I put a quick SOM into the current test patch to see how well it deals with this idealized object data. The SOM is a 2×2, trained using a constant learning rate of 0.5 and a constant neighbourhood size of 1. I did not keep track of the number of training iterations. As proposed the images were abstracted into a RGB histogram (768 values) and a 40×30 pixel edge-detection before being fed into the SOM.
The following images illustrate how the SOM would accumulate the images. These are not accumulated in PD, but manually, but are layered based on how the SOM would choose to accumulate them:
Note that the complex coaster images are reflected by three of the four clusters in the SOM. In particular the one with the most error (just above) was considered an outlier, and had an entire cluster to itself.