Surface Reconstruction from Parallel Curves with Application to Parietal Bone Fracture Reconstruction

A Comparative Study of Different Schemes Based on Bézier-like Functions with an Application of Craniofacial Fractures Reconstruction

Cranial implants, especially custom made implants, are complex, important and necessary in craniofacial fracture restoration surgery. However, the classical procedure of the manual design of the implant is time consuming and complicated. Different computer-based techniques proposed by different researchers, including CAD/CAM, mirroring, reference skull, thin plate spline and radial basis functions have been used for cranial implant restoration. Computer Aided Geometric Design (CAGD) has also been used in bio-modeling and specifically for the restoration of cranial defects in form of different spline curves, namely C1,C2,GC1GC2, rational curves, B-spline and Non-Uniform Rational B-Spline (NURBS) curves. This paper gives an in-depth comparison of existing techniques by highlighting the limitations and advantage in different contexts. The construction of craniofacial fractures is made using different Bézier-like functions (Ball, Bernstein and Timmer basis functions) and is analyzed in detail. The C1,GC1 and GC2 cubic Ball curves are performed well for construction of the small fractured part. Any form of fracture is constructed using this approach and it has been effectively applied to frontal and parietal bone fractures. However, B-spline and NURBS curves can be used for any type of fractured parts and are more friendly user.

Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter

Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.

Image Interpolation Using a Rational Bi-Cubic Ball

: This study deals with the application of new rational bi-cubic Ball function with six parameters in image interpolation, especially for the grayscale image. These six free parameters can be modified to get better and quality image resolution, and refine the shape of the interpolating surface. This bivariate rational Ball function has been extended from univariate cases by using a tensor product approach. The proposed scheme is tested for image upscaling with factors of two and four through an efficient algorithm. The effectiveness of the proposed scheme is measured by using an image quality assessment (IQA), such as peak-signal-to-noise-ratio (PSNR), root mean square error (RMSE) or feature similarity (FSIM) index. Numerical and graphical results with comparisons against some existing scheme are presented by using MATLAB. The proposed scheme resulted in higher PSNR and FSIM, and smaller RMSE. Thus, the new rational bi-cubic Ball with six parameters is better than the existing scheme via an efficient algorithm.