Implicit surface visualization of reconstructed biological molecules

An implicit surface of a density function is the set of points at which the value of the function is equal to a fixed threshold. An object that is defined as the collection of points at which the density function value is above the threshold can be visualized by displaying the implicit surface. Some methods for the reconstruction of biological macromolecules from their electron microscopic projections produce density functions that are specified by a linear combination of smoothly-varying radially-symmetric basis functions of finite support, also known as blobs. When density functions are determined by such a blob representation, the implicit surfaces are smoothly varying and the normal at any point on such a surface can be analytically calculated. This property can be utilized to produce high-quality visualizations by raycasting. While raycasting tends to be computationally expensive, we present a methodology that uses techniques of computer graphics and image processing to significantly reduce the cost of visualization.