Scaling method by using symmetrical middle-point slope control (SMSC)

#1. Field of the Invention

#The present invention relates to a method of data interpolation, and more particularly to a method of scaling up or down of different types of data such as graphics, image, video or audio data, and for application of polygon curve fitting in many area such as object moving tracking analysis, data analysis, a finder for objects of 2D shape or 3D surface in graphic areas.

#2. Description of Related Art

#The accompanying drawings are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. In the drawings,

#FIG. 1 is a schematic diagram illustrating the curve using the SMSC scaling method of present invention;

#FIG. 2 is a schematic diagram illustrating the behavior using the SMSC scaling method with different gain of slope at the start source point;

#The scaling principle SMSC used in the present invention is using two end points at x=0 and x=1 within the concerning region of 0≦x<1. In addition, a middle point at x=0.5 is set as f(0.5)=[f(0)+f(1)]/2. The function is taken as a quadratic function f(x)=ax2+bx+c, which passes the three points. Also and, a slop f′(0.5)=DG=[f(1)−f(0)]G is satisfied, wherein G is a gain factor greater than 1. After solving the coefficients of a, b, and c, the function is used to describe the scaled data. However, the function is considered with respect to the regions of 0≦x<0.5 and 0.5≦x<1. The two parts of the function are joined at the middle point. Preferably, the function is symmetric or substantially symmetric to the middle point. Embodiments are provided as examples for describing the features of the invention.

#FIG. 1 shows a curve using the SMSC method of present invention for scaling. A curve f(x) is provided as the input source data, on which a plurality of reference source points are located. Reference number 101 indicates the slope at the point 102, where points A, B, and C are the source points. Point 102 is the middle point between A and B. The scaling function f(x) 100 within the two adjacent points should pass the two end source point A, B and the middle point. Then each part of f(x) belonging to the range of two adjacent points is joint together to form a complete scaling function for any desired point.

#The advantages of the SMSC method of the invention are low-cost, simple, and less quality loss compared to other high-order (3′rd or more) interpolation methods. It uses only two samples f(0), f(1), with respect to points, i.e., A and B, to generate the scaling result but is able to produce a much sharper image than that of the Bilinear method. It is especially useful in the case when finite storage is implemented. In common applications, during vertical scaling the entire line of source image sample data must be stored in line buffer. Therefore, more source points require more storage capacity, and result in the increase of cost. The SMSC method of the present invention only requires two samples, and means that only two line buffers are needed for scaling, such as zooming or shrinking operations. The gain factor G affects the quality, where G>1 is generally considered to be good in adjusting the scaling operation into a better quality. Please note that the condition of G≠1 is not like the Bilinear method.