Abstract: Since the use of matrix forms (largely promoted in CAD/CAM) turns out to be both convenient and practical in representing parametric curves and surfaces. Furthermore, this implementation can be made extremely fast if appropriate matrix facilities are available in either hardware or software. We can break a curve down into smaller segments by truncating or subdividing it. There are many reasons for doing this. For example, we may truncate to isolate and extract that part of a curve surviving a model modification process, or subdivide it to compute points for displaying it. To truncate, subdivide, or change the direction of parameterization of a curve ordinarily requires a mathematical operation called reparamelerization. Ideally, this operation produces a change in the parametric interval so that neither the shape nor the position of the curve is changed. This effect is often referred to as shape invariance under parameterization and reparamelerization. This concept has been applied on interval Hermite curves. An algorithmic method for interval Hermite curve segmentation in matrix form is presented in this paper. To split the interval Hermite curve defined over the range u?[u_0,u_m ] at a point defined by u=u_1 means that the first and the second interval segments are to be defined over the ranges u?[u_0,u_1 ] and u?[u_1,u_m ] , respectively. The four fixed Kharitonov's polynomials (four fixed Hermite curves) associated with the original interval Hermite curve are obtained. The proposed algorithm is applied to the four fixed Kharitonov's polynomials (four fixed Hermite curves) in order to obtain the fixed control points for the first and second fixed segments, respectively. Finally the interval control points for the first and second interval segments of the given interval Hermite curve are found from fixed control points for the four fixed Kharitonov's polynomials (four fixed Hermite curves) of the first and second fixed segments. A numerical example is included in order to demonstrate the effectiveness of the proposed method.

Abstract: Connected Component labeling of a binary image is an important task especially when it is used in medical images for recognition purposes. This research is an advance step for applying a proposed algorithm for allocating connected components labeling of medical images. We explore and simulate iterative method towards the development of an automated system for the purpose of connected components labeling to be applied for constructing such labeling on colored images by repetition labeling on sub- images which are originally segmented from the original image. These sub-images are formed from the whole image segmentation process. The algorithm is a simulation process on colored images for practical medical image. Two process algorithm is applied for labeling. The first process is row-wise from left to right. The second one is column-wise, from top to bottom. One important application is the medical image simulation that shows an interesting topic related to heart failure and heart attack. The efficiency of the proposed algorithm is noticed compared with the conventional algorithms in term of memory space and accuracy as well. For the small size images 128 X 128, the iteration version was acceptable in term of computer time and it is recommended to be used to label specific medical images. We experimented 2 sizes: 128 X 128, 256 X 256 and The speed-up was obtained using 128 X 128 size, using all 8- connected neighbors instead of looking at 4 immediate neighbors, which yields to reduction in the number of iterations required with a little increase in search time.