User authentication is an important part of any system that must ensure valid access rights. One of the methods of biometric authentication is facial recognition, where an algorithm creates a concise representation of the subject's face from a facial image that can be used either to register the subject in the database or for authentication. However, facial recognition methods are not without their drawbacks. State-of-the-art facial recognition systems can very successfully determine a person's identity from a facial image, but they lack resistance to presentation attacks. One of the promising and newly researched biometric features, which have the ability to defend against such attacks, are the physical and behavioral components of visual speech features - the physical uniqueness of the lips with regard to the shape and imprint/texture of the lips and the behavioral uniqueness of the visual style of speech. This paper provides an overview of the developments of biometric authentication methods from simpler mathematical models to more modern and complex solutions based on deep learning. Following the overview, an innovative way of creating a computer vision based biometric authentication algorithm by exploiting the physical and behavioral features of the area around the lips during speech is presented. This was achieved by processing the GRID [5] dataset for compatibility with a triplet loss function and training a Siamese neural network to create a vector representation of a series of images of the lip region that captures the physical and behavioral features of speech. The GRID dataset consists of audio and video recordings of utterances that follow a strict pattern. The processing of the GRID dataset involves clipping video images that correspond to the area around the mouth for the selected part of the utterance. For this purpose, the Mediapipe framework and the associated FaceMesh model, which predicts face keypoints, are used. Tensors are created from the obtained data, from which it is possible to create positive and negative pairs. Positive pairs are used as input to train a 3D convolution-based double Siamese neural network, called LipAuth. The output of the LipAuth model branch is a vector representation of the physical and behavioral components of the user's lips while uttering a textual password. LipAuth model training is done by a modified loss function that performs hard-negative mining dynamically. The optimal model was trained using the Bayesian [33] hyperparameter search procedure. Model performance was measured on GRID dataset and our own dataset using equal-error rate, false acceptance rate, and false rejection rate.