Weakly Supervised Spatial Deep Learning for Earth Image Segmentation Based on Imperfect Polyline Labels

In recent years, deep learning has achieved tremendous success in image segmentation for computer vision applications. The performance of these models heavily relies on the availability of large-scale high-quality training labels (e.g., PASCAL VOC 2012). Unfortunately, such large-scale high-quality training data are often unavailable in many real-world spatial or spatiotemporal problems in earth science and remote sensing (e.g., mapping the nationwide river streams for water resource management). Although extensive efforts have been made to reduce the reliance on labeled data (e.g., semi-supervised or unsupervised learning, few-shot learning), the complex nature of geographic data such as spatial heterogeneity still requires sufficient training labels when transferring a pre-trained model from one region to another. On the other hand, it is often much easier to collect lower-quality training labels with imperfect alignment with earth imagery pixels (e.g., through interpreting coarse imagery by non-expert volunteers). However, directly training a deep neural network on imperfect labels with geometric annotation errors could significantly impact model performance. Existing research that overcomes imperfect training labels either focuses on errors in label class semantics or characterizes label location errors at the pixel level. These methods do not fully incorporate the geometric properties of label location errors in the vector representation. To fill the gap, this article proposes a weakly supervised learning framework to simultaneously update deep learning model parameters and infer hidden true vector label locations. Specifically, we model label location errors in the vector representation to partially reserve geometric properties (e.g., spatial contiguity within line segments). Evaluations on real-world datasets in the National Hydrography Dataset (NHD) refinement application illustrate that the proposed framework outperforms baseline methods in classification accuracy.

A Comparison of the Effects of Ultrasonic Cavitation on the Surfaces of 45 and 40Kh Steels

The ultrasonic treatment of metal products in liquid is used mainly to remove various kinds of contaminants from surfaces. The effects of ultrasound not only separate and remove contaminants, they also significantly impact the physical–mechanical and geometric properties of the surfaces of products if there is enough time for treatment. The aim of this study was to compare the dynamics of ultrasonic cavitation effects on the surface properties of 45 (ASTM M1044; DIN C45; GB 45) and 40Kh (AISI 5140; DIN 41Cr4; GB 40Cr) structural steels. During the study, changes in the structure, roughness, sub-roughness, and microhardness values of these materials were observed. The results showed significant changes in the considered characteristics. It was found that the process of cavitation erosion involves at least 3 stages. In the first stage, the geometric properties of the surface slightly change with the accumulation of internal stresses and an increase in microhardness. The second stage is characterized by structure refinement, increased roughness and sub-microroughness, and the development of surface erosion. In the third stage, when a certain limiting state is reached, there are no noticeable changes in the surface properties. The lengths of these stages and the quantitative characteristics of erosion for the considered materials differ significantly. It was found that the time required to reach the limiting state was longer for carbon steel than for alloy steel. The results can be used to improve the cleaning process, as well as to form the required surface properties of structural steels.

Inscribed Triangles in the Unit Sphere and a New Class of Geometric Constants

In this paper, we firstly investigate the constant H(X) proposed by Gao further by discussing several properties of it that have not yet been discovered. Secondly, we focus on a new constant GL(X) closely related to H(X), along with a variety of geometric properties. In addition, we show several relations among it and the several basic geometric constants via a few inequalities. Finally, we manage to characterize the geometric properties of its generalized forms GL(X,p) and CL(X) explicitly.

Parameterization of Mangrove Root Structure of Rhizophora stylosa in Coastal Hydrodynamic Model

Mangroves are able to attenuate tsunamis, storm surges, and waves. Their protective function against wave disasters is gaining increasing attention as a typical example of the green infrastructure/Eco-DRR (Ecosystem-based Disaster Risk Reduction) in coastal regions. Hydrodynamic models commonly employed additional friction or a drag forcing term to represent mangrove-induced energy dissipation for simplicity. The well-known Morison-type formula (Morison et al. 1950) has been considered appropriate to model vegetation-induced resistance in which the information of the geometric properties of mangroves, including the root system, is needed. However, idealized vegetation configurations mainly were applied in the existing numerical models, and only a few field observations provided the empirical parameterization of the complex mangrove root structures. In this study, we conducted field surveys on the Iriomote Island of Okinawa, Japan, and Tarawa, Kiribati. We measured the representative parameters for the geometric properties of mangroves, Rhizophora stylosa, and their root system. By analyzing the data, significant correlations for hydrodynamic modeling were found among the key parameters such as the trunk diameter at breast height (DBH), the tree height H, the height of prop roots, and the projected areas of the root system. We also discussed the correlation of these representative factors with the tree age. These empirical relationships are summarized for numerical modeling at the end.

Completely monotone sequences and harmonic mappings

In the present paper, we will study geometric properties of harmonic mappings whose analytic and co-analytic parts are (shifted) generated functions of completely monotone sequences.

On composition operators of Fibonacci matrix and applications of Hausdorff measure of noncompactness

The aim of the paper is introduced the composition of the two infinite matrices $\Lambda=(\lambda_{nk})$ and $\widehat{F}=\left( f_{nk} \right).$ Further, we determine the $\alpha$-, $\beta$-, $\gamma$-duals of new spaces and also construct the basis for the space $\ell_{p}^{\lambda}(\widehat{F}).$ Additionally, we characterize some matrix classes on the spaces $\ell_{\infty}^{\lambda}(\widehat{F})$ and $\ell_{p}^{\lambda}(\widehat{F}).$ We also investigate some geometric properties concerning Banach-Saks type $p.$Finally we characterize the subclasses $\mathcal{K}(X:Y)$ of compact operators by applying the Hausdorff measure of noncompactness, where $X\in\{\ell_{\infty}^{\lambda}(\widehat{F}),\ell_{p}^{\lambda}(\widehat{F})\}$ and $Y\in\{c_{0},c, \ell_{\infty}, \ell_{1}, bv\},$ and $1\leq p<\infty.$

Clairaut Submersion

In this chapter, we give the detailed study about the Clairaut submersion. The fundamental notations are given. Clairaut submersion is one of the most interesting topics in differential geometry. Depending on the condition on distribution of submersion, we have different classes of submersion such as anti-invariant, semi-invariant submersions etc. We describe the geometric properties of Clairaut anti-invariant submersions and Clairaut semi-invariant submersions whose total space is a Kähler, nearly Kähler manifold. We give condition for Clairaut anti-invariant submersion to be a totally geodesic map and also study Clairaut anti-invariant submersions with totally umbilical fibers. We also give the conditions for the semi-invariant submersions to be Clairaut map and also for Clairaut semi-invariant submersion to be a totally geodesic map. We also give some illustrative example of Clairaut anti-invariant and semi-invariant submersion.