comparing original and simplified TINs

I have two TINs (triangulated irregular network) of a terrain. First one (TIN1) is the original one, let's say with X number of points. And the other (TIN2) is simplified (the number of points were reduced by some decimation algorithm) one where let's say it was build from Y points, where X>Y. Now, how could I do the following comparison between these two TINs:

1) How TIN2 is similar to TIN1? or How TIN2 deviates from TIN1? or How could I compare the accuracy of the TIN2 with respect to TIN1?

2) What are the list of tools or methods that would help me to get the most of the information regarding the accuracy of the TIN2 with respect to TIN1?

If you could possibly point me to any papers, books, lin开发者_JS百科ks,...? Thanks a lot!

I was involved in a medical image processing contest that set some standard model-similarity measures. The full spec is here, section 6. The 4 measures used were -

1. Mean surface distance,

2. Max surface distance,

3. Root-mean-square surface distance,

4. Dice coefficient.

Each one of those might be useful to you, perhaps with some minor adaptations (e.g., the Dice similarity measures bounded volumes - you might want to set a fixed depth to bound the enclosed volume by both terrains).