T-Sutra: a surface tiling algorithm for volumetric image data

NemoImage

13, Number

6, 2001,

Part 2 of 2 Parts 10

E al@

METHODS

- ANALYSIS

T-Sutra: a surface tiling algorithm for volumetric image data R. E. Greenblatt, J. D. Nichols Source

Signal

Imaging,

kc.,

An efficient and accurate algorithm useful for 2D tilings of brain imaging and mesh reduction. These methods have been implemented in software Methods

San Diego

CA USA

data is described, including and applied to volumetric

topological defect correction brain imaging data.

and Results.

Surface triangularizations obtained from volumetric image data are useful for morphometric, visualization, and electromagnetic modeling applications. Methods may vary depending on input data preprocessing and in the construction of the triangular mesh. The Tetrahedral Surface Triangle (T-Sutra) algorithm described here is well suited for segmented, binarized volumetric image data on a regular lattice, that is, the kind of problem frequently encountered in brain imaging applications. We seek to construct a valid triangular representation of the boundary of a selected volume. We assume that the image voxels have already been classified into 3 types: interior, exterior, and surface. Voxel-based images have a natural dual representation, in which points in a discrete lattice represent voxels. Since 5 tetrahedra can tile a hexahedron, and 2 sets of 5 tetrahedra form a unit cell [I], we identify the 20 triangles that constitute the tetrahedral faces of the unit cell. This produces 2 disjoint seed point sets. To determine a valid tiling, we step through each seed point of one of the sets. If a seed point is a surface point, we inspect its neighbors to determine if one or more valid triples of surface points exists. The resulting candidate triangle is a valid surface triangle if one if its tetrahedral opposite vertices is interior, and the other tetrahedral opposite vertex is exterior. The direction of the exterior opposite vertex may be used to determine the surface triangle parity. Topological defects, including surface, tube, and volume defects, may be created during tiling. Surface defects occur when 2 non-adjacent surfaces come in direct contact, but the common edges, if they exist, cannot be connected to form a closed curve. Common edges that can be connected to form a closed curve give rise to tube defects. Volume defects arise when the surface divides the volume into disjoint regions. Two other defects may be identified, but they are constructively impermissible: holes and intersections. Following mesh construction, surface defects may be identified and repaired by a detailed consideration of the connectivity of the triangles adjacent to edges or vertices of interest. Disjoint volume defects may be identified by considering the connectivity of the set of all vertices, and small disjoint volumes deleted. Tube defects may be removed by mesh reduction. Mesh reduction proceeds through an intermediate polygonal tiling step, followed by a new triangularization [2]. We demonstrate that if the polygonal tiling meets certain topological and geometrical conditions, a valid triangular reduction is guaranteed. Starting from a valid triangular tiling, methods are described to generate a polygonal tiling that meets these (rather straightforward) conditions. Literature [ 11 Gueziec, [2] Lotjonen,

Cited A. and Hummel R. (1995). ZEEE Truns Visualization Camp Graphics, J., Reissman, P-J., Magnin, I.E., Nenonen, J., and Katila, T., (1998).

s134

1:328-342. IEEE Trans.

Magn.

34:2228-2233.