper, we present a new recursive algorithm for the…
Rough path theory provides one with the notion of signature, a graded family of tensors which characterise, up to a negligible equivalence class, and ordered stream of vector-valued data. In the last few years, use of the signature has…
The present letter gives a rigorous way from quantum to classical random walks by introducing an independent random fluctuation and then taking expectations based on a path integral approach.
We present an algorithm for constructing a map $\mathbb{P}^2\to\mathbb{P}^2$ with a given branching curve. The stepping stone is the ramification curve, which is obtained as the linear normalization of the branching curve.
Rough path theory is focused on capturing and making precise the interactions between highly oscillatory and non-linear systems. It draws on the analysis of LC Young and the geometric algebra of KT Chen. The concepts and the uniform…
We study the path planning problem for continuum-arm robots, in which we are given a starting and an end point, and we need to compute a path for the tip of the continuum arm between the two points. We consider both cases where obstacles…
This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a…