Abstract
Surface reconstruction is a very important issue with outstanding applications in fields such as medical imaging (computer tomography, magnetic resonance), biomedical engineering (customized prosthesis and medical implants), computer-aided design and manufacturing (reverse engineering for the automotive, aerospace and shipbuilding industries), rapid prototyping (scale models of physical parts from CAD data), computer animation and film industry (motion capture, character modeling), archaeology (digital representation and storage of archaeological sites and assets), virtual/augmented reality, and many others. In this paper we address the surface reconstruction problem by using rational Bezier surfaces. This problem is by far more complex than the case for curves we solved in a previous paper. In addition, we deal with data points subjected to measurement noise and irregular sampling, replicating the usual conditions of real-world applications. Our method is based on a memetic approach combining a powerful metaheuristic method for global optimization (the electromagnetism algorithm) with a local search method. This method is applied to a benchmark of five illustrative examples exhibiting challenging features. Our experimental results show that the method performs very well, and it can recover the underlying shape of surfaces with very good accuracy.
Highlights
1.1 MotivationThe problem of obtaining a mathematical surface fitting a given set of data points has been a very hot topic of research during the last few decades
In a previous paper presented at the conference ICSI 2015, we introduced a method to obtain the rational Bezier curve of a certain degree providing the optimal fit to a cloud of data points (Iglesias and Galvez 2015)
The method was based on a memetic approach combining a powerful metaheuristic method for global optimization to obtain a very good approximation of the optimal solution and a local search procedure for further solution refinement
Summary
1.1 MotivationThe problem of obtaining a mathematical surface fitting a given set of data points (usually referred to as surface approximation or surface reconstruction) has been a very hot topic of research during the last few decades. A well-known example is given by reverse engineering, a field where a (usually large) collection of data points is acquired from an already existing physical object. These data points are approximated by mathematical functions in order to obtain a fully usable digital model (Barhak and Fischer 2001; Hoffmann 2005; Ma and Kruth 1995). There are many advantages in this process: the digital models are easier and cheaper to modify than their real counterparts They can readily be transferred and become available anytime and anywhere by taking advantage of current high-speed telecommunication networks. Owing to these remarkable advantages, reverse engineering is becoming the prevalent technology
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