Arbitrary Topology Shape Reconstruction from Planar Cross Sections

Abstract

ments are usually obtained one slice at a time, where each slice is a 2D array of scalar values corresponding to meaIn computed tomography, magnetic resonance imaging and ultrasound imaging, reconstruction of the 3D object from the surements distributed over a plane passing through the 2D scalar-valued slices obtained by the imaging system is diffi-object. The set of planes generating the slices are usually cult because of the large spacings between the 2D slices. The parallel to each other and equispaced along some axis aliasing that results from this undersampling in the direction through the object.orthogonal to the slices leads to two problems, known as the Once these measurement slices have been obtained, the correspondence problem and the tiling problem. A third prob-goal is to enable a human to easily visualize, in 3D, this lem, known as the branching problem, arises because of the large collection of data. Many algorithms have been develstructure of the objects being imaged in these applications. oped for this purpose, but they can all be classified into Existing reconstruction algorithms typically address only one two categories [8]: volume rendering methods and surface or two of these problems. In this paper, we approach all three reconstruction methods.of these problems simultaneously. This is accomplished by imposing a set of three constraints on the reconstructed surface This paper concentrates on surface reconstruction methand then deriving precise correspondence and tiling rules from ods, all of which proceed by extracting the isosurfaces these constraints. The constraints ensure that the regions tiled corresponding to a specified image intensity. Each isosurby these rules obey physical constructs and have a natural face is represented as an assembly of simple surface primiappearance. Regions which cannot be tiled by these rules with-tives, such as triangles or other polygons. Once these surout breaking one or more constraints are tiled with their medial face primitives are calculated, they can be quickly rendered axis (edge Voronoi diagram). Our implementation of the above from different viewpoints using widely available graphics approach generates triangles of 3D isosurfaces from input hardware. This allows the user to quickly examine many which is either a set of contour data or a volume of image different viewing spaces. slices. Results obtained with synthetic and actual medical dataThis paper presents a surface-based algorithm which are presented. There are still specific cases in which our new achieves both faster rendering and lower likelihood of reapproach can generate distorted results, but these cases are much less likely to occur than those which cause distortions construction error than previous surface reconstruction alin other tiling approaches.

Reconstruction of Branching Surface and Its Smoothness by Reversible Catmull-Clark Subdivision

“…This idea has been proposed in [10,11] and has been implemented in [12]. The family of partial contour connection and hole filling has been proposed in references [1,13,14]) is characterized by matching partially the disjoint contours with the single contours of the neighboring plane, thus leaving a number of holes which are finally filled in final step. Goodman et al, [15] has treated one-to-two case in which a single hole is filled by an approximated chosen hyperboloid.…”

“…In the present formulation the correspondence problem is known which can be obtained from [1]. (b) Tiling means using slice chords to triangulate the strip lying between contours of two adjacent slices into tiling triangles.…”

“…Each tiling triangle consists of exactly two slice chords and one contour segment. Details of tiling can be obtained from [1,2]. In the current work focus is given on branching problems.…”

3D finite element meshing from imaging data

“…Since many 3D objects are sampled in terms of slices, Bajaj et. al introduced an approach to construct triangular surface meshes from the slice data [1], and tetrahedralize the solid region bounded by planar contours and the surface mesh [2].…”

Volume Measurement in Sequential Freehand 3-D Ultrasound

“…In the same way as with freehand 3D ultrasound, each of these applications has been implemented in software which is freely available on the internet 13 , and described in Appendix D.…”