Layered manufacturing for medical imaging data

Abstract

Layered manufacturing techniques have been successfully employed to construct scanned objects from three-dimensional medical image data sets. The printed physical models are useful tools for anatomical exploration, surgical planning, teaching, and related medical applications. Before fabricating scanned objects, we have to first build watertight geometrical representations of the target objects from medical image data sets. Many algorithms had been developed to fulfill this duty. However, some of these methods require extra efforts to resolve ambiguity problems and to fix broken surfaces. Other methods cannot generate legitimate models for layered manufacturing. To alleviate these problems, this article presents a modeling procedure to efficiently create geometrical representations of objects from computerized tomography scan and magnetic resonance imaging data sets. The proposed procedure extracts the iso-surface of the target object from the input data set at the first step. Then it converts the iso-surface into a three-dimensional image and filters this three-dimensional image using morphological operators to remove dangling parts and noises. At the next step, a distance field is computed in the three-dimensional image space to approximate the surface of the target object. Then the proposed procedure smooths the distance field to soothe sharp corners and edges of the target object. Finally, a boundary representation is built from the distance field to model the target object. Compared with conventional modeling techniques, the proposed method possesses the following advantages: (1) it reduces human efforts involved in the geometrical modeling process. (2) It can construct both solid and hollow models for the target object, and wall thickness of the hollow models is adjustable. (3) The resultant boundary representation guarantees to form a watertight solid geometry, which is printable using three-dimensional printers. (4) The proposed procedure allows users to tune the precision of the geometrical model to compromise with the available computational resources.

A Distance-Field-Based Pipe-Routing Method

“…Following the voxelization process, we invoke a numerical procedure to compute the shortest distance from each free-space voxel to the obstacles. This distance function is governed by the following Eikonal equation [ 16 , 17 ]: where u is the distance function to be solved, and S represents the surfaces of the obstacles, for which the distance function is set to zero.…”

“…In this research, we use the revised fast marching method (RFMM) proposed in [ 17 ] to compute u for Equation (1). The procedure of the RFMM can be described as follows: First, we find the voxels in the interiors of the obstacles and give them a negative distance to assert that these voxels are excluded from the pipe-routing computations.…”

“…The key steps of the proposed method can be briefly described as follows: First, by carrying out a voxelization computation, the proposed method splits the problem domain into a 3D image of voxels. A distance field [ 16 , 17 ] is then calculated in the free space to record the minimum distances between the free-space voxels and the obstacles. In the following step, the proposed algorithm creates a feasible space which strictly meets conditions 3–6 by peeling consecutive layers of the distance field and segmenting the 3D image.…”

A Voxel-Based Watermarking Scheme for Additive Manufacturing

“…where f is the propagation speed of the distance field. We compute the distance field by using the revised fast marching method (RFMM), developed in the research of [20]. In the computation, all the voxels in the AABB are grouped into three sets: DONE, CLOSE, and FAR.…”

“…These calculations are repeated until CLOSE becomes empty. The details of the RFMM can be found in the paper of [20]. The paper of [19] provides an alternative method for computing distance fields.…”