Learning from
simple ideas.
My research asks what geometric information a classifier should receive after landmark extraction. I study nine coordinate-, distance-, angle-, and hybrid-based representations, examining their invariances, clean accuracy, and end-to-end robustness to image corruption. A central result distinguishes the information a representation preserves from how readily a classifier can use it.
The study at a glance
Problem formulation
A labeled image dataset pairs each image Iᵢ with a class label γᵢ.
A pixel-based classifier learns a map from image intensities to labels.
We distinguish landmark extraction, aspect-ratio-corrected planar coordinates, geometric feature construction, and classification.
MediaPipe extracts 21 landmarks; Qi ∈ ℝ21×2 is their aspect-ratio-corrected planar configuration. Each feature map φr acts on Qi, not directly on the image or uncorrected landmark output.
The central object is the feature map: what geometry it preserves, what nuisance variation it removes, and how that choice affects classification.
H, W, C: image height, width, and channels · qr: feature dimension
What the revised study establishes
Controlled comparison. Nine geometric feature maps are evaluated using logistic regression and random forests, with participant-disjoint TRAIN (2,000), VAL (500), and TEST (1,000) cohorts. The primary metric balances accuracy across participants and counts extraction or prediction failures as incorrect.
Robustness beyond ideal transformations. Gaussian blur, exposure changes, JPEG compression, and rectangular occlusion are applied to images before landmark detection, measuring end-to-end behavior rather than only perturbations to extracted coordinates.
Geometric recoverability. For noncollinear usable labeled landmark configurations, the simple hybrid (axis-normalized coordinates plus normalized pairwise distances) and centered isotropic coordinates mutually determine one another, despite their different dimensions. Unsigned angular features are recoverable from the normalized distances.
Predictive accessibility. Information-equivalent encodings need not perform identically with a given classifier. Hybrid representations perform strongly, but the small full-versus-simple hybrid differences do not survive the manuscript's multiplicity-adjusted paired comparisons.
Illustrative transfer. The framework is also demonstrated with anatomical landmarks extracted from lateral cephalometric radiographs, as an illustration of portability rather than a second full benchmark.
Supplementary materials
Proofs of geometric invariance and recoverability, alongside participant-level statistical comparisons and the illustrative anatomical-landmark extension.
Invariance, Geometric Recoverability, and Angular Redundancy
Definitions and proofs for geometric invariance, mutual recoverability of landmark representations, and redundancy of unsigned angles.
View mathematical supplement (PDF) ↗Friedman, Wilcoxon, and Cephalometric Extension
Participant-level paired tests, Holm-adjusted comparisons, and supporting analysis of the cephalometric extension.
View statistical supplement (PDF) ↗