General principles of MPT
Ulf Grenander · 1994
Abstract The regular structures introduced in Part I, configuration spaces, image algebras, patterns, are qualitative in nature. For example, a configuration is either regular or not. In Chapters 7-11 we shall relax the regularities, allowing them to be gradual as measured by their probability of appearing in the ensemble we are observing. Expressed otherwise, we shall measure the degree of regularity or irregularity, see the morphogenetic device in Section 4.3.9.3. This metric approach, metric pattern theory, or MPT, leads us to introduce probability measures on spaces that contain and may be larger than the regular structures; see Note 7.A.