This video shows a side by side comparison of various meshes decimated with the edge collapse algorithm.
The algorithm is very simple:
-choose the shortest edge and remove it by collapsing its ends into a vertex. The vertex can be placed anywhere on the edge but I put it in the middle of the edge for simplicity's sake.
-repeat until the mesh is sufficiently simplified. In this case, I simply stop when 50% of the edges have been removed. The last clip shows the cow mesh at 80% decimation.