Improvements and Applications of Scale Space and Image Analysis

Hi-C technology has been developed to profile genome-wide chromosome conformation capture. In the first project, we propose SSSHiC, a new loop calling algorithm based on Significance in Scale Space (SSS), which can be used to understand Hi-C data at different levels of resolution. By applying SSSHiC to neuronal and glial Hi-C data, we detected loops that are potentially engaged in cell type specific gene regulation. In order to improve SSSHiC, in the second project, we propose advanced distribution theory for significance in scale space. The classical SSS was developed for image data, enabling the detection of both slopes and curvatures across multiple spatial scales. However, fully valid inference for 2-D SSS has remained unavailable, largely due to the more complex dependence structure of random fields. In this project, we use a completely different probability methodology which gives an advanced distribution theory for SSS, establishing a valid hypothesis testing procedure for both slope and curvature detection. Both classical and advanced SSS methods analyze curvature structures in 2-D images in an unsupervised manner; however, they are not directly applicable to supervised learning tasks, such as predicting specific labels from images. In the third project, we developed a Convolutional Neural Network (CNN) and Multiple Instance Learning (MIL) framework to classify estrogen receptor (ER) status and PAM50 subtypes from breast cancer histopathology images. We assessed performance using both within-dataset and cross-dataset validation across five independent datasets. In the fourth project, we develop a new assessment method to evaluate the quality of reported Covid-19 data. Throughout the previous Covid-19 period, numerous models and methods were applied to pandemic data. However, the abnormal results obtained from modeling state-level data in the United States prompted us to place greater emphasis on testing the data quality before employing any methods to model it.