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Florian Wolz

Publications and source records attributed to Florian Wolz.

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Benchmarking Content-Based Puzzle Solvers on Corrupted Jigsaw Puzzles

Content-based puzzle solvers have been extensively studied, demonstrating significant progress in computational techniques. However, their evaluation often lacks realistic challenges crucial for real-world applications, such as the reassembly of fragmented artefacts or shredded documents. In this work, we investigate the robustness of State-Of-The-Art content-based puzzle solvers introducing three types of jigsaw puzzle corruptions: missing pieces, eroded edges, and eroded contents. Evaluating both heuristic and deep learning-based solvers, we analyse their ability to handle these corruptions and identify key limitations. Our results show that solvers developed for standard puzzles have a rapid decline in performance if more pieces are corrupted. However, deep learning models can significantly improve their robustness through fine-tuning with augmented data. Notably, the advanced Positional Diffusion model adapts particularly well, outperforming its competitors in most experiments. Based on our findings, we highlight promising research directions for enhancing the automated reconstruction of real-world artefacts.

cs.CV

Gravitational closure of matter field equations

The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for diffeomorphism-invariant gravitational dynamics that can provide consistent evolution equations to the coefficients of a given system of matter field equations. Concretely, we show how starting from any linear local matter field equations whose principal polynomial satisfies three physicality conditions, one may calculate coefficient functions which then enter an otherwise immutable set of countably many linear homogeneous partial differential equations. Any solution of these so-called gravitational closure equations then provides a Lagrangian density for any type of tensorial geometry that features ultralocally in the initially specified matter Lagrangian density. Thus the given system of matter field equations is indeed closed by the so obtained gravitational equations. In contrast to previous work, we build the theory on a suitable associated bundle encoding the canonical configuration degrees of freedom, which allows to include necessary constraints on the geometry in practically tractable fashion. By virtue of the presented mechanism, one thus can practically calculate, rather than having to postulate, the gravitational theory that is required by specific matter field dynamics. For the special case of standard model matter one obtains general relativity.

gr-qc

Gravitational closure of weakly birefringent electrodynamics

We derive the gravitational dynamics of the tensorial geometry which underlies the most general linear theory of electrodynamics that features weak birefringence in vacuo. This derivation is performed by way of gravitational closure, which is a mechanism that employs the causal structure of any canonically quantizable matter dynamics on some tensorial spacetime geometry in order to derive canonical dynamics for the latter. The resulting eleven-parameter family of weak gravitational field equations allows to predict where vacuum birefringence will occur, if there is any.

hep-th