# Quantitative Evaluation of Focus Measure Operators in Optical Microscopy

## TL;DR

This paper evaluates focus measure operators in optical microscopy to help choose the best ones based on their performance characteristics.

## Contribution

A new method for evaluating focus measure operators using curve morphology and four derived metrics is introduced.

## Key findings

- The proposed metrics robustly characterize focus measure operators under varying conditions.
- Most operators' performance evaluations remain stable with changes in image parameters or content.
- The metrics provide a theoretical foundation for selecting and designing focus operators.

## Abstract

Given the variety of focus measure operators, selecting an appropriate one based on scene requirements is critical. This study designs evaluation metrics based on the morphological characteristics of focus measure curves. A multipoint linear fitting method is proposed to partition the curve into steep slope and gradual slope regions, from which four metrics are derived: the steep slope region width (Ws), the steep to gradual ratio (Rsg), the curvature of peak point (Cp), and the relative root mean square error (RRMSE). Several representative focus measure operators were chosen for experimental evaluation. The results demonstrate that when image acquisition parameters or image content change, the performance evaluations of most operators remain stable. Therefore, the proposed metrics robustly characterize the performance and features of various operators. These metrics serve as a valuable reference for selecting appropriate operators in optical microscopy and provide a theoretical foundation for designing new ones.