NEXT       TOP       BACK

1.  Computational efficiency

• Computing the exact trace of the MA proves difficult even in 2D.
• The challenges are similar to the ones observed in computing the Voronoi diagrams .

2. Storage requirements

• Tracing explicitly the MA sheets may require many order of magnitudes more data than the original M input data samples.
• This has lead many researchers to favor discrete approximations to the computation of the MA.

3. Robustness

• The MA is notorious for being sensitive to small perturbations and the presence of extraneous data.
• New symmetries are then created, and a significance ordering must somehow be defined to retrieve the relevant structures.

4. Usefulness

• Because of the previous constraints,  previous approaches have either made some assumptions on the type of inputs, or favored approximations to the true MA definition. This has considerably reduced the applicability of the MA.
• In particular, many approaches do not make explicit the graph structure of the MA which limits the possibility for manipulation, matching, etc.

5. Dynamic processes

• Necessary to avoid recomputing everything each time new information becomes available.
• Permits to localize processing (parallelism).
• Useful to perform shape regularization.

NEXT       TOP       BACK