Enhancement, Extraction, and Visualization of 3D Volume Data

Three-dimensional (3D) volume data has become increasingly common with the emergence and wide availability of modern 3D image acquisition techniques. The demand for computerized analysis and visualization techniques is constantly growing to utilize the abundant information embedded in these data. This thesis consists of three parts. The first part presents methods of analyzing 3D volume data by using second derivatives. Harmonic functions are used to combine the non-orthogonal second derivative operators into an orthogonal basis. Three basic features, magnitude, shape, and orientation, are extracted from the second derivative responses after diagonalizing the Hessian matrix. Two applications on magnetic resonance angiography (MRA) data are presented. One of them utilizes a scale-space and the second order variation to enhance the vascular system by discriminating for string structures. The other one employs the local shape information to detect cases of stenosis. The second part of the thesis discusses some modifications of the fast marching method in 2D and 3D space. By shifting the input and output grids relative to each other, we show that the sampled cost functions are used in a more consistent way. We present new algorithms for anisotropic fast marching which incorporate orientation information during the marching process. Three applications illustrate the usage of the fast marching methods. The first one extracts a guide wire as a minimum-cost path on a salience distance map of a line detection result of a flouroscopy image. The second application extracts the vascular tree from a whole body MRA volume. In the third application, a 3D guide wire is reconstructed from a pair of biplane images using the minimum-cost path formulation.