Delineation of alveolar bone aids the diagnosis and treatment of periodontal diseases. In current practice, conventional 2D radiography and 3D cone-beam computed tomography (CBCT) imaging are used as the non-invasive approaches to image and delineate alveolar bone structures. Recently, high-frequency ultrasound imaging is proposed as an alternative to conventional imaging methods to prevent the harmful effects of ionizing radiation. However, the manual delineation of alveolar bone from ultrasound imaging is time-consuming and subject to inter and intraobserver variability. This study proposes to use a convolutional neural network-based machine learning framework to automatically segment the alveolar bone from ultrasound images. The proposed method consists of a homomorphic filtering based noise reduction and a u-net machine learning framework for automated delineation. The proposed method was evaluated over 15 ultrasound images of tooth acquired from procine specimens. The comparisons against manual ground truth delineations performed by three experts in terms of mean Dice score and Hausdorff distance values demonstrate that the proposed method yielded an improved performance over a recent state of the art graph cuts based method.