Diffusion Models with Anisotropic Gaussian Splatting for Image Inpainting

Image inpainting is a fundamental task in computer vision, aiming to restore missing or corrupted regions in images realistically. While recent deep learning approaches have significantly advanced the state-of-the-art, challenges remain in maintaining structural continuity and generating coherent textures, particularly in large missing areas. Diffusion models have shown promise in generating high-fidelity images but often lack the structural guidance necessary for realistic inpainting. We propose a novel inpainting method that combines diffusion models with anisotropic Gaussian splatting to capture both local structures and global context effectively. By modeling missing regions using anisotropic Gaussian functions that adapt to local image gradients, our approach provides structural guidance to the diffusion-based inpainting network. The Gaussian splat maps are integrated into the diffusion process, enhancing the model's ability to generate high-fidelity and structurally coherent inpainting results. Extensive experiments demonstrate that our method outperforms state-of-the-art techniques, producing visually plausible results with enhanced structural integrity and texture realism.

HVT: A Comprehensive Vision Framework for Learning in Non-Euclidean Space

Data representation in non-Euclidean spaces has proven effective for capturing hierarchical and complex relationships in real-world datasets. Hyperbolic spaces, in particular, provide efficient embeddings for hierarchical structures. This paper introduces the Hyperbolic Vision Transformer (HVT), a novel extension of the Vision Transformer (ViT) that integrates hyperbolic geometry. While traditional ViTs operate in Euclidean space, our method enhances the self-attention mechanism by leveraging hyperbolic distance and M\"obius transformations. This enables more effective modeling of hierarchical and relational dependencies in image data. We present rigorous mathematical formulations, showing how hyperbolic geometry can be incorporated into attention layers, feed-forward networks, and optimization. We offer improved performance for image classification using the ImageNet dataset.

Studying the Effects of Self-Attention on SAR Automatic Target Recognition

Attention mechanisms are critically important in the advancement of synthetic aperture radar (SAR) automatic target recognition (ATR) systems. Traditional SAR ATR models often struggle with the noisy nature of the SAR data, frequently learning from background noise rather than the most relevant image features. Attention mechanisms address this limitation by focusing on crucial image components, such as the shadows and small parts of a vehicle, which are crucial for accurate target classification. By dynamically prioritizing these significant features, attention-based models can efficiently characterize the entire image with a few pixels, thus enhancing recognition performance. This capability allows for the discrimination of targets from background clutter, leading to more practical and robust SAR ATR models. We show that attention modules increase top-1 accuracy, improve input robustness, and are qualitatively more explainable on the MSTAR dataset.

A Comparison of Traditional and Deep Learning Methods for Parameter Estimation of the Ornstein-Uhlenbeck Process

We consider the Ornstein-Uhlenbeck (OU) process, a stochastic process widely used in finance, physics, and biology. Parameter estimation of the OU process is a challenging problem. Thus, we review traditional tracking methods and compare them with novel applications of deep learning to estimate the parameters of the OU process. We use a multi-layer perceptron to estimate the parameters of the OU process and compare its performance with traditional parameter estimation methods, such as the Kalman filter and maximum likelihood estimation. We find that the multi-layer perceptron can accurately estimate the parameters of the OU process given a large dataset of observed trajectories; however, traditional parameter estimation methods may be more suitable for smaller datasets.

A Single Graph Convolution Is All You Need: Efficient Grayscale Image Classification

Image classifiers often rely on convolutional neural networks (CNN) for their tasks, which are inherently more heavyweight than multilayer perceptrons (MLPs), which can be problematic in real-time applications. Additionally, many image classification models work on both RGB and grayscale datasets. Classifiers that operate solely on grayscale images are much less common. Grayscale image classification has diverse applications, including but not limited to medical image classification and synthetic aperture radar (SAR) automatic target recognition (ATR). Thus, we present a novel grayscale (single channel) image classification approach using a vectorized view of images. We exploit the lightweightness of MLPs by viewing images as a vector and reducing our problem setting to the grayscale image classification setting. We find that using a single graph convolutional layer batch-wise increases accuracy and reduces variance in the performance of our model. Moreover, we develop a customized accelerator on FPGA for the proposed model with several optimizations to improve its performance. Our experimental results on benchmark grayscale image datasets demonstrate the effectiveness of the proposed model, achieving vastly lower latency (up to 16$\times$ less) and competitive or leading performance compared to other state-of-the-art image classification models on various domain-specific grayscale image classification datasets.

Benchmarking Deep Learning Classifiers for SAR Automatic Target Recognition

Synthetic Aperture Radar SAR Automatic Target Recognition ATR is a key technique of remote-sensing image recognition which can be supported by deep neural networks The existing works of SAR ATR mostly focus on improving the accuracy of the target recognition while ignoring the systems performance in terms of speed and storage which is critical to real-world applications of SAR ATR For decision-makers aiming to identify a proper deep learning model to deploy in a SAR ATR system it is important to understand the performance of different candidate deep learning models and determine the best model accordingly This paper comprehensively benchmarks several advanced deep learning models for SAR ATR with multiple distinct SAR imagery datasets Specifically we train and test five SAR image classifiers based on Residual Neural Networks ResNet18 ResNet34 ResNet50 Graph Neural Network GNN and Vision Transformer for Small-Sized Datasets (SS-ViT) We select three datasets MSTAR GBSAR and SynthWakeSAR that offer heterogeneity We evaluate and compare the five classifiers concerning their classification accuracy runtime performance in terms of inference throughput and analytical performance in terms of number of parameters number of layers model size and number of operations Experimental results show that the GNN classifier outperforms with respect to throughput and latency However it is also shown that no clear model winner emerges from all of our chosen metrics and a one model rules all case is doubtful in the domain of SAR ATR