Shape-based Transfer Function Using Laplace-Beltrami Operator

We exploit the Laplace-Beltrami operator to represent shapes which in turn is used for designing a shape based transfer function for volume rendering. Laplace-Beltrami spectral measures are isometry invariant and are one of the most powerful ways to represent shape, also called “Shape-DNA”. Isosurfaces are extracted from the volume data and the Laplace-Beltrami operator is applied on these extracted isosurfaces. We use the Laplace-Beltrami spectrum of the extracted isosurfaces and the corresponding eigenvalues and eigenvectors for representing shape. These eigenvalues and eigenvectors are used to design the transfer function based on shape. We call these eigenvectors shape eigenvectors as they successfully define various shapes in a model. These shape eigenvectors are represented as parallel lines and the color and opacity values are varied using an interface which is a modified form of parallel coordinates, termed as parallel segmentation. We demonstrate the results of our method on several standard datasets. As we are using the shape eigenvectors to design the transfer function, we call this transfer function as shape-frequency based transfer function.