## Average Geometry

First, we pick corresponding points on both faces. We take these coordinates, average them, and then compute a triangularization. We will try to fit both faces to this averaged geometry. Hover over the image to see the original.

## The Mid-Way Face

Then, taking our average geometry, we can compute a set of transformation functions that will allow us to transform triangles from one face to the average.
We can apply these transformations, morphing both faces into the same average geometry, and take 50% of the colors each.
This results in the mid-way face, i.e. the morph that considers both faces equally.

## Full Morph Sequence

Now, we can consider unequal morphs, where one face contributes more to the total than the other. As we vary this parameter, we can generate a set of images that smoothly transition to produce an appealing morph sequence.
Hooray! This works well, even though it looks a bit off because of the differences between our hair.

## Smiling Danes

We can extend this idea of face morphing to more than two images. For example, given an image set of Danish faces (here), we can produce averages in a very similar way — triangulating all the faces, computing an average geometry, then taking a fraction of each individual face in order to sum up to the average. Here is an example of an average smiling Danish face:

### More Geometry Fun

Now, we can play with the geometry a bit. On the left is my face warped into the average geometry, and on the right is the average male Danish face warped into my geometry:

We can also warp some of the individuals in the dataset to the average geometry. Some clearly work better than others:

### Caricatures

Instead of warping my face toward the mean, we can warp it away from the mean to accentuate features that differ from the average. On the left is the original image for comparison; the right side features the caricature (using the average Danish male):

Lovely. The caricature elongates the face to be even longer & skinner, and generally makes it more angular (e.g. my chin). Doin' wonders for self-confidence.