Contour compression using wavelet and Piecewise Linear transforms

The efficiency of the Periodic Haar Piecewise-Linear (PHL) transform and the Wavelet Transform (WT) in the compression of contour data is presented in this paper. The periodic Haar piecewise linear transform PHL is introduced. This transform is generally based on integrating the periodic Haar functions. Test contours extracted from binary images are represented by two one-dimensional sequences x(i) and y(i) representing the cartesian coordinates of the boundary points of the contour. The contour sequences are transformed and some of the spectral coefficients are selected for inverse transformation. The threshold and zonal methods of compression are investigated. Comparison of the PHL transform and the Wavelet transform with respect to the mean square error versus the compression ratio is reported. It is shown that the Daubechies-4 Wavelet and the PHL transforms have a close performance at low compression ratios, however, the PHL transform has a better compression efficiency at high compression ratios.