Extracting information of objects independent of their observations — Projection invariants ofn-dimensional objects —

Abstract

When we observe an object under investigation, we often obtain only a certain part of the original information, that is, information projected from a space where the original information exists, to its subspace. We are then required to deal with such partial information to investigate the object. When original information is subject to a given class of admissible transformations,projection invariants, functions in terms of the projected information whose values are unaffected by the class of admissible transformations, provide an essential relationship between the original information and the projected one. This paper presents a study on projection invariants under the conditions that then-dimensional projective space is projected into the (n−1)-dimensional space and the class of admissible transformations involves projective transformations. We show the existence of a projection invariant derived from theH-type collection of (n+i+j) linear subspaces of dimension (n−2), wherei andj are given integers such that 1≤i≤j≤n-i. The nonsingularity condition, i.e., the condition under which the projection invariant is nonsingular, is also given.