Geodesic-based manifold learning for parameterization of triangular meshes
Por:
Acosta, D.A., Ruiz, O.E., Arroyave, S., Ebratt, R., Cadavid, C., Londono, J.J., Acosta, Diego A.
Publicada:
1 nov 2016
Resumen:
Reverse Engineering (RE) requires representing with free forms (NURBS,
Spline, B,zier) a real surface which has been point-sampled. To serve
this purpose, we have implemented an algorithm that minimizes the
accumulated distance between the free form and the (noisy) point sample.
We use a dual-distance calculation point to / from surfaces, which
discourages the forming of outliers and artifacts. This algorithm seeks
a minimum in a function that represents the fitting error, by using as
tuning variable the control polyhedron for the free form. The topology
(rows, columns) and geometry of the control polyhedron are determined by
alternative geodesic-based dimensionality reduction methods: (a)
graph-approximated geodesics (Isomap), or (b) PL orthogonal geodesic
grids. We assume the existence of a triangular mesh of the point sample
(a reasonable expectation in current RE). A bijective composition
mapping allows to estimate a size of the control polyhedrons favorable
to uniform-speed parameterizations. Our results show that orthogonal
geodesic grids is a direct and intuitive parameterization method, which
requires more exploration for irregular triangle meshes. Isomap gives a
usable initial parameterization whenever the graph approximation of
geodesics on be faithful. These initial guesses, in turn, produce
efficient free form optimization processes with minimal errors. Future
work is required in further exploiting the usual triangular mesh
underlying the point sample for (a) enhancing the segmentation of the
point set into faces, and (b) using a more accurate approximation of the
geodesic distances within , which would benefit its dimensionality
reduction.
Filiaciones:
Acosta, D.A.:
DDP Research Group, Universidad EAFIT, K. 49 7-sur-50, Medellin, Colombia
Ruiz, O.E.:
Laboratory of CAD CAM CAE, Universidad EAFIT, K. 49 7-sur-50, Medellin, Colombia
Arroyave, S.:
Laboratory of CAD CAM CAE, Universidad EAFIT, K. 49 7-sur-50, Medellin, Colombia
Ebratt, R.:
Laboratory of CAD CAM CAE, Universidad EAFIT, K. 49 7-sur-50, Medellin, Colombia
Cadavid, C.:
Laboratory of CAD CAM CAE, Universidad EAFIT, K. 49 7-sur-50, Medellin, Colombia
Londono, J.J.:
Laboratory of CAD CAM CAE, Universidad EAFIT, K. 49 7-sur-50, Medellin, Colombia
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