The Ultrasound Visualization Pipeline - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 271

A detailed categorization of reconstruction algorithms was done by Rohling et
al. [ 61 ] and Solberg et al. [ 70 ]. We adopt the categorization by Solberg et al. into
voxel- , pixel- and function-based methods and complete it with recent works.
Voxel-based methods , i.e., backward compounding , run through the voxel grid
and assign each of them a value estimated by an interpolation method such as the
Stradx system [ 59 ]. It allows for real-time visualization of freehand ultrasound, in-
cluding plane re-slicing based on nearest-neighbor interpolation and later also for
direct volume rendering [ 58 ]. They blend images generated by re-slicing as de-
scribed in their previous work. Gee et al. also used nearest neighbor interpolation for
direct plane re-slicing [ 21 ]. The reconstructed plane is intended for direct viewing—
implying only one re-sampling stage. Linear, bilinear and trilinear interpolationmeth-
ods have also been used [ 6 , 74 ]. Recent developments by Wein et al. improve both
quality and performance by applying a backward-warping paradigm implemented
on dedicated graphics hardware [ 80 ].
Karamalis et al. used interpolation on the GPU for high-quality volume recon-
struction [ 33 ]. They select an optimal orientation of reconstruction slices based on the
orientation of the scans and reconstruct the volume by following this direction. Each
sampling layer is reconstructed from scans which intersect this layer by interpolating
intensity values between the intersections. The visualization pipeline includes two
re-sampling steps: one during the reconstruction and one while volume rendering.
Pixel-based methods , i.e., forward compounding , traverse each pixel of all ac-
quired 2D images and update the value of one or several voxels of the target grid.
Gobbi and Peters used splatting as a high-quality interpolation method and described
a technique that operates in real-time while the data is captured [ 25 ].
Function-based methods employ a specific function to interpolate between vox-
els. In most applications, the shape of the underlying data is not considered. Rohling
et al. investigated the quality of interpolation using splines, which is a polynomial
function [ 60 ]. They compared this techniquewith other standardmethods and showed
that it produces more accurate reconstructions.
Tetrahedron-based methods reconstruct a 3D model built from tetrahedra using
an iterative subdivision of an initial tetrahedron instead of a regular grid [ 63 ]. The
subdivision terminates if all tetrahedra contain one data point. Each point is assigned
a value which corresponds to the barycentric coordinates of the data point in this
tetrahedron. This strategy is adaptive; the model adapts as new data is streamed in.
We listed selected algorithms in categories based on how they were implemented.
If choosing a specific algorithm, one must choose between speed and quality. Solberg
et al. compared the performance of some of the algorithms [ 70 ]. From all listed
methods, the radial-based function reconstruction by Rohling et al. [ 61 ] delivers
reconstructions of the best quality but it is also the most computationally expensive.
However, the increasingly powerful dedicated graphics hardware for computational
acceleration solves this problem.