The purpose of this investigation was to evaluate the diagnostic performance of two convolutional neural networks (CNNs), namely ResNet-152 and VGG-19, in analyzing, on panoramic images, the rapport that exists between the lower third molar (MM3) and the mandibular canal (MC), and to compare this performance with that of an inexperienced observer (a sixth year dental student). Utilizing the k-fold cross-validation technique, 142 MM3 images, cropped from 83 panoramic images, were split into 80% as training and validation data and 20% as test data. They were subsequently labeled by an experienced radiologist as the gold standard. In order to compare the diagnostic capabilities of CNN algorithms and the inexperienced observer, the diagnostic accuracy, sensitivity, specificity, and positive predictive value (PPV) were determined. ResNet-152 achieved a mean sensitivity, specificity, PPV, and accuracy, of 84.09%, 94.11%, 92.11%, and 88.86%, respectively. VGG-19 achieved 71.82%, 93.33%, 92.26%, and 85.28% regarding the aforementioned characteristics. The dental student’s diagnostic performance was respectively 69.60%, 53.00%, 64.85%, and 62.53%. This work demonstrated the potential use of deep CNN architecture for the identification and evaluation of the contact between MM3 and MC in panoramic pictures. In addition, CNNs could be a useful tool to assist inexperienced observers in more accurately identifying contact relationships between MM3 and MC on panoramic images.