# A combinatorial interpretation of Gaussian blur

## TL;DR

This paper introduces the collapsing sum, a new combinatorial operator on matrices, providing a novel interpretation of Gaussian blur and establishing explicit relations between the two.

## Contribution

The paper presents the collapsing sum operator and its combinatorial properties, offering a new perspective on Gaussian blur in image processing.

## Key findings

- Established a direct relation between Gaussian blur and collapsing sum
- Provided combinatorial properties of the collapsing sum operator
- Enhanced understanding of Gaussian blur through combinatorial interpretation

## Abstract

Gaussian blur is a commonly-used method to filter image data. This paper introduces the collapsing sum, a new operator on matrices that provides a combinatorial interpretation of Gaussian blur. We study the combinatorial properties of this operator and prove the explicit relation between Gaussian blur and the collapsing sum.