Bone age assessment (BAA) is a widely used clinical practice for the biological development of adolescents. The Tanner Whitehouse (TW) method is a traditionally mainstream method that manually extracts multiple regions of interest (ROIs) related to skeletal maturity to infer bone age. In this paper, we propose a deep learning-based method for fully automatic ROIs localization and BAA. The method consists of two parts: a U-net-based backbone, selected for its strong performance in semantic segmentation, which enables precise and efficient localization without the need for complex pre- or post-processing. This method achieves a localization precision of 99.1% on the public RSNA dataset. Second, an InceptionResNetV2 network is utilized for feature extraction from both the ROIs and the whole image, as it effectively captures both local and global features, making it well-suited for bone age prediction. The BAA neural network combines the advantages of both ROIs-based methods (TW3 method) and global feature-based methods (GP method), providing high interpretability and accuracy. Numerical experiments demonstrate that the method achieves a mean absolute error (MAE) of 0.38 years for males and 0.45 years for females on the public RSNA dataset, and 0.41 years for males and 0.44 years for females on an in-house dataset, validating the accuracy of both localization and prediction.