Heatmap regression (HR) has become one of the mainstream approaches for face alignment and has obtained promising results under constrained environments. However, when a face image suffers from large pose variations, heavy occlusions and complicated illuminations, the performances of HR methods degrade greatly due to the low resolutions of the generated landmark heatmaps and the exclusion of important high-order information that can be used to learn more discriminative features. To address the alignment problem for faces with extremely large poses and heavy occlusions, this paper proposes a heatmap subpixel regression (HSR) method and a multi-order cross geometry-aware (MCG) model, which are seamlessly integrated into a novel multi-order high-precision hourglass network (MHHN). The HSR method is proposed to achieve high-precision landmark detection by a well-designed subpixel detection loss (SDL) and subpixel detection technology (SDT). At the same time, the MCG model is able to use the proposed multi-order cross information to learn more discriminative representations for enhancing facial geometric constraints and context information. To the best of our knowledge, this is the first study to explore heatmap subpixel regression for robust and high-precision face alignment. The experimental results from challenging benchmark datasets demonstrate that our approach outperforms state-of-the-art methods in the literature.

Recently, heatmap regression has been widely explored in facial landmark detection and obtained remarkable performance. However, most of the existing heatmap regression-based facial landmark detection methods neglect to explore the high-order feature correlations, which is very important to learn more representative features and enhance shape constraints. Moreover, no explicit global shape constraints have been added to the final predicted landmarks, which leads to a reduction in accuracy. To address these issues, in this article, we propose a multiorder multiconstraint deep network (MMDN) for more powerful feature correlations and shape constraints’ learning. Especially, an implicit multiorder correlating geometry-aware (IMCG) model is proposed to introduce the multiorder spatial correlations and multiorder channel correlations for more discriminative representations. Furthermore, an explicit probability-based boundary-adaptive regression (EPBR) method is developed to enhance the global shape constraints and further search the semantically consistent landmarks in the predicted boundary for robust facial landmark detection. It is interesting to show that the proposed MMDN can generate more accurate boundary-adaptive landmark heatmaps and effectively enhance shape constraints to the predicted landmarks for faces with large pose variations and heavy occlusions. Experimental results on challenging benchmark data sets demonstrate the superiority of our MMDN over state-of-the-art facial landmark detection methods.

Fuzzy clustering techniques, especially fuzzy C-means (FCM) and its weighted variants, are typical partitive clustering models that are widely used for revealing possible hidden structures in data. Although they can quantitatively depict the overlapping areas with a partition matrix, their performances deteriorate when dealing with high-dimensional data because the distance computations may be negatively impacted by the irrelevant features, and then the concentration effect may arise. Moreover, they are sensitive to noisy environments. To tackle these obstacles, a robust jointly sparse fuzzy clustering method (RJSFC) is proposed in this study. The representative prototypes, sparse membership grades, and an orthogonal projection matrix are simultaneously learnt when optimizing RJSFC. The obtained low-dimensional embeddings can preserve the local neighborhood structure, and the clustering is conducted in the transformed lower dimensional space rather than the original space, which improves the capability of fuzzy clustering for dealing with high-dimensional scenarios. Furthermore, ${L_{2,1}}$ -norm is exploited as the basic metric for both loss and regularization parts in RJSFC, the robustness of the model and the interpretability of the extracted features are enhanced. The notions of fuzzy clustering, neighborhood structure preservation, and feature extraction are seamlessly integrated into a unified model. The limitation of the previous two-stage clustering framework when dealing with high-dimensional data entailing dimensionality reduction and clustering procedures separately can be effectively addressed. Extensive experimental results on various well-known datasets demonstrate the usefulness of RJSFC when comparing with some state-of-the-art methods.

Outlier detection refers to the identification of anomalous samples that deviate significantly from the distribution of normal data and has been extensively studied and used in a variety of practical tasks. However, most unsupervised outlier detection methods are carefully designed to detect specified outliers, while real-world data may be entangled with different types of outliers. In this study, we propose a fuzzy rough sets-based multi-scale outlier detection method to identify various types of outliers. Specifically, a novel fuzzy rough sets-based method that integrates relative fuzzy granule density is first introduced to improve the capability of detecting local outliers. Then, a multi-scale view generation method based on granular-ball computing is proposed to collaboratively identify group outliers at different levels of granularity. Moreover, reliable outliers and inliers determined by the three-way decision are used to train a weighted support vector machine to further improve the performance of outlier detection. The proposed method innovatively transforms unsupervised outlier detection into a semi-supervised classification problem and for the first time explores the fuzzy rough sets-based outlier detection from the perspective of multi-scale granular balls, allowing for high adaptability to different types of outliers. Extensive experiments carried out on both artificial and UCI datasets demonstrate that the proposed outlier detection method significantly outperforms the state-of-the-art methods, improving the results by at least 8.48% in terms of the Area Under the ROC Curve (AUROC) index.

High-resolution point clouds (HRPCD) anomaly detection (AD) plays a critical role in precision machining and high-end equipment manufacturing. Despite considerable 3D-AD methods that have been proposed recently, they still cannot meet the requirements of the HRPCD-AD task. There are several challenges: i) It is difficult to directly capture HRPCD information due to large amounts of points at the sample level; ii) The advanced transformer-based methods usually obtain anisotropic features, leading to degradation of the representation; iii) The proportion of abnormal areas is very small, which makes it difficult to characterize. To address these challenges, we propose a novel group-level feature-based network, called Group3AD, which has a significantly efficient representation ability. First, we design an Intercluster Uniformity Network (IUN) to present the mapping of different groups in the feature space as several clusters, and obtain a more uniform distribution between clusters representing different parts of the point clouds in the feature space. Then, an Intracluster Alignment Network (IAN) is designed to encourage groups within the cluster to be distributed tightly in the feature space. In addition, we propose an Adaptive Group-Center Selection (AGCS) based on geometric information to improve the pixel density of potential anomalous regions during inference. The experimental results verify the effectiveness of our proposed Group3AD, which surpasses Reg3D-AD by the margin of 5% in terms of object-level AUROC on Real3D-AD. We provide the code and supplementary information on our website: https://github.com/M-3LAB/Group3AD.