To create usable data sets across two images, I saved a list of coordinate points on each image, making sure
to keep a consistent order of where I clicked at which index. I saved this list to a .json file so
that
I did not have to re-configure every time I ran my code.
Image 1 points
Image 2 points
Ordering of points
With a list of correspondences (i.e. coordinates) ready, I could create a triangularization using scipy.spatial.Delaunay.
This created a "grid" that enclosed each pixel in a triangle. However I did not just triangularize either list of
points. First, I had to find the average or mid-way grid between my source images.
Delaunay returns a list of simplices for each triangle, which represents the vertices of each triangle
using the index of the coordinate from the inputted lists. For example, a triangle would be represented as [12
23 19] which meant its vertices were the 12th, 23th, and 19th coordinates in the input list. Since the
correspondences are consistent, we can use these indices to find the corresponding triangle's vertex coordinates in
each source image.
We're interested in an affine transform that relates the "mid-way" triangle to a "source" triangle. Using linear algebra, I found this affine transform matrix. Then, looping over every triangle in the mid-way grid, I can apply the two affine transform matrices to every pixel. This gives me a pixel coordinate inside both source image spaces. To find the color at this pixel in the mid-way grid, I take the average color between the mapped pixels in each source image.
N consistent correspondences for two images N points midtri in the mid-way triangularization tri to the corresponding triangle in both source imagestri mid 
Image 1
Image 2
Halfway morph
To create a smooth sequence from image 1 to image 2, we can use some parameter frac between 0 and 1.
This allows me to linearly interpolate the structure (i.e. correspondences points) and color between two images. In
this resulting animation, I have 45 images that linearly interpolate between my start and end images.
Morphing between Image 1 and Image 2
To find the average face in a data set of multiple faces, I can find the average shape by adding together all the correspondences and dividing by the number of faces. (This is just an arithmetic average of coordinate points). Thankfully, there are annotated data sets available, so I used a set of 37 Danish scientists' faces.
We can find the average appearance by applying affine transforms to every pixel in the image, as before. (Each triangle in the image has a different affine transform to the corresponding triangle in the average image.)
Average across 7 faces
14-1f
14-1f => Average
38-1m
38-1m => Average
B warped with average
Average warped with B
I can extract a subset of my Danish scientist image set — there is a limited amount of female scientists, conveniently labeled as "1f". This creates an average *female* face. Notice the blurriness away from the face. Since there are fewer data points, each outlier contributes more weight to the final image.
Average across females (N = 8)
Average across all (N = 37)
This average female image is closer to my own facial features. So, it provides a good candidate of comparison to
make a caricature of myself. I can create a caricature by creating corresponding points, just as before. Then, I can
find the difference between the corresponding points, im_points - avg_points, and multiply a constant
alpha. Then, we can add this difference to avg_points. This exaggerates the difference and
creates a caricuature.
alpha = 1.0
alpha = 1.25
alpha = 1.5
alpha = 1.75
Just for fun, I can animate my face from happy to pouty!
Happy
Sad
Sequence