Quantum Pairwise Symmetry: Applications in 2D Shape Analysis

TL;DR

This paper introduces a quantum-based method for analyzing symmetry in 2D shapes using quantum triangles and a complex-valued kernel to improve robustness against noise and clutter.

Contribution

It proposes a novel quantum primitive for symmetry measurement and a complex-valued kernel for noise-resistant shape analysis in 2D.

Findings

Quantum triangles effectively characterize symmetry.

The complex-valued kernel enhances robustness to noise.

Method improves accuracy in noisy, cluttered environments.

Abstract

A pair of rooted tangents -- defining a quantum triangle -- with an associated quantum wave of spin 1/2 is proposed as the primitive to represent and compute symmetry. Measures of the spin characterize how "isosceles" or how "degenerate" these triangles are -- which corresponds to their mirror or parallel symmetry. We also introduce a complex-valued kernel to model probability errors in the parameter space, which is more robust to noise and clutter than the classical model.