Multi-Modal Partial Surface Matching for Intra-Operative Registration

An important task for computer-assisted surgical interventions is the alignment of pre- and intra-operative spaces allowing the transfer of pre-operative information to the current patient situation, known as intra-operative registration. Registration is usually performed by using markers or image-based techniques. Another approach is the intra-operative acquisition of organ surfaces by 3D range scanners, which are then matched to pre-operatively generated surfaces. However, this approach is not trivial, as methods for intra-operative surface matching must be able to deal with noise, distortions, deformations, and the availability of only partially overlapping, nearly flat surfaces. For these reasons, surface matching for intra-operative registration has so far only been used to account for displacements that occur in local scales, while the actual alignment is still performed manually. The main contributions of this thesis are two different approaches for automatic surface matching in intra-operative environments. The focus here is the registration of surfaces acquired by different modalities, dealing with the aforementioned issues and without relying on unique landmarks. For the first approach, surfaces are converted to graph representations and correspondences between them are identified by means of graph matching. Graphs are obtained automatically by segmenting the surfaces into regions with similar properties. As the graph matching problem is known to be NP-hard, it was solved by iteratively computing node similarity scores, and converting it to a linear assignment problem. In the second approach, correspondences are identified by the selection of two spatial configurations of landmarks that can be better fitted to each other, according to an error metric. This error metric does not only incorporate a fitting error, but also a new measure for spatial configuration reliability. The optimization problem is solved by means of a greedy algorithm. Evaluation of the two approaches was performed with several experiments, simulating intra-operative conditions. While the graph matching approach proved to be robust for the registration of small partial data, the point-based approach proved to be more reliable for noisy surfaces. Apart from being a significant contribution to the field of feature-less partial surface matching, this work represents a great effort towards the achievement of a fully automatic, marker-less, registration system for computer-assisted surgery guidance

On de Sitter Spacetime and String Theory

We review various aspects of de Sitter spacetime in string theory: its status as an effective field theory spacetime solution, its relation to the vacuum energy problem in string theory, its (global) holographic definition in terms of two entangled and non-canonical conformal field theories, as well as a realization of a realistic de Sitter universe endowed with the observed visible matter and the necessary dark sector in order to reproduce the realistic cosmological structure. In particular, based on the new insight regarding the cosmological constant problem in string theory, we argue that in a doubled, T-duality-symmetric, phase-space-like and non-commutative generalized-geometric formulation, string theory can naturally lead to a small and positive cosmological constant that is radiatively stable and technically natural. Such a formulation is fundamentally based on a quantum spacetime, but in an effective spacetime description of this general formulation of string theory, the curvature of the dual spacetime is the cosmological constant of the observed spacetime, while the size of the dual spacetime is the gravitational constant of the same observed spacetime. Also, the three scales associated with intrinsic non-commutativity of string theory, the cosmological constant scale and the Planck scale, as well as the Higgs scale, can be arranged to satisfy various seesaw-like formulae. Along the way, we show that these new features of string theory can be implemented in a particular deformation of cosmic-string-like models.Comment: 116 pages, 4 figure

Discrete Geometry

[no abstract available

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Progress in Group Field Theory and Related Quantum Gravity Formalisms

Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research