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-graph holds the complete structural information of multi-band images as directed acyclic graphs (DAGs). Such DAGs are more general and more powerful at the cost of non-trivial object filtering algorithms. Then, we introduce two algorithms to filter duplicated and partial components in the component-graphs. Experiments demonstrate that our proposed approach significantly improves object detection on both multi-band simulated and real astronomical images.The second part turns our attention to ConvNet direction.We introduce a real dataset of annotated astronomical objects.Based on this dataset, we propose two models: a ConvNet-based model and a hybrid model. The ConvNet-based model tailors astronomical contexts with three novel components, including a normalization layer, an object differentiation module, and a smoothness regularizer. Besides, the hybrid model uses both Morphology and ConvNet. In the hybrid method, morphological modules select region proposals while ConvNet extracts relevant information from the selected proposals. Ablation studies show that the two proposed models outperform the state of the art on both synthetic and real datasets