2D wavelet transform data compression with error level guarantee for Z-map models

Most of workpiece shapes in NC milling simulations are in Z-map representations that require a very large amount of data to precisely hold a high resolution model. An irreversible compression algorithm for Z-map models using a two-dimensional Haar wavelet transform is proposed to resolve this tight memory situation for an ordinary PC. A shape model is first transformed by using Haar wavelet to build a wavelet synopsis tree while the maximum errors caused by virtually truncating high-frequency components are simultaneously calculated. The total amount of the shape data can be reduced by truncating particular sections of the wavelet components that satisfy the error threshold given by the user. Our algorithm guarantees that any error due to its irreversible compression processes is smaller than the specified level measured against the original model. A series of experiments were conducted using an Apple iMac with a 3.2 GHz CPU and 8 GB of memory. The experiments were performed with 16 sample shape models on 512×512 to 8192×8192 grids to evaluate the compression efficiency of the proposed method. Experimental results confirmed that our compression algorithm requires approximately 20–30 ms for 512×512 models and 7 s for 8192×8192 models under a maximum error level of 10× 10−6 m (a typical criteria for NC milling simulations). The compressed binaries outputted by the proposed method are generally 25–35% smaller than the baseline results by gzip, one of common reversible compression libraries, while these two methods require almost the same level of computational costs. Highlights Discarding diagonal components in WT significantly reduces data amount. The proposed method outperforms a reversible method by 25–35% in size reduction. Most of computational time is consumed by the reversible compression step. The proposed method compresses 5122 models in 20 ms, 81922 models in 7 s.