**3.3 Volume reconstruction**

The volume reconstruction methods are the most important part in the 3D ultrasound reconstruction process, which involved the implementation of interpolation and approximation algorithm to get the 3D volume data and put them in a 3D volume grid based on the spatial information acquired from the tracking system. The volume reconstruction also aims to reduce computational requirements without damaging or losing the underlying shape of the data [18]. Before the volume reconstruction methods start, the coordinate system and volume grid of reconstructed volume need to be established, such as volume size, axes of volume, origin of axes, and the size of voxel [23]. The volume coordinate configuration uses principal component analysis (PCA), which is a statistical tool that estimates the largest difference of collected data

**Figure 5.** *Noise and artifacts [7]: (a) speckle noise; (b) transducer malfunction, and (c) elevational focal zone.*

that the volume can enclose all the data values [23]. The bounding box technique is configured by computing the volume size by filling the voxel with pixels from a series of 2D ultrasound frames, and then the maximum point and the minimum point can be obtained. The bounding box is fast and simple to determine the volume coordinate configuration [8]. The minimum point is set as the origin of the volume. After the volume coordinate is configured, the volume reconstruction can be performed. There are several methods of volume reconstruction and they are pixel-based method (PBM), voxel-based method (VBM), and also function-based method (FBM). In addition, the Visualization Toolkit (VTK) is the most common software package for volume reconstruction and visualization, such as in [4, 11, 14, 16, 17, 24].

### *3.3.1 Pixel-based method (PBM)*

The pixel-nearest neighbor (PNN) method is the example of pixel-based method (PBM), which is used to reconstruct the 3D volume by traveling across each pixel of acquired 2D ultrasound frames. In general, PNN consists of two important steps, which are bin-filling step and hole-filling step [25]. First, the bin-filling step is also known as distribution step and it travels across each pixel in all the 2D ultrasound frames, and then the nearest voxel in the 3D reconstructed volume is filled with that pixel value [4,8]. The method to assign pixel to voxel is based on the corresponding position and orientation information of 2D frames [9]. In this way, the 2D pixels can be transformed into voxels in the 3D volume space. If there have been multiple pixels assigned to a single voxel, the pixel values are averaged [4]. The bin-filling step might lead to empty voxel. Hence, hole-filing phase is used to identify and fill the empty voxel, usually by using the average, maximum, minimum, or a median of the neighbor filled voxels value [8, 9]. The selection of neighbor voxels is determined by a parameter value that represents the distance [24] or the radius of spherical region [8] from an empty voxel to be filled. However, the disadvantages of PNN method are causing blurred result and losing important information of 2D frames [9]. Besides that, some artifacts have been observed on the boundaries between the bin-filled area with original texture pattern and the hole-filled area with smoothed texture pattern [8].

Some research works are done in order to recover the disadvantages of PNN, especially in the hole-filling steps. Fast marching method (FMM) is proposed in the hole-filling step to interpolate empty voxel to preserve the sharp edges in the image and hence reduce the artifacts of the smoothed texture pattern [8]. Besides that, an improved Olympic operation is also proposed to estimate the empty voxel effectively [26]. Based on the observation, the PNN method is still favorable among the researchers in the field of 3D ultrasound reconstruction because of its simplicity to use as well as its capability to avoid complex computational time. Many improved PNN also has been proposed to create higher-quality reconstruction results.

#### *3.3.2 Voxel-based method (VBM)*

The voxel-based method (VBM) is used to reconstruct the 3D volume by traveling across each voxel in a volume grid and gathering the pixel values from input 2D ultrasound frames and computing them by various methods. The newly computed value is then placed at that voxel. The most common methods in VBM are voxelnearest neighbor (VNN) and distance-weighted (DW). The VNN travels across each volume voxel and selects the nearest pixel value from a set of 2D frames to be put on that voxel. This method is capable to preserve the original texture patterns from 2D ultrasound frames; however, its downside is that large distance of the voxel to the 2D frames will generate large reconstruction artifacts and also it tends to preserve the speckle noise from corrupted ultrasound echo [8, 9].

**81**

*A Survey on 3D Ultrasound Reconstruction Techniques DOI: http://dx.doi.org/10.5772/intechopen.81628*

in a volume.

*3.3.3 Function-based method (FBM)*

function exceeds its supposed target.

3D ultrasound reconstruction.

*3.4.1 Multiplanar reformatting*

**3.4 3D visualization**

of some information on the original 2D ultrasound frames [9].

As for the DW method, it also travels across each volume voxel first. Then, its local neighborhood pixels of 2D ultrasound frames are weighted by the inverse distances between the pixels and that voxel [27]. Lastly, the average value of those pixels is placed on the voxel. The DW method is able to suppress speckle noise [8]. On the other hand, it also smoothens the 3D reconstructed volume, causing the loss

Besides that, the implementation of kernel regression can also help estimate the whole voxels in a volume, which is filled by bin-filling stage with more details and suppressing speckle noises, but it suffers from computational speed [9]. Although there is a use of bin-filling step, the use of kernel regression in this sense is considered a VBM as it also requires the reconstruction process to travel across each voxel

The functional-based method (FBM) takes a set of input data and uses a function like polynomial to reconstruct 3D ultrasound volume [28]. The radial basis function (RBF) is one of the FBMs that used an estimate function to compute a spline that passes through the pixels that form a shape in the 2D ultrasound frames [9, 27]. The created splines need to be as identical and smooth as the original shapes in the 2D frames. The approximation requirement is required because of the existence of measurement errors, as well as to reduce the overshoots in order to have the gray-level range of interpolated voxels to be same as that of the original 2D ultrasound frames [27]. The mentioned measurement errors are such as the tissue motion, position sensor error, and calibration error during the data acquisition process. In addition, the overshoot is a situation in signal processing where the signal or

