# Face Morphing, a Modern Threat to Border Security: Recent Advances and Open Challenges
## 4 Morphing Face Images
### Face Alignment  
The goal of the image alignment step is to obtain a warping of the two original images so that the locations of the corresponding landmarks (detected in the previous step) are matched. Warping is basically a geometric transformation applied to the pixel locations of both images. Early morphing techniques relied on scattered data interpolation [39], whereby the new pixel position pixels is interpolated based on the nearby control points (landmarks). More advanced approaches include the Free-Form Deformation (FFD) technique [40; 41] in which the image is embedded in a grid of control points (i.e., the pixellocations are expressed as a function of the grid-point locations). This way, applying a desired deformation to the grid, results also to an analogous deformation of the image. In feature-based image metamorphosis [42], the deformation is controlled by the grid lines, which is particularly advantageous for manual morphing as the user can position lines instead of points. In [43] the optimal affine transformation based on either landmarks or lines via the minimization of the moving least squares, while in [30] a morphing process by simulating the image as a mass spring system is proposed.  
The most widely used warping technique by state-of-the-art morphing algorithms is based on the Delaunay triangulation of the detected landmarks [5; 9; 22; 44; 45]; that is the partitioning of the images into a set of non-overlapping triangles whose vertices lie on the detected landmarks. The goal here is to obtain a matching between corresponding landmarks by applying geometrical transformations (rotations, translations and distortions) of the obtained Delaunay triangles.  
The steps involved in the warping process can be analyzed into the following steps [45; 46]:  
1. Generate triangular facial mesh: Obtain Delaunay triangulation of the detected landmark locations.
2. Create interpolated facial mesh by blending original landmark locations, i.e., \[\mathcal{L}^{i}_{w}=\alpha_{w}\,\mathcal{L}^{i}_{1}+(1-\alpha_{w})\,\mathcal{ L}^{i}_{2},\quad i=1,\ldots,N\] where \(\mathcal{L}^{i}_{w}\), \(\mathcal{L}^{i}_{1}\), \(\mathcal{L}^{i}_{2}\), denote the blended and the (two) original landmark locations, respectively, while \(N\) is the number of used landmarks. \(\alpha_{w}\) is a blending coefficient taking values in \([0,1]\) that controls the contribution of each of the two original faces in determining the location of the landmarks on the final morphed face. For example, \(\alpha_{w}=0\) (or, \(1\)) signifies that the landmark locations on the morphed image (and loosely speaking its general form and shape) will coincide with on of the involved originals.
3. Warp both original faces to the interpolated mesh: Apply affine transform to map the pixel locations of each the original triangles, to the locations of the corresponding interpolated triangle.  
In addition, to avoid ghost and blur artifacts and to obtain more natural warping results, the projection of the face images into a 3D space prior to warping has been proposed [47; 48].