# Extended probabilistic Rand index and the adjustable moving window-based pixel-pair sampling method

## TL;DR

This paper introduces an extended probabilistic Rand index that considers both similarity and dissimilarity, along with an adjustable moving window pixel-pair sampling method, improving segmentation evaluation consistency and efficiency.

## Contribution

It proposes the EPR index for broader value variation and the AWPS sampling method for adaptive pixel-pair selection, addressing limitations of existing approaches.

## Key findings

- EPR index has twice the effective range of PR.
- AWPS method improves sampling adaptiveness based on segmentation granularity.
- Proposed methods demonstrate effective and efficient segmentation evaluation.

## Abstract

The probabilistic Rand (PR) index has the following three problems: It lacks variations in its value over images; the normalized probabilistic Rand (NPR) index to address this is theoretically unclear, and the sampling method of pixel-pairs was not proposed concretely. In this paper, we propose methods for solving these problems. First, we propose extended probabilistic Rand (EPR) index that considers not only similarity but also dissimilarity between segmentations. The EPR index provides twice as wide effective range as the PR index does. Second, we propose an adjustable moving window-based pixel-pair sampling (AWPS) method in which each pixel-pair is sampled adjustably by considering granularities of ground truth segmentations. Results of experiments show that the proposed methods work effectively and efficiently.

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Source: https://tomesphere.com/paper/1906.07893