Abd Rahni Mt Piah

Positivity-preserving scattered data interpolation

The construction of a C1 interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. This study is motivated by earlier work in which sufficient conditions are derived on Bezier points in order to ensure that surfaces comprising cubic Bezier triangular patches are always positive. In the current work, simpler and more relaxed conditions are derived on the Bezier points. The gradients at the data sites are then calculated to ensure that these conditions are satisfied. Each triangular patch of the interpolating surface is formed as a convex combination of three cubic Bezier triangular patches. Its construction is local. A number of examples are presented.

Craniofacial Reconstruction Using Rational Cubic Ball Curves

This paper proposes the reconstruction of craniofacial fracture using rational cubic Ball curve. The idea of choosing Ball curve is based on its robustness of computing efficiency over Bezier curve. The main steps are conversion of Digital Imaging and Communications in Medicine (Dicom) images to binary images, boundary extraction and corner point detection, Ball curve fitting with genetic algorithm and final solution conversion to Dicom format. The last section illustrates a real case of craniofacial reconstruction using the proposed method which clearly indicates the applicability of this method. A Graphical User Interface (GUI) has also been developed for practical application.

An improved fuzzy cellular neural network (IFCNN) for an edge detection based on parallel RK(5,6) approach

Parallel RK(5,6) algorithms are employed to validate the potential behaviour under improved fuzzy cellular neural network paradigm for an edge detection problem is the novelty of this paper. The function of the simulator is capable of performing raster fuzzy cellular neural network simulation for any kind as well as any size of input image. The raster pseudo code exploits the latency properties of improved fuzzy cellular neural network coupled with different parallel numerical integration algorithms. Results provide a better understanding about single layer/raster behaviour simulation.

Range Restricted C2 Interpolant to Scattered Data

The construction of a range restricted bivariate C2 interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. Sufficient conditions are derived on Bezier points in order to ensure that surfaces comprising quintic Bezier triangular patches are always positive and satisfy C2 continuity conditions. The first and second derivatives at the data sites are then calculated (and modified if necessary) to ensure that these conditions are satisfied. Its construction is local and easily extended to include as upper and lower constraints to the interpolating surfaces of the form z = C(x,y) where C is a polynomial of degree less or equal to 5. A number of examples are presented.

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

Maxillofacial trauma are common, secondary to road traffic accident, sports injury, falls and require sophisticated radiological imaging to precisely diagnose. A direct surgical reconstruction is complex and require clinical expertise. Bio-modelling helps in reconstructing surface model from 2D contours. In this manuscript we have constructed the 3D surface using 2D Computerized Tomography (CT) scan contours. The fracture part of the cranial vault are reconstructed using GC1 rational cubic Ball curve with three free parameters, later the 2D contours are flipped into 3D with equidistant z component. The constructed surface is represented by contours blending interpolant. At the end of this manuscript a case report of parietal bone fracture is also illustrated by employing this method with a Graphical User Interface (GUI) illustration.

Conic Curve Fitting Using Particle Swarm Optimization: Parameter Tuning

We solve curve fitting problems using Particle Swarm Optimization (PSO). PSO is used to optimize control points and weights of two conic curves to a set of data points. PSO is used to find the best middle control point and weight for both conic curves to provide piecewise conics that preserve G^1 continuity. We present numerical result using parameter changes in PSO scheme. We obtain appropriate parameter values of PSO that provide best error and fastest time to solve curve fitting problem.

G/sup 1/ scattered data interpolation with minimized sum of squares of principal curvatures

One of the main focus of scattered data interpolation is fitting a smooth surface to a set of non-uniformly distributed data points which extends to all positions in a prescribed domain. In this paper, given a set of scattered data V = {(x/sub i/, y/sub i/), i=1,...,n} /spl isin/ R/sup 2/ over a polygonal domain and a corresponding set of real numbers {z/sub i/}/sub i=1//sup n/, we wish to construct a surface S which has continuous varying tangent plane everywhere (G/sup 1/) such that S(x/sub i/, y/sub i/) = z/sub i/. Specifically, the polynomial being considered belong to G/sup 1/ quartic Bezier functions over a triangulated domain. In order to construct the surface, we need to construct the triangular mesh spanning over the unorganized set of points, V which will then have to be covered with Bezier patches with coefficients satisfying the G/sup 1/ continuity between patches and the minimized sum of squares of principal curvatures. Examples are also presented to show the effectiveness of our proposed method.

NURBS curves with the application of multiple bones fracture reconstruction

Abstract The challenging task of treating trauma to cranio-maxillofacial requires advanced radiological imaging and high clinical skills. The reconstruction of facial fractures focuses on the rehabilitation of patients functionally as well as in aesthetics. In this article we used NURBS curves to construct the multiple bones fracture using CT scan data in Digital Imaging and Communications in Medicine (DICOM) format. The reconstruction process of multiple bones fracture start with the boundary extraction followed by corner detection, optimization of knots, weights, construction of fractured part inner outer curve for each CT scan slice using NURBS curves and finally the construction of fractured part in DICOM format. The construction process using proposed method is based on DICOM data only that does not require any technique such as technical help, mirror imaging, to take average thickness of skull bone or reference skull, etc. The constructed fractured implant is custom made for each patient. We present a real case in which multiple bones fracture has been constructed using NURBS curves. The proposed method has also been validated quantitatively and qualitatively using self supposed fractured data.

Positivity preserving curves using rational cubic Ball interpolant

A rational cubic Ball function which has four shape parameters in its description has been used to preserve the shape of positive data. Conditions are derived on one of the shape parameters in such a way that they preserve shape of the data, while the others three parameters remain free to enable the user to modify the shape of the curve. The degree of smoothness is C1. Outputs from numerical experiments are presented.

Shape Preserving Data Interpolation Using Rational Cubic Ball Functions

A smooth curve interpolation scheme for positive, monotone, and convex data is developed. This scheme uses rational cubic Ball representation with four shape parameters in its description. Conditions of two shape parameters are derived in such a way that they preserve the shape of the data, whereas the other two parameters remain free to enable the user to modify the shape of the curve. The degree of smoothness is . The outputs from a number of numerical experiments are presented.