Exploratory Characterization of Optical Filters and Visual Acuity Responses Using Estimated Algorithmic Complexity

Purpose: To explore the estimated algorithmic complexity of encoded optical-filter transmittance spectra and visual-response data using the Block Decomposition Method (BDM), alongside conventional optical descriptors and symbol-frequency Shannon entropy. Methods: Four filters with different pigmentation times were each measured in a single spectral acquisition. Visual thresholds for detection, separation, alignment, and recognition were measured under baseline and four filter conditions in 235 eyes from 118 participants. Each spectrum and task–condition response column was independently min–max normalized and discretized. Wavelength-ordered one-dimensional BDM was the primary spectral analysis; two-dimensional arrangements were supplementary. Sensitivity to encoding, block size, observation order, remainder handling, and matrix representation was assessed. Visual changes were summarized descriptively within eyes; unavailable participant linkage prevented adjustment for fellow-eye dependence. Results: Under the original binary encoding, spectral Shannon entropy increased with pigmentation time, whereas one-dimensional normalized BDM (nBDM) ranged from 0.010058 to 0.010326 and followed a different filter ordering. Several spectral and visual-response rankings changed across computational settings. Within-eye mean threshold changes were negative across filters for detection and recognition, while separation and alignment showed different patterns. Visual-response nBDM described the encoded sequences and did not directly quantify these threshold changes. Conclusions: BDM provided an exploratory characterization conditional on the selected representation and analysis settings. Sensitivity analyses did not establish sampling uncertainty or statistical robustness. The findings do not validate filter classes or demonstrate clinical benefit, causality, or prediction of visual outcomes from spectral complexity. Repeated measurements, broader filter sampling, participant-linked data, and independent validation are required to assess practical utility.