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Immunological Approach for Full NURBS Reconstruction of Outline Curves from Noisy Data Points in Medical Imaging

Curve reconstruction from data points is an important issue for advanced medical imaging techniques, such as computer tomography (CT) and magnetic resonance imaging (MRI). The most powerful fitting functions for this purpose are the NURBS (non-uniform rational B-splines). Solving the general reconstruction problem with NURBS requires computing all free variables of the problem (data parameters, breakpoints, control points, and their weights). This leads to a very difficult non-convex, nonlinear, high-dimensional, multimodal, and continuous optimization problem. Previous methods simplify the problem by guessing the values for some variables and computing only the remaining ones. As a result, unavoidable approximations errors are introduced. In this paper, we describe the first method in the literature to solve the full NURBS curve reconstruction problem in all its generality. Our method is based on a combination of two techniques: an immunological approach to perform data parameterization, breakpoint placement, and weight calculation, and least squares minimization to compute the control points. This procedure is repeated iteratively (until no further improvement is achieved) for higher accuracy. The method has been applied to reconstruct some outline curves from MRI brain images with satisfactory results. Comparative work shows that our method outperforms the previous related approaches in the literature for all instances in our benchmark.