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We present a method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy. In this procedure, a coarse grid of training points is used at the initial training stages, while more points are added at later stages based on the value of the residual at a larger set of evaluation points. This method increases the robustness of the neural network approximation and can result in significant computational savings, particularly when the solution is non-smooth. Numerical results are presented for benchmark problems for scalar-valued PDEs, namely Poisson and Helmholtz equations, as well as for an inverse acoustics problem.

This paper presents an automatic solution to the problem of detecting and counting cars in unmanned aerial vehicle (UAV) images. This is a challenging task given the very high spatial resolution of UAV images (on the order of a few centimetres) and the extremely high level of detail, which require suitable automatic analysis methods. Our proposed method begins by segmenting the input image into small homogeneous regions, which can be used as candidate locations for car detection. Next, a window is extracted around each region, and deep learning is used to mine highly descriptive features from these windows. We use a deep convolutional neural network (CNN) system that is already pre-trained on huge auxiliary data as a feature extraction tool, combined with a linear support vector machine (SVM) classifier to classify regions into "car" and "no-car" classes. The final step is devoted to a fine-tuning procedure which performs morphological dilation to smooth the detected regions and fill any holes. In addition, small isolated regions are analysed further using a few sliding rectangular windows to locate cars more accurately and remove false positives. To evaluate our method, experiments were conducted on a challenging set of real UAV images acquired over an urban area. The experimental results have proven that the proposed method outperforms the state-of-the-art methods, both in terms of accuracy and computational time.

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In this paper, a geometry-based image retrieval system is developed for multi-object images. We model both shape and topology of image objects using a structured representation called curvature tree (CT). The hierarchy of the CT reflects the inclusion relationships between the image objects. To facilitate shape-based matching, triangle-area representation (TAR) of each object is stored at the corresponding node in the CT. The similarity between two multi-object images is measured based on the maximum similarity subtree isomorphism (MSSI) between their CTs. For this purpose, we adopt a recursive algorithm to solve the MSSI problem and a very effective dynamic programming algorithm to measure the similarity between the attributed nodes. Our matching scheme agrees with many recent findings in psychology about the human perception of multi-object images. Experiments on a database of 13500 real and synthesized medical images and the MPEG-7 CE-1 database of 1400 shape images have shown the effectiveness of the proposed method.

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Scene classification is a highly useful task in Remote Sensing (RS) applications. Many efforts have been made to improve the accuracy of RS scene classification. Scene classification is a challenging problem, especially for large datasets with tens of thousands of images with a large number of classes and taken under different circumstances. One problem that is observed in scene classification is the fact that for a given scene, only one part of it indicates which class it belongs to, whereas the other parts are either irrelevant or they actually tend to belong to another class. To address this issue, this paper proposes a deep attention Convolutional Neural Network (CNN) for scene classification in remote sensing. CNN models use successive convolutional layers to learn feature maps from larger and larger regions (or receptive fields) of the scene. The attention mechanism computes a new feature map as a weighted average of these original feature maps. In particular, we propose a solution, named EfficientNet-B3-Attn-2, based on the pre-trained EfficientNet-B3 CNN enhanced with an attention mechanism. A dedicated branch is added to layer 262 of the network, to compute the required weights. These weights are learned automatically by training the whole CNN model end-to-end using the backpropagation algorithm. In this way, the network learns to emphasize important regions of the scene and suppress the regions that are irrelevant to the classification. We tested the proposed EfficientNet-B3-Attn-2 on six popular remote sensing datasets, namely UC Merced, KSA, OPTIMAL-31, RSSCN7, WHU-RS19, and AID datasets, showing its strong capabilities in classifying RS scenes.