Position paper: Towards an observer-oriented theory of shape comparison

TL;DR

This paper proposes a new observer-oriented metric framework for shape comparison, formalizing the observer's role through operators on function spaces to improve invariance and relevance in shape analysis.

Contribution

It introduces a novel mathematical model for shape comparison based on observer formalization, bridging data representation and invariance considerations.

Findings

The model formalizes the observer's influence on shape data.

The approach provides a theoretical basis for invariant shape comparison.

Illustrative examples support the model's potential applications.

Abstract

In this position paper we suggest a possible metric approach to shape comparison that is based on a mathematical formalization of the concept of observer, seen as a collection of suitable operators acting on a metric space of functions. These functions represent the set of data that are accessible to the observer, while the operators describe the way the observer elaborates the data and enclose the invariance that he/she associates with them. We expose this model and illustrate some theoretical reasons that justify its possible use for shape comparison.