12 research outputs found
Conjugate Product Graphs for Globally Optimal 2D-3D Shape Matching
We consider the problem of finding a continuous and non-rigid matching
between a 2D contour and a 3D mesh. While such problems can be solved to global
optimality by finding a shortest path in the product graph between both shapes,
existing solutions heavily rely on unrealistic prior assumptions to avoid
degenerate solutions (e.g. knowledge to which region of the 3D shape each point
of the 2D contour is matched). To address this, we propose a novel 2D-3D shape
matching formalism based on the conjugate product graph between the 2D contour
and the 3D shape. Doing so allows us for the first time to consider
higher-order costs, i.e. defined for edge chains, as opposed to costs defined
for single edges. This offers substantially more flexibility, which we utilise
to incorporate a local rigidity prior. By doing so, we effectively circumvent
degenerate solutions and thereby obtain smoother and more realistic matchings,
even when using only a one-dimensional feature descriptor. Overall, our method
finds globally optimal and continuous 2D-3D matchings, has the same asymptotic
complexity as previous solutions, produces state-of-the-art results for shape
matching and is even capable of matching partial shapes
CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes
Jointly matching multiple, non-rigidly deformed 3D shapes is a challenging,
-hard problem. A perfect matching is necessarily
cycle-consistent: Following the pairwise point correspondences along several
shapes must end up at the starting vertex of the original shape. Unfortunately,
existing quantum shape-matching methods do not support multiple shapes and even
less cycle consistency. This paper addresses the open challenges and introduces
the first quantum-hybrid approach for 3D shape multi-matching; in addition, it
is also cycle-consistent. Its iterative formulation is admissible to modern
adiabatic quantum hardware and scales linearly with the total number of input
shapes. Both these characteristics are achieved by reducing the -shape case
to a sequence of three-shape matchings, the derivation of which is our main
technical contribution. Thanks to quantum annealing, high-quality solutions
with low energy are retrieved for the intermediate -hard
objectives. On benchmark datasets, the proposed approach significantly
outperforms extensions to multi-shape matching of a previous quantum-hybrid
two-shape matching method and is on-par with classical multi-matching methods.Comment: Computer Vision and Pattern Recognition (CVPR) 2023; 22 pages, 24
figures and 5 tables; Project page: https://4dqv.mpi-inf.mpg.de/CCuantuMM
SIGMA: Scale-Invariant Global Sparse Shape Matching
We propose a novel mixed-integer programming (MIP) formulation for generating
precise sparse correspondences for highly non-rigid shapes. To this end, we
introduce a projected Laplace-Beltrami operator (PLBO) which combines intrinsic
and extrinsic geometric information to measure the deformation quality induced
by predicted correspondences. We integrate the PLBO, together with an
orientation-aware regulariser, into a novel MIP formulation that can be solved
to global optimality for many practical problems. In contrast to previous
methods, our approach is provably invariant to rigid transformations and global
scaling, initialisation-free, has optimality guarantees, and scales to high
resolution meshes with (empirically observed) linear time. We show
state-of-the-art results for sparse non-rigid matching on several challenging
3D datasets, including data with inconsistent meshing, as well as applications
in mesh-to-point-cloud matching.Comment: 14 page
Efficient Deformable Shape Correspondence via Kernel Matching
We present a method to match three dimensional shapes under non-isometric
deformations, topology changes and partiality. We formulate the problem as
matching between a set of pair-wise and point-wise descriptors, imposing a
continuity prior on the mapping, and propose a projected descent optimization
procedure inspired by difference of convex functions (DC) programming.
Surprisingly, in spite of the highly non-convex nature of the resulting
quadratic assignment problem, our method converges to a semantically meaningful
and continuous mapping in most of our experiments, and scales well. We provide
preliminary theoretical analysis and several interpretations of the method.Comment: Accepted for oral presentation at 3DV 2017, including supplementary
materia
ATHENA Research Book
The ATHENA European University is an alliance of nine Higher Education Institutions with the mission of fostering excellence in research and innovation by facilitating international cooperation. The ATHENA acronym stands for Advanced Technologies in Higher Education Alliance. The partner institutions are from France, Germany, Greece, Italy, Lithuania, Portugal, and Slovenia: the University of Orléans, the University of Siegen, the Hellenic Mediterranean University, the Niccolò Cusano University, the Vilnius Gediminas Technical University, the Polytechnic Institute of Porto, and the University of Maribor. In 2022 institutions from Poland and Spain joined the alliance: the Maria Curie-Skłodowska University and the University of Vigo.
This research book presents a selection of the ATHENA university partners' research activities. It incorporates peer-reviewed original articles, reprints and student contributions. The ATHENA Research Book provides a platform that promotes joint and interdisciplinary research projects of both advanced and early-career researchers