Lossy Compression of Z-Map Based Shape Models Using Daubechies Wavelet Transform and Quickselect

Abstract

We propose an algorithm for lossy compression of computer-aided design models in Z-map representation. Our method employs Daubechies wavelet functions, which are smoother than those of the Haar wavelet used in a previous work for the lossy compression of shape models. A significant reduction in the amount of data of the compressed shape model was achieved using the proposed lossy in which the least significant coefficients of the wavelet synopsis were deleted. The nonlinear filtering of coefficients was based on the quickselect algorithm, which was seven to ten times faster than a normal quicksort algorithm and allowed us to accelerate the entire process. We conducted a series of experiments using shape models with 512 × 512–8192 × 8192 resolutions to evaluate our technique using various wavelet functions. The proposed method performed the process in 50–90 ms for the models at 1024 × 1024 resolution and reduced the output binary size by 75%–90% compared with those compressed using a previous method. Some Daubechies wavelets, such as D4 and D6, were found superior in lossy compression using nonlinear filtering based on the order of magnitude of wavelet coefficients.