Fatimah Yahya

An Automatic Generation of G^1 Curve Fitting of Arabic Characters

An Arabic font is difficult to fit as it is cursive in character, having varying curves and cusps. Here, the Arabic character is represented as an outline font fitted with G1 rational Bezier cubic curves. As a method in reverse engineering, the Arabic character is created by way of digitizing an image that already exists and then fitting G1 curves automatically to the outline of the digitized image. The outline font representation is done in several phases - contour extraction of font image, corner points detection and lastly contour segment fitting. Image is considered as binary and boundary is obtained accordingly. Eigenvalues of covariance matrix and the concept of region of support are employed to search for the corners of the Arabic characters which are of varying degrees of smoothness. G 1 rational Bezier cubics, iteratively determined, are used in the last step. The weights are adjusted automatically to get curves that are as close as need be to the digitized data points. This technique can be extended to visualizing outlines of other contour-based images automatically

Composite contour generation for Beta-spline surface reconstruction

Branching is a process of connecting two adjacent contours called base and branch contours where the numbers of sub contours for each of both contours are different. All points between the contours have to be correctly paired to avoid a twisting surface. In contours connection, continuity is an issue to ensure the surface fit to the required smoothness. Therefore, two main steps to be focused in surface reconstructions are branching technique and surface continuity. This study used composite contour generation as the branching technique which generates an intermediate contour as combination of modified base and branch contours. Although the inserted new contour will disturb the position of original contours, the continuity can be preserved if the fitted surface is Beta-spline. Beta-spline is built with G2 continuity condition, and the changes of the data points position will not affect the continuity. Hence, surface fitting using Beta-spline will simplify the reconstruction process. The result shows sever...

Automatic G1 Surface Reconstruction from Serial Cross-Sectional Images

Biomedical imaging facilities today like MRI, PET, CT scan and confocal microscopy produce sequentially parallel cross sectional images. Recon-structing trustworthy 3D explicit models which enable better understanding of the topology and shape of structure is crucial in facilitating diagnosis, improves surgical planning and aid in biological research. Our technique produce a surface from G1cross sectional contour curves of images. Surface accuracy is controlled by a tolerance measure. Features can be isolated and identified for corresspondence. First the boundaries of the region of interest are extracted and corner points detected. G1rational Bezier cubics, iteratively determined, are fitted piecewise between these corners and approximating the boundary. as close as need be. Adjacent contour curves are blended together to form the surface. Technique is fully automatic.

Dyadic Segmentation for Parallel Beta-Spline Surface Reconstruction from Multi-slice Images

Accuracy is one of the most important requirements of a reconstructed surface. However, this criterion needs high computation too since large number of data points is involved. Therefore, distribution of data points is the best way to solve this problem. In this paper, dyadic rational technique is employed in segmenting the data points into several processors. Then, the surface reconstruction process is done independently in each processor. Finally, all the surfaces are combined in the master processor. This project used low-cost self-developed parallel laboratory named Ars Cluster in UiTM Shah Alam. Therefore, the parallel process in this project is time-saving and cost-saving.

G 2 Beta-spline: An ideal surface representation of multi-slice medical images

This paper focuses on multi-slice image reconstruction for CT images using Beta-spline. In reconstructing multi-slice images especially from living image, issues like continuity and accuracy contours arise. Commonly, high continuity is hard to be achieved because of the accuracy requirement and vice versa. Thus the image reconstruction process is prolonged to fulfill these constraints. This paper used cubic Beta-spline as the fitted surface in the image reconstruction process. Beta-spline is already has G2 continuity which is unaffected by the changes in data points position. Surface fitting using Beta-spline has also simplified the branching surface case with the preserved continuity. This study shows the whole image reconstruction process using cubic Beta-spline, and the data used are CT images of human head, Stanford bunny and human pelvic. The produced images show that Beta-spline has capability to produce necessary images within the required continuity and accuracy.

3-Dimensional Beta-spline wireframe of human face contours

Human head is one of the most detail parts of human body. Reconstruction of human head must be precise to avoid misinformation of the product. Furthermore, head reconstruction especially face is used in several significant applications such as face recognition, head surgery, and face simulation. This study employs cubic Beta-spline as the fitted curve based on its capability to maintain the second degree of continuity, and its shape parameters which can be controlled locally. 69 layers of 2-dimensional human head contours from Computerised Tomography (CT) images are used in this research. Contour points of each layer are extracted, and fitted with piecewise cubic Beta-spline curves. All the layers then stacked together and form a Beta-spline head wireframe. The result shows that Beta-spline gives necessary smooth images and preserves important features of the head and face.

G1 quadratic trigonometric beta spline with a shape parameter

In order to complement a fast developing imaging technology, effective methods are needed to process the data produced into meaningful and impactful representation or visualization. These representations are usually in the form of lines, curves and surfaces. This paper presents the construction of a new quadratic trigonometric Beta spline functions with a shape parameter to design or fit curves. The shape parameter plays the role of controlling the behavior of the curve besides producing smooth shaped curves without altering the control points. The spline satisfies all the geometric properties of the usual quadratic Bezier curve. The properties are proved in this research. The curve approaches the middle control point as the parameter values are varied and can be made to be as close as possible to the control polygon. Trigonometric function is also interesting in the sense that it guarantees smooth curves even at high parametric speed. The degree of continuity is examined in joining two adjacent constructed curves. Several results are presented to show the usefulness of this spline functions.

Numerical solution of Painlev’e equation I by Daftardar-Gejji and Jafari method

Painleve II equation is one of the six second-order ordinary differential equations namely Painleve equations. This paper presented the numerical solution for Painleve equation II via a new iterative method called Daftardar–Gejji and Jafari method (DJM). Comparison of the results obtained by DJM with those obtained by other methods such as optimal homotopy asymptotic method (OHAM), homotopy perturbation method (HPM), Sinc-collocation method, Chebyshev series method (CSM) and variational iterative method (VIM), revealed the effectiveness of the method.