The basic procedure for image morphing is as follows:

- Select corresponding points
- Warp one set of points towards another and vice versa
- Blend the results of the warping

A more detailed explaination of each of the steps is shown below. The full results are shown on the Results page.

### Selecting points

Deciding what points to select is a nontrivial matter. If given more time, I might have attempted to implement a feature detection system to algorithmically select the points. However, since my focus was on the actual morphing, I manually selected points. For a given image set I selected the same number of points in the same order for each image in the set (or pair). These points were more or less distributed throughout the regions of expected warping at points which would be easily identifiable across different images based on a simple set of rules. For example, point 26 and 27 for the face warping corresponded the centers of the left and right eyes respectively. Shown below are some examples of the points used for certain images.

In some cases, choosing the wrong points caused issues. For example, if the chosen feature when out of view or crossed some other feature such that the triangles were no longer in the same order, the warping no longer worked as well. This was especially true in my attempts to use image warping to show animation. In the example below, the first two images warp fine, however, the third and fourth do not work as well.

### Warping

The actual warping of an image is a matter of determining and applying a spatial transformation based on the pairs of control points. There are of course a variety of different methods to achieve this. In my implementation, I chose to use a local weighted mean which has the benefit of accounting for distortion which varies locally. Since I figured that different facial features would vary differently from one face to the next (eg. larger nose but smaller eyes) I decided that this would be the best choice for determining the transform to apply. To actually create the transform I used the MATLAB function cp2tform, which follows the following basic algorithm for the local weighted mean:

for each control point neighbors = the 12 closest control points use neighbors and their corresponding pairs to infer a second-order polynomial radius of influence = center point - furthest neighbor

The triangles connecting the points on the images shown earlier were the result of finding the Delaunay triangulation, which in some cases may be used to infer an affine mapping between the two set of points. I ultimately decided to use a higher order polynomial rather than the linear affine transform since the method using the Delaunay triangulation placed more restrictions upon the points used which made it more difficult to run when using certain image sets. The results from either method are shown below for comparison.

local weighted mean | piecewise linear |

## Using image morphing

### Transistions

Image morphing can be used to warp between two images smoothly. For one image, the points are warped toward the other image. The steps are essentially just incremental steps where each step warps the points towards points that are a certain distance from the desired final points.
At the same time, the q is warped towards p. One image starts out unwarped and the other completely warped and are warped in opposite directions such that the end result is the inverse of the initial state. |

I also tried to see how well morphing would work with images that were not very similar at all.