Using a mixed wave/ diffusion process to elicit the symmetry set

Classifying symmetry sets

“…However, existing local symmetry algorithms [2,3,4,5,6,7,8,9,10,11,12,13] and theoretical descriptions [14,15,16,17,18,19] are all unsatisfactory. Some algorithms are slow [8,9], Some handle only restricted classes of inputs [5,6,7] or detect only restricted classes of symmetries [10].…”

“…Some algorithms are slow [8,9], Some handle only restricted classes of inputs [5,6,7] or detect only restricted classes of symmetries [10]. Some are hard to analyze [3]. Converting the raw symmetry sets into nice-looking regions requires complex post-processing [2,8,9,12,13].…”

Spline Smoothing: A Special Case of Diffusion Smoothing

“…In return, we name it a treatment with the "convex corner cling" boundary condition formulated as in (9).…”

“…4) It can also be applied to intensity data processing, drifting object smoothing [5] and symmetry axis elicitting [9], etc.…”

Extracting structure from an affine view of a 3D point set with one or two bilateral symmetries

“…These have generally assumed that the imaged object is within a similarity transformation of the image (viewed in a fronto-parallel plane) so that the imaging process does not destroy the mirror symmetry [2,3,16]. Some authors have included the effects of shear [7,11,19], but have generally limited consideration to 2D objects.…”