3D Reconstruction Made Easy
3D Reconstruction Made Easy
3D Reconstruction Made Easy
Giacomo Luccichenti
Filippo Cademartiri
3D reconstruction techniques made easy:
Francesca Romana Pezzella
Giuseppe Runza
know-how and pictures
Manuel Belgrano
Massimo Midiri
Umberto Sabatini
Stefano Bastianello
Gabriel P. Krestin
Fig. 3 Ray casting. In ray casting, virtual lines are projected from the values of the missing points that form the virtual lines are obtained by
flat panel to the volume. The value of the pixel of the flat panel is interpolation from the known samples of the volume. Red squares:
obtained from the values of the points forming the virtual lines. A ray interpolated points; yellow square: pixel; green circles: points of the
may not intersect the points that represent volume’s voxels. The volume (voxels)
not correspond to the screen’s pixels. One way to avoid the visualisation of the structures (Fig. 4) [9]. The problem
fractional values is to perform a ray casting. With this op- to represent a curved surface on a flat screen occurs sim-
eration projection rays are built from the screen’s pixels to ilarly in cartography or in photography. In other words,
the volume (Fig. 3) [5, 8]. These rays may not correspond to optimal projection should display wide surface with min-
the volume’s voxels. In this case the values of the points imal distortion (Fig. 5).
forming the rays are obtained through interpolation. Build-
ing the rays from a hypothetic observer point of view en-
hances the depth perception. Projection geometry affects Assigning a value to the screen pixel
Sum
The value of the pixel from which a ray is cast can cor-
respond to the sum of the values of the points along this ray.
Fig. 4 In order to enhance the depth perception, the virtual lines that
are projected in ray casting are built from a location corresponding to
the observer eye. From the virtual source, the rays diverge, pass
through the flat screen and then through the volume. The distance
between the origin of the lines and the volume enhance the depth Fig. 5 Example of virtual endoscopy (e.g. projected solid angle) with
perception, although the volume is deformed. This geometry is sim- good lumen visualization of the trachea. The position of viewpoint is
ilar to the optic system of a camera showed in (a), while the resulting image is showed in (b)
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Fig. 8 Example of pitfall of MIP. In presence of ascending aorta dissection, 1 mm thick axial images (a) show clearly the dissected flap.
Performing a “slab axial MIP” with increasing thickness (b–c); (thickness=8 mm, 20 mm) the dissected flap progressively disappears
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(Fig. 8). Hence, to avoid errors, axial slices must always be Classification is the operation that defines how each point
checked. Finally, two separated hyper-intense structures (or along the ray contributes to the pixel value on the picture
hyper-attenuating) along the direction of the rays appear (Figs. 12, 13) [5, 8, 12]. The contribution may range from
superimposed due to the absence of the depth cue (Fig. 9) 100 to 0% opacity. An opacity function curve correlates the
[10, 11]. Rotating the volume, in order to obtain different voxel value with its opacity. The pixel value of the screen
projection views, and analysing them as with fluoroscopic will be obtained from the contribution of the opacities of the
images may avoid this problem. It is also possible to trim points along the ray. Only voxels, the values of which lay
the volume to reduce the computational costs and exclude within selected interval, are represented. The voxels that are
the overlapping structures. outside of this interval are transparent. In CT, voxel value
Attention should be addressed to the window settings, corresponds to the attenuation in Hounsfield Units (HU).
which affect structure’s dimensions. In addition, due to the The shape of the curve defines the visibility of the structures
projective nature of the MIP image, measurements are not in keeping with their attenuation (Fig. 12, 13) [13]. The
reliable (Fig. 10). pixel value can be represented through grey- or a colour
scale, which may enhance the depth perception and the
densitometric information. While in SSD the pixel’s value
Shaded surface display (SSD) depends on the virtual distance of the volume from the
screen, in VR it depends on the pixel’s value enclosing
This technique represents the surface of a structure. In SSD densitometric information. In other words, VR provides
the pixel’s value of the final picture corresponds to the both spatial and densitometric information (Figs. 9, 12, 13).
Fig. 12 Classification. The shape of the opacity function curve defines the anatomical structures that is visualised according to the
attenuation value. From left to right, the soft tissues are progressively made transparent
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particularly in the z-axis [27–29]. Among parameters that pitch [30, 31]. In addition, wide collimations generate
can be set by the operator, collimation, pitch and recon- partial volume effects due to the averaging of the densities
struction increment are particularly important. within the volume.
Narrow collimations increase image noise and spatial High pitch entails object distortion along the z-axis,
resolution and vice versa [25, 30]. Since 3D images display aliasing, and a rotation artifact [23, 24, 26, 32]. For large
information enclosed in axial slices, exceeding in collima- volume coverage a thin collimation and a high table feed
tion width produces 3D images that look blurred. Collima- should be preferred rather than the opposite option, because
tion should be set according to the object size and the helical higher longitudinal resolution is obtained [30]. While ex-
Fig. 18 Three-dimensional
image blurring. Using thicker
slices to perform three-dimen-
sional VR results in a blurring of
the images
tensive volume coverage with high-resolution is limited in contrast resolution, minimizing aliasing [6, 27, 30, 34, 35].
SLCT due to tube’s heating, MSCT solve this problem [33]. A drawback of overlapping slices is the increased number of
The reconstruction increment (RI) is responsible for the images. On the other hand, high RI generate aliasing [26].
gaps between the images. Narrow RI increases spatial and
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Effective slice width is the thickness of the reconstructed can be applied in two-dimensional images [36]. Sharp ker-
slice in MSCT and may differ from the thickness of the nels and filters are used to enhance the edges of high-
detector. Given an effective slice width, thinner collima- contrast structures (lung parenchyma or bone). Yet, in this
tions provide higher image quality but enhance artifacts instance image noise is amplified (Fig. 20). Smooth kernels
[24]. or filters enhance CNR reducing image noise.
Convolution kernels are applied before back-projection
of raw data for image reconstruction. Alternatively filters
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