Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The fshape framework for the variability analysis of functional shapes   This article introduces a full mathematical and numerical framework for
treating functional shapes (or fshapes) following the landmarks of shape spaces
and shape analysis. Functional shapes can be described as signal functions
supported on varying geometrical supports. Analysing variability of fshapes'
ensembles require the modelling and quantification of joint variations in
geometry and signal, which have been treated separately in previous approaches.
Instead, building on the ideas of shape spaces for purely geometrical objects,
we propose the extended concept of fshape bundles and define Riemannian metrics
for fshape metamorphoses to model geometrico-functional transformations within
these bundles. We also generalize previous works on data attachment terms based
on the notion of varifolds and demonstrate the utility of these distances.
Based on these, we propose variational formulations of the atlas estimation
problem on populations of fshapes and prove existence of solutions for the
different models. The second part of the article examines the numerical
implementation of the models by detailing discrete expressions for the metrics
and gradients and proposing an optimization scheme for the atlas estimation
problem. We present a few results of the methodology on a synthetic dataset as
well as on a population of retinal membranes with thickness maps.

10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat