Shape-based Biomedical Visualization

We exploit the Laplace-Beltrami (LB) operator to represent shapes, which in turn is used to visualize certain standard datasets specifically for biomedical applications. LB spectral measures are isometry invariant and are one of the most powerful ways to represent shape, also called “Shape-DNA”. We define a shape signature by finding the eigenvalues and eigenvectors of the LB matrix for the given model. For computational simplicity we use the isosufaces instead of using the volume data directly. Isosurfaces are extracted from the volume data and the LB matrix is evaluated on these extracted isosurfaces. The eigenvalues and eigenvectors of the LB matrix for the extracted isosurfaces are used to represent shapes. We call these eigenvectors shape eigenvectors as they successfully define various shapes in a model. We use an interface which looks like a modified form of parallel coordinates where the shape eigenvectors are represented by parallel lines. This interface is called parallel segmentation and it can be used for visualizing selected regions in the 3D model by just varying the values using the cursor. We demonstrate the results of our method on several standard datasets and show the effectiveness of our method for biomedical visualization. KeywordsLaplace-Beltrami; Shape-DNA; shape eigenvectors; shape signature; parallel segmentation