Representation of a Curve Using a Spline Function

Abstract

In the image processing systems such as the measurement system of patterns, the processing of curved figures is important. In the processing we must first translate the input sequence of dots data into an efficient and compact expression.
H. Freeman has studied the use of the chain code as a model. In this paper, a spline model using 3rd degree B-spline functions is introduced and its modeling procedure is presented. In the chain code model, a curved figure is represented as a sequence of incremental codes of 3 bits and an ordered set of characteristic points in the spline model.
From the input data, a spline model is made automatically through the initial approximation phase and the iterative local modification phases.
In the local modification phase, two characteristic points most dominant with respect to the difference between the model and the input data are moved to improve the performance.
To evaluate the model, an arc and two hand written curves are selected as examples, and the modeling procedure is examined. The comparison between the data length of the above 2 models are also examined.
By using this modeling procedure, a compact and efficient spline model can be obtained.