# Derivate-based Component-Trees for Multi-Channel Image Segmentation

## TL;DR

This paper introduces derivate-based component-trees for multi-channel images, enabling segmentation techniques like MSER to be extended to hyperspectral and color images with improved efficiency and applicability.

## Contribution

The paper presents a novel derivate-based component-tree structure for multi-channel images, extending classical methods to hyperspectral and color images with a linear-time construction.

## Key findings

- Efficient linear-time construction of derivate-based component-trees.
- Enables segmentation of multi-channel images similar to MSER.
- Improves runtime scalability with increasing number of channels.

## Abstract

We introduce the concept of derivate-based component-trees for images with an arbitrary number of channels. The approach is a natural extension of the classical component-tree devoted to gray-scale images. The similar structure enables the translation of many gray-level image processing techniques based on the component-tree to hyperspectral and color images. As an example application, we present an image segmentation approach that extracts Maximally Stable Homogeneous Regions (MSHR). The approach very similar to MSER but can be applied to images with an arbitrary number of channels. As opposed to MSER, our approach implicitly segments regions with are both lighter and darker than their background for gray-scale images and can be used in OCR applications where MSER will fail. We introduce a local flooding-based immersion for the derivate-based component-tree construction which is linear in the number of pixels. In the experiments, we show that the runtime scales favorably with an increasing number of channels and may improve algorithms which build on MSER.