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Giang V. Nguyen

Publications and source records attributed to Giang V. Nguyen.

4 recordsLinked to original sources
arXiv2023

Asymptotics of the exterior conformal modulus of an arbitrary quadrilateral under stretching map

In this paper, we focus on studying the distortion of the exterior conformal modulus of a quadrilateral of sufficiently arbitrary form under the stretching map along the abscissa axis with coefficient $H\to\infty$. By using the properties of quasiconformal transformations and taking into account some facts from the theory of elliptic integrals, we confirm that the asymptotic behavior of this modulus does not depend on the shape of the boundary of the quadrilateral. Especially, it is equivalent to $(1/π)\log H$ as $H\to\infty$. Therefore, we give a solution to the Vuorinen problem for the exterior region of an arbitrary quadrilateral.

math.CV↗
arXiv2023

Asymptotics of the exterior conformal modulus of a symmetric quadrilateral under stretching map

In this work, we study the distortion of the exterior conformal modulus of a symmetric quadrilateral, when stretched in the direction of the abscissa axis with the coefficient $H\to \infty$. By using some facts from the theory of elliptic integrals, we confirm that the asymptotic behavior of this modulus does not depend on the shape of the boundary of the quadrilateral; moreover, it is equivalent to $(1/π)\log H$ as $H\to \infty$.

math.CV↗
arXiv2021

Simple Multi-Resolution Representation Learning for Human Pose Estimation

Human pose estimation - the process of recognizing human keypoints in a given image - is one of the most important tasks in computer vision and has a wide range of applications including movement diagnostics, surveillance, or self-driving vehicle. The accuracy of human keypoint prediction is increasingly improved thanks to the burgeoning development of deep learning. Most existing methods solved human pose estimation by generating heatmaps in which the ith heatmap indicates the location confidence of the ith keypoint. In this paper, we introduce novel network structures referred to as multi-resolution representation learning for human keypoint prediction. At different resolutions in the learning process, our networks branch off and use extra layers to learn heatmap generation. We firstly consider the architectures for generating the multi-resolution heatmaps after obtaining the lowest-resolution feature maps. Our second approach allows learning during the process of feature extraction in which the heatmaps are generated at each resolution of the feature extractor. The first and second approaches are referred to as multi-resolution heatmap learning and multi-resolution feature map learning respectively. Our architectures are simple yet effective, achieving good performance. We conducted experiments on two common benchmarks for human pose estimation: MSCOCO and MPII dataset. The code is made publicly available at https://github.com/tqtrunghnvn/SimMRPose.

cs.CV↗