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

• URL: http://arxiv.org/abs/2601.03326v1
• Date: Tue, 06 Jan 2026 15:24:20 GMT
• Title: Higher order PCA-like rotation-invariant features for detailed shape descriptors modulo rotation
• Authors: Jarek Duda,
• Abstract summary: PCA can be used for rotation invariant features, describing a shape with its $p_ab=E[(x_i-E[x_a])(x_b-E[x_b)]$ comodimating shape by ellipsoid.<n>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))
• Score: 0.2320648715016106
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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, or shape similarity metric allowing their inexpensive comparison (modulo rotation) without costly optimization over rotations.

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