Delaunay Triangulation of Facial Landmarks

Introduction

The determination and extraction of facial features are essential in a plethora of applications such as personal identification, 3D face modeling, and model-based video coding. Researchers have developed several methods for facial feature segmentation in order to localize the facial subareas. Among these methods, the Delaunay triangulation is very effective due to its ability to adapt to different face variations.

The Delaunay triangulation method is widely used in numerous interesting applications where triangulation of facial landmarks is often performed. These triangles are then exploited for further processing. The underlying applications of this technique in computer vision are mainly the ones listed below:

• Face morphing is the fusion of two people’s faces so that the resulting facial image looks like both people.

• Face effects are applied in social media filters.

• **Facial emotion recognition **analyzes facial expressions from both static digital images and video streams.

What is the Delaunay Triangulation?

The Delaunay triangulation technique consists of creating a mesh of adjacent, nonoverlapping triangles from a predefined dataset of distinct points.

This technique implies the following conditions:

• The triangulation doesn’t occur when the given points are in the same line.

• The circumcircle of any drawn triangle should have empty interiors so that no point in the dataset stays inside the circumcircle of any triangle. This condition is often known as the Delaunay condition.

The slideshow below exhibits a graphical representation of the Delaunay triangulation concept and its step-by-step implementation: