Harmonic Radial Pre-Filtering for Medical Image Classification: An Empirical Study of Tusi-Couple-Derived Sampling on Mammography and Colonoscopy

Abstract

We study a deterministic, parameter-free pre-processing transform that resamples a 2D image crop into a structured (angle × radius) grid using a phase-delayed harmonic radial sampling scheme derived from the geometry of the Tusi couple, a 13th-century mechanical construction in which a point on a circle rolling inside a circle of twice its diameter traces a straight line. The transform is applied upstream of a convolutional network, using the same architecture for both raw-pixel and transformed inputs, isolating the effect of the input representation from any change in model design. At the resolution used in our primary experiment (48 angles × 112 radial samples, a 9.33× reduction in input values relative to a 224×224 raw crop), an identically-parameterized CNN (389,633 parameters) processing the transformed representation requires 9.33× fewer multiply-add operations (79.29M vs. 740.00M) and runs 5.79× faster on CPU (4.90 ms vs. 28.40 ms per image), while matching or exceeding the raw-pixel baseline's accuracy, sensitivity, and F1 score on both of two medical imaging tasks tested: mammographic mass classification (CBIS-DDSM) and colonoscopy polyp detection (Kvasir-SEG). This efficiency result is specific to the plain, architecture-matched CNN at this input resolution; it is a consequence of the transform's information density, not a general property of the transform itself, and disappears if the transform's output resolution is matched to the raw input. Separately, in an exploratory (non-controlled) setting, an architecture that treats the same transformed representation as 48 independent 1D radial signals rather than a 2D image reaches 90.8% accuracy and 0.884 F1 on polyp detection, the strongest result in this work, but was not evaluated for computational efficiency and is a distinct model from the one carrying the efficiency claim above. On the polyp task, the preliminary single 80/20 split reported in an earlier version of this work has been replaced by 5-fold stratified cross-validation over all 2,400 images. Under cross-validation the transformed input leads the raw-pixel baseline on all four pooled out-of-fold metrics and leads on ROC-AUC in every one of the five folds, with roughly half the between-fold spread (0.973 ± 0.006 vs. 0.957 ± 0.010). This reverses the direction reported from the single split, in which the baseline held a narrow AUC edge; that edge does not replicate. The AUC difference is consistent in direction but borderline by conventional thresholds (DeLong p = 0.085 on pooled out-of-fold predictions; paired across folds p = 0.037), and we report both tests rather than the more favourable one. The mammography results remain single-run and are reported as such.