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

arXiv: https://arxiv.org/abs/1603.02008 · HTML: https://mlsanity.com/paper/1603.02008/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2016.

## Built on by (most cited first, 3 of 3)

- [GENEOnet: A new machine learning paradigm based on Group Equivariant Non-Expansive Operators. An application to protein pocket detection](https://mlsanity.com/paper/2202.00451/) (2022)
- [A novel approach to graph distinction through GENEOs and permutants](https://mlsanity.com/paper/2406.08045/) (2024)
- [On the geometric and Riemannian structure of the spaces of group equivariant non-expansive operators](https://mlsanity.com/paper/2103.02543/) (2021)

## Abstract (arXiv)

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.