Higher order PCA-like rotation-invariant features for detailed shape descriptors modulo rotation

2026/01/06 by Jarek Duda · 1 voice
Computer Science · #Image Retrieval and Classification Techniques #Image and Object Detection Techniques #Medical Image Segmentation Techniques #cs.CV #cs.LG

paper · pdf · doi:10.48550/arxiv.2601.03326

openalex publication_date 2026/01/06 · arxiv published 2026/01/06 · openalex created_date 2026/01/09 · arxiv updated 2026/07/06 · openalex updated_date 2026/07/28

Abstract

PCA can be used for rotation invariant features, describing a shape with its p_ab=E[(x_i-E[x_a])(x_b-E[x_b])] covariance matrix approximating shape by ellipsoid, allowing for rotation invariants like its traces of powers. However, real shapes are usually much more complicated, hence there is proposed its extension to e.g. p_abc=E[(x_a-E[x_a])(x_b-E[x_b])(x_c-E[x_c])] order-3 or higher tensors describing central moments, or polynomial times Gaussian allowing decodable shape descriptors of arbitrarily high accuracy, and their analogous rotation invariants. Its practical applications could be rotation-invariant features to include shape modulo rotation e.g. for molecular shape descriptors, or for up to rotation object recognition in 2D images/3D scans maybe also for 3D scene understanding, or shape similarity metric allowing inexpensive comparison of objects modulo rotation avoiding costly optimization over rotations.

Citations

• Biology-inspired joint distribution neurons based on Hierarchical Correlation Reconstruction allowing for multidirectional propagation of values and densities
• Time delay multi-feature correlation analysis to extract subtle dependencies from EEG signals
• Adaptive exponential power distribution with moving estimator for nonstationary time series
• Polynomial-based rotation invariant features
• Rapid parametric density estimation
• Normalized rotation shape descriptors and lossy compression of molecular shape
• The MNIST Database of Handwritten Digit Images for Machine Learning Research [Best of the Web]
• A Generalized Solution of the Orthogonal Procrustes Problem

Discussions

• arxiv.org/pdf/2601.03326 Detailed description of shape modulo rotation - extending PCA to higher order tensor/polynomial - e.g. for chemoinformatics, evaluating shape similarity, 2D image/3D object se [bsky, 2 points, 0 comments]

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