Identification of the mandibular canal path in Computed Tomography (CT) scans is important in dental implantology. Typically, prior to the implant planning, dentists find a sagittal plane where the mandibular canal path is maximally observed, to manually identify the mandibular canal. However, this is time-consuming and requires extensive experience. In this paper, we propose a deep-learning-based framework to detect the desired sagittal plane automatically. This is accomplished by utilizing two main techniques: 1) a modified version of the iterative transformation network (ITN) method for obtaining initial planes, and 2) a fine searching method based on a convolutional neural network (CNN) classifier for detecting the desirable sagittal plane. This combination of techniques facilitates accurate plane detection, which is a limitation of the stand-alone ITN method. We have tested on a number of CT datasets to demonstrate that the proposed method can achieve more satisfactory results compared to the ITN method. This allows dentists to identify the mandibular canal path efficiently, providing a foundation for future research into more efficient, automatic mandibular canal detection methods.