Efficient representation of 2D contour using non-uniform sampling

Abstract

This paper presents a method of representation of an image boundary using non-uniform sampling technique. The boundary can be reconstructed back by Lagrange's interpolation of the samples. The proposed method uses an iterative procedure, which starts with uniform samples of the boundary. Then these samples are reduced to minimum by split and merge technique, which leads to non-uniform sampling of the boundary. The split and merge technique optimizes the number of control points required to represent a curve, thus achieving high compression ratios. The image boundary contour is optimally sampled to 'n' number of intervals. Then the curve is generated using Lagrange's interpolation method that passes through these n+1 points. The curve regenerated through interpolation is then compared with the original contour by weighted distance transform method Tsang, PWM et al., (1994). If the error is less than the tolerable range, then we merge two sample points to make one point and if the error is more than the tolerable range, then a new sample is added in the middle of two samples. The process is repeated till we get optimum number of sample points to reconstruct the contour. Thus only those sample points are retained which are necessary for reconstruction.