# Optimizing autofocus under multispectral lighting via enhanced SIFT and Pearson correlation coefficient

## TL;DR

This paper introduces a new autofocus method for multispectral imaging using enhanced SIFT and Pearson correlation to improve speed and accuracy.

## Contribution

The novel contribution is the SIFT Quad-Tenen function and Pearson-Hill climbing algorithm for efficient multispectral autofocus.

## Key findings

- The SIFT Quad-Tenen function improves image sharpness evaluation stability and sensitivity.
- The Pearson-Hill climbing algorithm significantly enhances focusing speed and accuracy.

## Abstract

The use of inexpensive black and white cameras in conjunction with multi-band lighting offers the highest accuracy and cost benefits among the several techniques for accomplishing multispectral images. The focus point shifts with varied wavelength illumination, since the lens optical glass has varying refractive indices for different wavelength light sources. Thus, quick and precise focusing is essential for enhancing system efficiency as a whole. To solve this problem, this study proposes a multispectral quick focusing method. First, analyzes the current methods for evaluating image sharpness and proposes an improved Tenengrad function for the focused scene that could extract gradient information from the image in several directions and improve sharpness evaluation. The improved gradient extraction method combines the Scale Invariant Feature Transformation (SIFT) algorithm to form a new multi-scale image sharpness evaluation function, SIFT Quad-Tenen. To improve the focusing efficiency and optimize the focusing process, a search strategy combining a climbing search algorithm and a traversal method was proposed. Finally, considering the similarity of images between different wavelength bands under multi-light source conditions, the Pearson correlation coefficient is introduced to improve the focusing speed and accuracy. The experimental results demonstrate the superiority of the SIFT Quad-Tenen evaluation function in terms of stability and sensitivity, as well as the significant improvement of the focusing speed and accuracy of the Pearson-Hill climbing algorithm.