Deep Gaussian Optical Bandpass Filter Design for Fermentation Index Estimation in Cocoa Beans

Cocoa beans fermentation is a key process that defines the sensory quality of cocoa-based products such as chocolate. However, current methods for estimating the Fermentation Index (FI), such as cut tests and chemical analysis are destructive, delayed, and costly. Recent approaches have explored non-destructive techniques based on spectral information and specific band selection, but these methods often prioritize statistical performance while ignoring physical constraints, selecting un-realistic spectral bands. To address this, we propose a physically feasible and efficient framework for F1 estimation that combines spectral dimensionality reduction with a fermentation prediction model, aligned with commercial optical hardware limitations. The method consists of designing a set of Gaussian Optical Bandpass Filters, optimized in terms of central wavelength and bandwidth, and integrating them into a learning pipeline jointly trained with a lightweight neural network regression model. The proposed model achieves an R2 of 0.959 using six filters, closely matches the full spectrum baseline <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\mathrm{R}2\ =0.963)$</tex> while reducing the input dimensionality by over 98%, outperforming the latest band selection methods in R2 and MAE scores.