Kernel methods are widely utilized in machine learning field to learn, from training data, a latent function in a reproducing kernel Hilbert space. It is well known that the approximator thus obtained usually achieves a linear representation, which brings various computational benefits, while maintaining great representation power (i.e., universal approximation). However, when non-negativity constraints are imposed on the function's outputs, the literature usually takes the kernel method-based approximators as offering linear representations at the expense of limited model flexibility or good representation power by allowing for their nonlinear forms. The main contribution of this paper is to derive a sufficient condition for a positive definite kernel so that it may construct flexible and linear approximators of non-negative functions. We call a kernel function that offers these attributes an inverse M-kernel; it is a generalization of the inverse M-matrix. Furthermore, we show that for a one-dimensional input space, universal exponential/Abel kernels are inverse M-kernels and construct linear universal approxima-tors of non-negative functions. To the best of our knowledge, it is the first time that the existence of linear universal approximators of non-negative functions has been elucidated. We confirm the effectiveness of our results by experiments on the problems of non-negativity-constrained regression, density estimation, and intensity estimation. Finally, we discuss issues and perspectives on multi-dimensional input settings.

Understanding pain-related facial behaviors is essential for digital healthcare in terms of effective monitoring, assisted diagnostics, and treatment planning, particularly for patients unable to communicate verbally. Existing data-driven methods of detecting pain from facial expressions are limited due to interpretability and severity quantification. To this end, we propose GraphAU-Pain, leveraging a graph-based framework to model facial Action Units (AUs) and their interrelationships for pain intensity estimation. AUs are represented as graph nodes, with co-occurrence relationships as edges, enabling a more expressive depiction of pain-related facial behaviors. By utilizing a relational graph neural network, our framework offers improved interpretability and significant performance gains. Experiments conducted on the publicly available UNBC dataset demonstrate the effectiveness of the GraphAU-Pain, achieving an F1-score of 66.21% and accuracy of 87.61% in pain intensity estimation.

Estimating the location and intensity of tropical cyclones holds crucial significance for predicting catastrophic weather events. In this study, we approach this task as a detection and regression challenge, specifically over the North Indian Ocean (NIO) region where best tracks location and wind speed information serve as the labels. The current process for cyclone detection and intensity estimation involves physics-based simulation studies which are time-consuming, only using image features will automate the process for significantly faster and more accurate predictions. While conventional methods typically necessitate substantial prior knowledge for training, we are exploring alternative approaches to enhance efficiency. This research aims to focus specifically on cyclone detection, intensity estimation and related aspects using only image input and data-driven approaches and will lead to faster inference time and automate the process as opposed to current NWP models being utilized at SAC. In context to algorithm development, a novel two stage detection and intensity estimation module is proposed. In the first level detection we try to localize the cyclone over an entire image as captured by INSAT3D over the NIO (North Indian Ocean). For the intensity estimation task, we propose a CNN-LSTM network, which works on the cyclone centered images, utilizing a ResNet-18 backbone, by which we are able to capture both temporal and spatial characteristics.

Automatic facial action unit (AU) recognition is used widely in facial expression analysis. Most existing AU recognition systems aim for cross-participant non-calibrated generalization (NCG) to unseen faces without further calibration. However, due to the diversity of facial attributes across different identities, accurately inferring AU activation from single images of an unseen face is sometimes infeasible, even for human experts -- it is crucial to first understand how the face appears in its neutral expression, or significant bias may be incurred. Therefore, we propose to perform one-frame calibration (OFC) in AU recognition: for each face, a single image of its neutral expression is used as the reference image for calibration. With this strategy, we develop a Calibrating Siamese Network (CSN) for AU recognition and demonstrate its remarkable effectiveness with a simple iResNet-50 (IR50) backbone. On the DISFA, DISFA+, and UNBC-McMaster datasets, we show that our OFC CSN-IR50 model (a) substantially improves the performance of IR50 by mitigating facial attribute biases (including biases due to wrinkles, eyebrow positions, facial hair, etc.), (b) substantially outperforms the naive OFC method of baseline subtraction as well as (c) a fine-tuned version of this naive OFC method, and (d) also outperforms state-of-the-art NCG models for both AU intensity estimation and AU detection.

