A unified setting for projections in pattern recognition

摘要

We develop in this paper the categorical setting for pattern recognition problems and in particular for projections. We first state under which conditions images I ∈ I and deformations can be organized in a category (I, Δ) = IΔ. Then we focus our attention on a particular class of probes: projections, which we characterize by means of retracts of categories. Several theorems and corollaries concerning image categories, recognition categories and projections are stated, and indications about skeletons are given in the concluding remarks.