The present article investigates the application of deep learning methods to monitor combustion instabilities based on time-averaged flame images. Experiments on BASIS (Beihang Axial Swirler Independently-Stratified) burner are carried out in a wide range of operating conditions to cover various flame shapes. We design a CNN (Convolutional Neural Networks) named BIM (BASIS Image Monitor) to extract features from flame shapes and determine the thermoacoustic states of the flames ahead of time. Experiments of 112 operating conditions are conducted, and their images are fed into BIM for training and testing purposes. BIM achieves around 99% prediction accuracy after a short training process lasting less than 20 minutes. Features extracted by BIM and visualized by Class Activation Maps (CAM) method reflect the underlying statistical links between flame images and their stabilities. Several phenomena (lift-off flame, flame-wall interaction, outer shear layer (OSL) flame and fuel mixing process) and their contributions to stabilities can be captured and quantified by CAM. After that, we test BIM with eight unknown operating conditions, and BIM can still perform well, identifying their stabilities and unstable features accurately. This paper explores the monitoring accuracy and feature extraction abilities of CNN in combustion. The BIM model shows potential to be a precursor in monitoring and active control systems of combustion instabilities.