Facial Expression Analysis remains a challenging task due to unexpected task-irrelevant noise, such as identity, head pose, and background. To address this issue, this paper proposes a novel framework, called Norface, that is unified for both Action Unit (AU) analysis and Facial Emotion Recognition (FER) tasks. Norface consists of a normalization network and a classification network. First, the carefully designed normalization network struggles to directly remove the above task-irrelevant noise, by maintaining facial expression consistency but normalizing all original images to a common identity with consistent pose, and background. Then, these additional normalized images are fed into the classification network. Due to consistent identity and other factors (e.g. head pose, background, etc.), the normalized images enable the classification network to extract useful expression information more effectively. Additionally, the classification network incorporates a Mixture of Experts to refine the latent representation, including handling the input of facial representations and the output of multiple (AU or emotion) labels. Extensive experiments validate the carefully designed framework with the insight of identity normalization. The proposed method outperforms existing SOTA methods in multiple facial expression analysis tasks, including AU detection, AU intensity estimation, and FER tasks, as well as their cross-dataset tasks. For the normalized datasets and code please visit {https://norface-fea.github.io/}.

Predicting typhoon intensity accurately across space and time is crucial for issuing timely disaster warnings and facilitating emergency response. This has vast potential for minimizing life losses and property damages as well as reducing economic and environmental impacts. Leveraging satellite imagery for scenario analysis is effective but also introduces additional challenges due to the complex relations among clouds and the highly dynamic context. Existing deep learning methods in this domain rely on convolutional neural networks (CNNs), which suffer from limited per-layer receptive fields. This limitation hinders their ability to capture long-range dependencies and global contextual knowledge during inference. In response, we introduce a novel approach, namely "Typhoon Intensity Transformer" (Tint), which leverages self-attention mechanisms with global receptive fields per layer. Tint adopts a sequence-to-sequence feature representation learning perspective. It begins by cutting a given satellite image into a sequence of patches and recursively employs self-attention operations to extract both local and global contextual relations between all patch pairs simultaneously, thereby enhancing per-patch feature representation learning.

Traffic management is a serious problem in many cities around the world. Even the suburban areas are now experiencing regular traffic congestion. Inappropriate traffic control wastes fuel, time, and the productivity of nations. Though traffic signals are used to improve traffic flow, they often cause problems due to inappropriate or obsolete timing that does not tally with the actual traffic intensity at the intersection. Traffic intensity determination based on statistical methods only gives the average intensity expected at any given time. However, to control traffic accurately, it is required to know the real-time traffic intensity. In this research, image processing and machine learning have been used to estimate actual traffic intensity in real time. General-purpose electronic hardware has been used for in-situ image processing based on the edge-detection method. A deep neural network (DNN) was trained to infer traffic intensity in each image in real time. The trained DNN estimated traffic intensity accurately in 90% of the real-time images during road tests. The electronic system was implemented on a Raspberry Pi single-board computer; hence, it is cost-effective for large-scale deployment.

As a fine-grained and local expression behavior measurement, facial action unit (FAU) analysis (e.g., detection and intensity estimation) has been documented for its time-consuming, labor-intensive, and error-prone annotation. Thus a long-standing challenge of FAU analysis arises from the data scarcity of manual annotations, limiting the generalization ability of trained models to a large extent. Amounts of previous works have made efforts to alleviate this issue via semi/weakly supervised methods and extra auxiliary information. However, these methods still require domain knowledge and have not yet avoided the high dependency on data annotation. This paper introduces a robust facial representation model MAE-Face for AU analysis. Using masked autoencoding as the self-supervised pre-training approach, MAE-Face first learns a high-capacity model from a feasible collection of face images without additional data annotations. Then after being fine-tuned on AU datasets, MAE-Face exhibits convincing performance for both AU detection and AU intensity estimation, achieving a new state-of-the-art on nearly all the evaluation results. Further investigation shows that MAE-Face achieves decent performance even when fine-tuned on only 1\% of the AU training set, strongly proving its robustness and generalization performance.

What is the best way to learn a universal face representation? Recent work on Deep Learning in the area of face analysis has focused on supervised learning for specific tasks of interest (e.g. face recognition, facial landmark localization etc.) but has overlooked the overarching question of how to find a facial representation that can be readily adapted to several facial analysis tasks and datasets. To this end, we make the following 4 contributions: (a) we introduce, for the first time, a comprehensive evaluation benchmark for facial representation learning consisting of 5 important face analysis tasks. (b) We systematically investigate two ways of large-scale representation learning applied to faces: supervised and unsupervised pre-training. Importantly, we focus our evaluations on the case of few-shot facial learning. (c) We investigate important properties of the training datasets including their size and quality (labelled, unlabelled or even uncurated). (d) To draw our conclusions, we conducted a very large number of experiments. Our main two findings are: (1) Unsupervised pre-training on completely in-the-wild, uncurated data provides consistent and, in some cases, significant accuracy improvements for all facial tasks considered. (2) Many existing facial video datasets seem to have a large amount of redundancy. We will release code, and pre-trained models to facilitate future research.