Quantum Pairwise Symmetry: Applications in 2D Shape Analysis
This work addresses symmetry analysis in 2D shape processing, offering a novel approach with potential applications in computer vision and graphics.
The paper tackled the problem of representing and computing symmetry in 2D shapes by proposing a quantum triangle primitive with spin measures, and introduced a complex-valued kernel for more robust probability error modeling compared to classical methods.
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.