History

• 2000-2008: Márquez proposed in the context of her Doutorado's thesis a procedure for a coarse registration of two range images. She reduced the registration problem into the matching of one range image (discrete points) and one coarse mesh that approximates another range image. She also applied the radial flow model for deriving the sufficient conditions for obtaining non-self-intersection simplified polyline.
• 2004-2007: Adler da Silva improved in the context of his Mestrado's thesis the implementation of the self-intersection free line simplification algorithm.
• 1998-2000: Márquez implemented the topological surgeries proposed by da Silva in her Mestrado thesis. She also integrated in the radial flow model the "circle criterion" proposed by Lawson to improve the quality of the triangulated mesh.
• 1995-1999: In her Doutorado's thesis, da Silva restricted her attention to scala-valued problems, or more specifically, to a set of samples from a range image - z_i=f(x_i,y_i). Based on the point insertion oriented inflating balloon model proposed by Chen and Medioni, da Silva proposed the radial flow model which consists in growing the initial approximation in several radial fronts until it is sufficiently close to the sample points. While the closed mesh inflates, one or more points may be inserted at each iteration. Da Silva also proved how one can explore the spatial relationship of the sample points of a range image to control self-intersections and to infer the most probable topology of the reconstructed mesh.