<p><em>Curvilinear structure detection in images has been investigated for decades. In general, the detection of curvilinear structures includes two aspects, binary segmentation of the image and  inference of the graph representation of the curvilinear network. In our work, we propose a connected-tube model based on a marked point process (MPP) for addressing the two issues. The proposed tube model is applied to fiber detection in microscopy images by combining connected-tube and ellipse models. Moreover, a tube-based segmentation algorithm has been proposed to improve the segmentation accuracy. Experiments on fiber-reinforced polymer images, satellite images, and retinal vessel images will be presented. Additionally, we extend the 2D tube model to a 3D tube model, with each tube be modeled as a cylinder. To investigate the supervised curvilinear structure detection method, we focus on the application of road detection in satellite images and propose a two-stage learning strategy for road segmentation. A probability map is generated in the first stage by a selected neural network, then we attach the probability map image to the original RGB images and feed the resulting four images to a U-Net-like network in the second stage to get a refined result.</em></p> <p><br></p> <p><em>Anomaly detection in time series is a key step in diagnosing abnormal behavior in some systems. Long Short-Term Memory networks (LSTMs) have been demonstrated to be useful for anomaly detection in time series, due to their predictive power. However, for a system with thousands of different time sequences, a single LSTM predictor may not perform well for all the sequences. To enhance adaptability, we propose a stacked predictor framework. Also, we propose a novel dynamic thresholding algorithm based on the prediction errors to extract the potential anomalies. To further improve the accuracy of anomaly detection, we propose a post-detection verification method based on a fast and accurate time series subsequence matching algorithm.</em></p> <p><br></p> <p><em>To detect anomalies from multi-channel time series, a bi-directional transformer-based predictor is applied to generate the prediction error sequences, and a statistical model referred as an anomaly marked point process (Anomaly-MPP) is proposed to extract the anomalies from the error sequences. The effectiveness of our methods is demonstrated by testing on a variety of time series datasets.</em></p>