Workflow for 3D volume reconstruction

The following chapter summarizes the most important concepts described in articles [Ref1], [Ref2], [Ref3]. It is strongly recommended to read those first.

Briefly, there are two different measurement systems involved:

1. US (UltraSound) system: this system, based on ultra-sounds reflexion, is able to acquire 2D images regarding subcutaneous body structures including tendons, muscles, joints, vessels and internal organs. This system is normally composed by a probe, containing the sensors able to record reflected ultrasounds. The pixels of each image can be expressed in the scan reference frame P. Normally, all the acquired images are stored into DICOM files.

2. Marker-based optoelectronic system (opto): an ensemble of cameras capturing, at the same time, the 3D position of (active or passive) markers. The position is expressed with respect to a global reference frame T. The positions of the markers is normally stored in a binary C3D file.

The start-acquisition and stop-acquisition triggers for both devices are supposed to be hardware-synchronized. The two systems have different acquisition frequencies, normally the opto system one being higher.

By putting some markers on the US probe, it is possible to construct a probe reference frame R. Thus, it is possible to know, for very time frame of the combined data acquisition, the attitude (rotation + translation) of the US probe with respect to T. Since the position of the 2D scans with respect to R can be found by a procedure called Calibration, then it also possible to know the attitude of each 2D scan (and each pixel into it) into T.

Let the attitude from frame A to B be expressed by a 4x4 matrix containing rotation matrix and position vector: . Let be the pixel coordinates vector in a generic reference frame H.

What mentioned above is expressed by the following equation: .

These are the steps performed during a full processing session:

Devices delay estimation and compensation

Although we strongly suggest to hardware-trigger both devices with a common start-stop acquisition trigger, this is not always possible or anyway there is still a time delay to be compensated later. We provide the possibility to estimate and compensate this time delay.

Probe spatial calibration

This is aimed at calculating (see [Ref2]). Briefly, it is based on solving a system of equations similar to the one above (by expressing in a more convenient calibration phantom reference frame C) and imposing to respect some constraints.

Below a schematic overview of the calibration protocol. US probe is scanning the bottom of a water tank. Here, the constraint is that, for all the US image, that a the vertical coordinate of is always 0 for all the time frames.

../_images/probe_calib.png

Calibration quality assessment

This is the process of estimating both precision and accuracy of the calibration phase. Precision gives an indication of the dispersion of measures around their mean. Accuracy gives an indication of the difference between the mean of the measures and the real value. For details, read [Ref1]. This measure can be, for instance, the known position of a point in space (Point accuracy) or the known dimension of an object (Distance accuracy).

3D Voxel reconstruction

Here, the 2D US scans are “aligned” in the 3D space by using the equation above. A 3D voxel-array is created, containing the grey values of all the repositioned original pixels. The voxel-array (a parallelepipedon) should be the smallest one containing the sequence of realigned scans, in order to avoid RAM waste.

Gaps filling

After all the scans are correctly positioned in the 3D space, there are inevitably “gaps” in the voxel-array, i.e., voxels for which the grey value is unknown. The quick-and-dirty way, known as VNN (Voxel Nearest Neighbour), consists of filling a gap by using the closest voxel having an assigned grey value. But other more sophisticated techniques are available.

Further analysis

The gaps-filled voxel-array can be served for other further analysis, such as features extraction like body structure border extraction and volume calculation.

Below, we show the result of manual border identification and surface mesh reconstruction of a human calf muscle (by using MeVisLab):

../_images/3d_mesh_muscle.png