This work investigates object detection algorithms with application to astronomical images. We specifically target to detect faint astronomical sources which value near the image background level. Our main directions include Mathematical Morphology (MM) and Convolutional Neural Network (ConvNet). The contributions of this study are presented in two parts:The first part proposes a novel morphological-based approach based on component-graphs and statistical hypothesis tests. The component-graphs can efficiently handle multi-band images while the statistical hypothesis tests can identify components that are significantly different from the background level. Beyond the classical component-trees and their multivariate extensions, the component-g...