Model selection for choosing between different representations

Traditionally, model selection criteria have been used to choose the best model to describe a given data set. However, information theoretic selection criteria can also be used to choose between representing a given data, say, D, using a single model m, or by dividing D into two data sets, say, D_A and D_B, and describing them using two different models, m_A, and m_B. Such decisions must often be made, for example, in merging and splitting curves and surfaces in contour extraction and segmentation.

As mentioned before, model selection criteria based on Bayes's rule select the model that maximizes P(D|m, I). For selecting between the two representations, the probability of data $\{D_{A},\; D_{B}\}$, given models $\{m_{A}, m_{B}\}$ and prior information I, $P(D_{A},\; D_{B}\vert m_{A},\; m_{B},\;I)$, must be compared to $P(D \vert m, \;I)$. Similarly, for criteria based on K-L distances, the best representation is chosen by comparing $(d(\hat{\mbox{\boldmath${\theta}$}}_{m_A},\mbox{\boldmath${\theta}$}_{\ast}) + d(\hat{\mbox{\boldmath${\theta}$}}_{m_B},\mbox{\boldmath${\theta}$}_{\ast}))$ and $d(\hat{\mbox{\boldmath${\theta}$}}_{m},\mbox{\boldmath${\theta}$}_{\ast})$. Finally, for criteria based on MDL, the best representation is chosen by comparing the lengths (len_mA + len_mB) and len_m [6,5].

These criteria work across models, do not require user defined thresholds or empirical heuristics, and can be used to merge artificial surface boundaries, preserve discontinuities, and split bridging fits. Experimental results, in the context of surface reconstruction from range data, have shown that these criteria work well even at small step heights and crease discontinuities [5].