Multiscale volume representation by a DoG wavelet

This article presents a method for decomposing volume data into 3D DoG (difference of Gaussians) functions by using the frame theory of nonorthogonal wavelets. Since we can think of a DoG function as a pair of Gaussian functions, we can consider this method an automatic generation of Blinn´s blobby objects (1982). We can also use this representation method for data compression by neglecting the insignificant coefficients, since the wavelet coefficients have significant values only where the volume density changes. Further, since the DoG function closely approximates a ∇²G (Laplacian of Gaussian) function, the representation can be considered a hierarchy of the 3D edges on different resolution spaces. Using the spherically symmetric feature of the 3D DoG function, we can easily visualize the 3D edge structure by the density reprojection method. We apply our representation method to medical CT volume data and show its efficiency in describing the spatial structure of the volume