Besides RBF, Bayesian framework can be used to infer the voxel values in a volume grid by assuming a 3D parametric function that has basic function centered at every voxel, and the volume grid is modeled using piecewise smooth Markov random field (PS-MRF) with typical 6-connected neighborhood system [7, 29]. The work of [7] showed that the PS-MRF can work with irregular spaced B-scan images and to reduce the speckle noise and preserve boundary. However, it requires extreme computation time and needs to use GPU and parallel programming to overcome this limitation. The FBMs able to create a high-quality 3D volume from the 2D ultrasound frames; however, they require intensive computational power as well as speed, which imply that these methods are not widely studied in the field of

After volume reconstruction, the 3D visualization method is used to display the volume data from the volume gird for the operator and physicians to see the result of ultrasound scanning. This is useful for them to analyze the scanned anatomy and assist in diagnosis, as well as for image-guided surgery. The 3D visualization process is also the last step to complete the fully functioning 3D ultrasound reconstruction. The common rendering algorithms or techniques for 3D visualization are multipla-

The multiplanar reformatting method is a visualization technique where 2D ultrasound planes, also known as resliced image, are extracted from the 3D ultrasound

nar reformatting, volume rendering, and surface rendering.

### *A Survey on 3D Ultrasound Reconstruction Techniques DOI: http://dx.doi.org/10.5772/intechopen.81628*

*Artificial Intelligence - Applications in Medicine and Biology*

reconstruction and visualization, such as in [4, 11, 14, 16, 17, 24].

*3.3.1 Pixel-based method (PBM)*

*3.3.2 Voxel-based method (VBM)*

that the volume can enclose all the data values [23]. The bounding box technique is configured by computing the volume size by filling the voxel with pixels from a series of 2D ultrasound frames, and then the maximum point and the minimum point can be obtained. The bounding box is fast and simple to determine the volume coordinate configuration [8]. The minimum point is set as the origin of the volume. After the volume coordinate is configured, the volume reconstruction can be performed. There are several methods of volume reconstruction and they are pixel-based method (PBM), voxel-based method (VBM), and also function-based method (FBM). In addition, the Visualization Toolkit (VTK) is the most common software package for volume

The pixel-nearest neighbor (PNN) method is the example of pixel-based method (PBM), which is used to reconstruct the 3D volume by traveling across each pixel of acquired 2D ultrasound frames. In general, PNN consists of two important steps, which are bin-filling step and hole-filling step [25]. First, the bin-filling step is also known as distribution step and it travels across each pixel in all the 2D ultrasound frames, and then the nearest voxel in the 3D reconstructed volume is filled with that pixel value [4,8]. The method to assign pixel to voxel is based on the corresponding position and orientation information of 2D frames [9]. In this way, the 2D pixels can be transformed into voxels in the 3D volume space. If there have been multiple pixels assigned to a single voxel, the pixel values are averaged [4]. The bin-filling step might lead to empty voxel. Hence, hole-filing phase is used to identify and fill the empty voxel, usually by using the average, maximum, minimum, or a median of the neighbor filled voxels value [8, 9]. The selection of neighbor voxels is determined by a parameter value that represents the distance [24] or the radius of spherical region [8] from an empty voxel to be filled. However, the disadvantages of PNN method are causing blurred result and losing important information of 2D frames [9]. Besides that, some artifacts have been observed on the boundaries between the bin-filled area with original texture pattern and the hole-filled area with smoothed texture pattern [8]. Some research works are done in order to recover the disadvantages of PNN, especially in the hole-filling steps. Fast marching method (FMM) is proposed in the hole-filling step to interpolate empty voxel to preserve the sharp edges in the image and hence reduce the artifacts of the smoothed texture pattern [8]. Besides that, an improved Olympic operation is also proposed to estimate the empty voxel effectively [26]. Based on the observation, the PNN method is still favorable among the researchers in the field of 3D ultrasound reconstruction because of its simplicity to use as well as its capability to avoid complex computational time. Many improved

PNN also has been proposed to create higher-quality reconstruction results.

preserve the speckle noise from corrupted ultrasound echo [8, 9].

The voxel-based method (VBM) is used to reconstruct the 3D volume by traveling across each voxel in a volume grid and gathering the pixel values from input 2D ultrasound frames and computing them by various methods. The newly computed value is then placed at that voxel. The most common methods in VBM are voxelnearest neighbor (VNN) and distance-weighted (DW). The VNN travels across each volume voxel and selects the nearest pixel value from a set of 2D frames to be put on that voxel. This method is capable to preserve the original texture patterns from 2D ultrasound frames; however, its downside is that large distance of the voxel to the 2D frames will generate large reconstruction artifacts and also it tends to

**80**

As for the DW method, it also travels across each volume voxel first. Then, its local neighborhood pixels of 2D ultrasound frames are weighted by the inverse distances between the pixels and that voxel [27]. Lastly, the average value of those pixels is placed on the voxel. The DW method is able to suppress speckle noise [8]. On the other hand, it also smoothens the 3D reconstructed volume, causing the loss of some information on the original 2D ultrasound frames [9].

Besides that, the implementation of kernel regression can also help estimate the whole voxels in a volume, which is filled by bin-filling stage with more details and suppressing speckle noises, but it suffers from computational speed [9]. Although there is a use of bin-filling step, the use of kernel regression in this sense is considered a VBM as it also requires the reconstruction process to travel across each voxel in a volume.
