# Part-based approximations for morphological operators using asymmetric auto-encoders

## TL;DR

This paper introduces a novel auto-encoder approach for part-based, interpretable, and online morphological image decomposition, outperforming existing methods on MNIST datasets.

## Contribution

It proposes a sparse, non-negative auto-encoder with a deep encoder and shallow decoder for online, interpretable image decomposition.

## Key findings

- Outperforms state-of-the-art online methods on MNIST and Fashion MNIST.
- Introduces a new metric based on morphological dilation invariance.
- Demonstrates effective part-based representation of image datasets.

## Abstract

This paper addresses the issue of building a part-based representation of a dataset of images. More precisely, we look for a non-negative, sparse decomposition of the images on a reduced set of atoms, in order to unveil a morphological and interpretable structure of the data. Additionally, we want this decomposition to be computed online for any new sample that is not part of the initial dataset. Therefore, our solution relies on a sparse, non-negative auto-encoder where the encoder is deep (for accuracy) and the decoder shallow (for interpretability). This method compares favorably to the state-of-the-art online methods on two datasets (MNIST and Fashion MNIST), according to classical metrics and to a new one we introduce, based on the invariance of the representation to morphological dilation.