# Quantitative Kernel estimation from traffic signs using slanted edge spatial frequency response as a sharpness metric

## TL;DR

This paper introduces a method to estimate blurring in automotive cameras using traffic sign images and spatial frequency response, aiming to monitor camera sharpness over time.

## Contribution

A novel PCA-based kernel estimation method using synthetic and real data for automotive camera sharpness monitoring.

## Key findings

- The proposed method achieves SSIM values between 0.808 and 0.945 for estimated and true blurred regions.
- Validation on real-life camera images showed SSIM > 0.82, indicating promising accuracy for in-field monitoring.

## Abstract

Sharpness is a critical optical property of automotive cameras, measured by the spatial frequency response (SFR) within the end-of-line (EOL) test after manufacturing. This work presents a method to estimate the blurring kernel of an automotive camera, which could be the first step toward state monitoring of automotive cameras. To achieve this, Principal Component Analysis (PCA) was performed, using synthetic kernels generated by Zemax. The PCA model was built with approximately 1300 base kernels representing spatially variant point spread functions (PSFs). This model generates kernel samples during the estimation process. Synthetic images were created by convolving the synthetic kernels with reference traffic sign images and compared with real-life data captured by an automotive camera. These synthetic data were utilized for algorithm development, and later on, validation was performed on real-life data. The algorithm extracts two \documentclass[12pt]{minimal}
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\begin{document}$$45\times 45$$\end{document} pixels regions of interest (ROIs) containing slanted edges from the blurred image and crops matching ROIs from a reference sharp image. Each candidate kernel was used to blur the reference ROIs, and the resulting SFR was compared with the blurred ROIs’ SFR. Differential evolution optimization minimizes the SFR difference, selecting the kernel that best matches the observed blur. The final kernel was evaluated against the true kernel for accuracy. The structural similarity index measure (SSIM) between the original and estimated blurred ROIs ranges from 0.808 to 0.945. For true vs. estimated kernels, SSIM varies from 0.92 to 0.98. Pearson correlation coefficients range from 0.84 to 0.99, Cosine similarity from 0.86 to 0.99, and mean squared error (MSE) from \documentclass[12pt]{minimal}
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\begin{document}$$1.1 \times {10}^{-5}$$\end{document} to \documentclass[12pt]{minimal}
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\begin{document}$$8.3 \times {10}^{-5}$$\end{document}. Validation on real-life camera images showed that the SSIM between the estimated and blurred ROI was >0.82, showing promising accuracy in kernel estimation, which could be used towards in-field monitoring of camera sharpness degradation.