arXiv subjects

Georg Merz

Publications and source records attributed to Georg Merz.

5 recordsLinked to original sources

arXiv2025

Deep Learning-based Compression Detection for explainable Face Image Quality Assessment

The assessment of face image quality is crucial to ensure reliable face recognition. In order to provide data subjects and operators with explainable and actionable feedback regarding captured face images, relevant quality components have to be measured. Quality components that are known to negatively impact the utility of face images include JPEG and JPEG 2000 compression artefacts, among others. Compression can result in a loss of important image details which may impair the recognition performance. In this work, deep neural networks are trained to detect the compression artefacts in a face images. For this purpose, artefact-free facial images are compressed with the JPEG and JPEG 2000 compression algorithms. Subsequently, the PSNR and SSIM metrics are employed to obtain training labels based on which neural networks are trained using a single network to detect JPEG and JPEG 2000 artefacts, respectively. The evaluation of the proposed method shows promising results: in terms of detection accuracy, error rates of 2-3% are obtained for utilizing PSNR labels during training. In addition, we show that error rates of different open-source and commercial face recognition systems can be significantly reduced by discarding face images exhibiting severe compression artefacts. To minimize resource consumption, EfficientNetV2 serves as basis for the presented algorithm, which is available as part of the OFIQ software.

cs.CV↗

arXiv2018

On Newton-Okounkov bodies of Graded Linear Series

We generalize the theory of Newton-Okounkov bodies of big divisors to the case of graded linear series. One of the results is the generalization of slice formulas and the existence of generic Newton-Okounkov bodies for birational graded linear series. We also give a characterization of graded linear series which have full volume in terms of their base locus.

math.AG↗

arXiv2018

Newton-Okounkov bodies and normal toric degenerations

Anderson proved that the finite generation of the value semigroup $\Gamma_{Y_\bullet}(D)$ in the construction of the Newton-Okounkov body $\Delta_{Y_\bullet}(D)$ induces a toric degeneration of the corresponding variety $X$ to some toric variety $X_0$. In this case the normalization of $X_0$ is the normal toric variety corresponding to the rational polytope $\Delta_{Y_\bullet}(D)$. Since $X_0$ is not normal in general this correspondence is rather implicit. In this article we investigate in conditions to assure that $X_0$ is normal, by comparing the Hilbert polynomial with the Ehrhart polynomial. In the case of del Pezzo surfaces this will result in an algorithm which outputs for a given divisor $D$ a flag $Y_\bullet$ such that the value semigroup in question is indeed normal. Furthermore, we will find flags on del Pezzo surfaces and on some particular weak del Pezzo surfaces which induce normal toric degenerations for all possible divisors at once. We will prove that in this case the global value semigroup $\Gamma_{Y_\bullet}(X)$ is finitely generated and normal.

math.AG↗

arXiv2017

On the Mori theory and Newton-Okounkov bodies of Bott-Samelson varieties

We prove that on a Bott-Samelson variety $X$ every movable divisor is nef. This enables us to consider Zariski decompositions of effective divisors, which in turn yields a description of the Mori chamber decomposition of the effective cone. This amounts to information on all possible birational morphisms from $X$. Applying this result, we prove the rational polyhedrality of the global Newton-Okounkov body of a Bott-Samelson variety with respect to the so called `horizontal' flag. In fact, we prove the stronger property of the finite generation of the corresponding global value semigroup.

math.AG↗

arXiv2017

Khovanskii bases of Cox-Nagata rings and tropical geometry

The Cox ring of a del Pezzo surface of degree 3 has a distinguished set of 27 minimal generators. We investigate conditions under which the initial forms of these generators generate the initial algebra of this Cox ring. Sturmfels and Xu provide a classification in the case of degree 4 del Pezzo surfaces by subdividing the tropical Grassmannian $\operatorname{TGr}(2,\mathbb{Q}^5)$. After providing the necessary background on Cox-Nagata rings and Khovanskii bases, we review the classification obtained by Sturmfels and Xu. Then we describe our classification problem in the degree 3 case and its connections to tropical geometry. In particular, we show that two natural candidates, $\operatorname{TGr}(3,\mathbb{Q}^6)$ and the Naruki fan, are insufficient to carry out the classification.

math.AG↗