Optical coherence tomography (OCT) is a well-established bedside imaging modality that allows analysis of skin structures in a non-invasive way. Automated OCT analysis of skin layers is of great relevance to study dermatological diseases. In this paper, an approach to detect the epidermal layer along with the follicular structures in healthy human OCT images is presented. To the best of the authors' knowledge, the approach presented in this paper is the only epidermis detection algorithm that segments the pilosebaceous unit, which is of importance in the progression of several skin disorders such as folliculitis, acne, lupus erythematosus, and basal cell carcinoma. The proposed approach is composed of two main stages. The first stage is a Convolutional Neural Network based on U-Net architecture. The second stage is a robust post-processing composed by a Savitzky-Golay filter and Fourier Domain Filtering to fully define the borders belonging to the hair follicles. After validation, an average Dice of 0.83 ± 0.06 and a thickness error of 10.25 μm is obtained on 270 human skin OCT images. Based on these results, the proposed method outperforms other state-of-the-art methods for epidermis segmentation. It demonstrates that the proposed image segmentation method successfully detects the epidermal region in a fully automatic way in addition to defining the follicular skin structures as main novelty.