Image geolocalization is a fundamental yet challenging task, aiming at inferring the geolocation on Earth where an image is taken. State-of-the-art methods employ either grid-based classification or gallery-based image-location retrieval, whose spatial generalizability significantly suffers if the spatial distribution of test images does not align with the choices of grids and galleries. Recently emerging generative approaches, while getting rid of grids and galleries, use raw geographical coordinates and suffer quality losses due to their lack of multi-scale information. To address these limitations, we propose a multi-scale latent diffusion model called LocDiff for image geolocalization. We developed a novel positional encoding-decoding framework called Spherical Harmonics Dirac Delta (SHDD) Representations, which encodes points on a spherical surface (e.g., geolocations on Earth) into a Hilbert space of Spherical Harmonics coefficients and decodes points (geolocations) by mode-seeking on spherical probability distributions. We also propose a novel SirenNet-based architecture (CS-UNet) to learn an image-based conditional backward process in the latent SHDD space by minimizing a latent KL-divergence loss. To the best of our knowledge, LocDiff is the first image geolocalization model that performs latent diffusion in a multi-scale location encoding space and generates geolocations under the guidance of images. Experimental results show that LocDiff can outperform all state-of-the-art grid-based, retrieval-based, and diffusion-based baselines across 5 challenging global-scale image geolocalization datasets, and demonstrates significantly stronger generalizability to unseen geolocations.

Spatial representation learning (SRL) aims at learning general-purpose neural network representations from various types of spatial data (e.g., points, polylines, polygons, networks, images, etc.) in their native formats. Learning good spatial representations is a fundamental problem for various downstream applications such as species distribution modeling, weather forecasting, trajectory generation, geographic question answering, etc. Even though SRL has become the foundation of almost all geospatial artificial intelligence (GeoAI) research, we have not yet seen significant efforts to develop an extensive deep learning framework and benchmark to support SRL model development and evaluation. To fill this gap, we propose TorchSpatial, a learning framework and benchmark for location (point) encoding,which is one of the most fundamental data types of spatial representation learning. TorchSpatial contains three key components: 1) a unified location encoding framework that consolidates 15 commonly recognized location encoders, ensuring scalability and reproducibility of the implementations; 2) the LocBench benchmark tasks encompassing 7 geo-aware image classification and 10 geo-aware imageregression datasets; 3) a comprehensive suite of evaluation metrics to quantify geo-aware models’ overall performance as well as their geographic bias, with a novel Geo-Bias Score metric. Finally, we provide a detailed analysis and insights into the model performance and geographic bias of different location encoders. We believe TorchSpatial will foster future advancement of spatial representationlearning and spatial fairness in GeoAI research. The TorchSpatial model framework and LocBench benchmark are available at https://github.com/seai-lab/TorchSpatial, and the Geo-Bias Score evaluation framework is available at https://github.com/seai-lab/PyGBS.

A dual hesitant fuzzy set (DHFS) describes the uncertainty in the real world by using the membership degree and nonmembership degree. It can collect fuzzy information comprehensively and apply them into decision-making tasks efficiently. In this article, we extract some characteristics, such as the average function, variance function, hesitancy degree to describe a dual hesitant fuzzy element, and develop novel distance measures of DHFSs based on these characteristics. Further, we investigate their properties and prove the triangle inequality of distance measure. Finally, we apply it in practical medical diagnosis to illustrate the validity of our proposed distance measures.

Recently, several recurrent neural network (RNN)-based models have been proposed to delineate the outlines of buildings from very high resolution (VHR) remote sensing images. These models first use convolutional neural networks (CNNs) to recognize the boundary fragments by learning probability maps of both edges and corners and then feed them into RNN to find and link a set of sequent corners into external boundaries of buildings. However, caused by the category imbalance of edges and corners, the local ambiguity of edge detection is very serious, which significantly affects the accuracy of predicted outline corners. To tackle this challenge, this article introduces a convolutional RNN embedded with line segment information (LSI-RNN), a novel network that aims to directly detect line segment instead of edges. To achieve this, LSI-RNN utilizes an additional cotraining branch to generate an attraction field map (AFM) by neural discriminative dimensionality reduction (NDDR) layer. Consequently, the conventional classification problem of edges is converted to a regression problem of line segments, thus solving the aforementioned issues. Experimental results over three remote sensing datasets with different spatial resolutions show that the proposed method consistently outperforms other state-of-the-art methods.