In this paper, we propose a new vertex adjustment method which is based on the size ratio of an object and that of a polygon. In the conventional polygonal approximation methods, the sizes of an object and an approximating polygon are quite different, therefore there are so many error pixels between them. The proposed method reduces the size of error regions by adjusting the size of the polygon to that of an object. Simulation results show outstanding performance of the proposed method.

For object analysis and recognition, an original shape often needs to be described by using a small number of vertices. Polygonal approximation is one of the useful methods for the description. In this paper, we propose the curvature-based polygonal approximation (CBPA) method that is an application of the weighted polygonal approximation problem which minimizes the number of vertices of an approximate curve for a given error tolerance (the weighted minimum number problem). The CBPA method considers the curvature information of each vertex of an input curve as the weight of the vertex, and it can be executed in O(n2) time where n is the number of vertices of the input curve. Experimental results show that this method is effective even in the case when relatively few vertices are given as an original shape of a planar object, such as handwritten letters, figures (freehand curves) and wave-form data.

We propose a new algorithm for minimizing the number of vertices of an approximate curve by keeping the error within a given bound (min-# problem) with the parallel-strip error criterion. The best existing algorithm which solves this problem has O (n2 log n) time complexity. Our algorithm which uses the Cone Intersection Method does not have an improved time complexity, but does have a high efficiency. In particular, for practical data such as those which represent the boundaries or the skeletons of an object, the new algorithm can solve the min-# problem in nearly O(n2) time.

A technique was developed to reduce ECG data efficiently within a controlled accuracy. The sampled and digitized data of the original waveform of an ECG is transformed in three major processes. They are the calculation of a beat-to-beat variation, a polygonal approximation and the calculation of the difference between consecutive node points. Then, an adaptive coding technique is applied to minimize redundancies in the data. It was demonstrated that the ECG waveform sampled in 200 Hz, 10 bit/sample, 5 µV/digit could be reduced with the bit reduction ratio of about 10% and within the reconstruction error of about 2.5%. A polygonal approximation method, called MSAPA, was newly developed as a modification of the well known method, SAPA. It was shown that the MSAPA gave better reduction efficiency and smaller reconstruction error than the SAPA, when it was applied to the beat-to-beat variation waveform. The importance of the low-pass filtering as a preprocessing for the polygonal approximation was confirmed in concrete examples. The efficiency of the proposed technique was compared with the cased in which the polygonal approximation was not used. Through these analyses, it was found that the redundancy elimination of the coding technique worked effectively in the proposed technique.