Volume warping for adaptive isosurface extraction

A method of generating a refined isosurface within an original volume based upon an importance function, comprising the steps of:

• inputting the original volume;
• forming an initial, regular grid within said original volume, said regular grid comprised of a multitude of uniformly spaced apart vertices;
• calculating an importance function for the original volume, said importance function identifying areas of high importance and areas of low importance on said original volume;
• using the importance function to warp the original volume, including the steps of:
• using the importance function to warp said regular grid to form a relaxed grid having a higher Tessellation density in the areas of high importance on said original volume and having a lower Tessellation density in the areas of low importance on said original volume, said relaxed grid defining a warping function, and
• using said warping function to return said relaxed grid to a regular grid shape within said original volume to obtain a warped volume;
• extracting an isosurface from the warped volume;
• unwarping the extracted isosurface with the warping function to obtain a refined isosurface;
• and using said refined isosurface to help form a dataset to visualize said original volume.

A method of equalizing a quantity of information for each unit volume within an original volumetric dataset used to visualize an original volume, including the steps of:

• embedding a initial tridimensional uniform grid in the original volumetric dataset;
• obtaining an importance function, wherein the importance function delineates volumetric regions of higher importance and regions of lower importance in the original volumetric dataset;
• applying said importance function to the initial tridimensional uniform grid embedded in the original volumetric dataset to relax said tridimensional grid such that grid vertices of said tridimensional grid have a higher concentration in regions of higher importance and a lower concentration in regions of lower importance, and forming a relaxed tridimensional grid;
• returning said relaxed grid to a regular grid shape within said original volume thereby resampling the original volumetric dataset using the relaxed tridimensional grid and forming a resampled volumetric dataset;
• extracting an isosurface from the resampled volumetric dataset forming an extracted isosurface including extracted vertices;
• unwarping said extracted vertices of the extracted isosurface using the relaxed grid to form a resampled volumetric dataset to visualize said original volume;
• and
• reducing the size of the resampled volumetric dataset.