Semi-automatic teeth segmentation in 3D models of dental casts using a hybrid methodology - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 365

First of all, the structure of the point cloud as a flow graph through the K closest neighbors,
which are joined together using links with different weights. Additionally, points are joined to
a source and a sink, used to represent the object and the background.
The first weight is given to all edges of the point cloud and is called SmoothCost (SC), com-
puted using Equation (2) :
(2)
where dist is the distance between the points and σ is a free input parameter that allows modi-
fying the smoothing efect.
The next step of the algorithm is to establish the cost of the data. In this case it is necessary
to make use of the source ( t ) and sink ( s ), where the source is related to the central point of the
object to segment (given manually) and sink with any point belonging to background, where
the following penalty calculated by Equation (3) .
(3)
where distocenter is the expected distance to the center of the object in a horizontal plane, and
is computed as in Equation (4) :
(4)
Radius is an input parameter and can be considered as the range from the center of the ob-
ject where the points belong to a region of interest by assigning a higher weight. On the other
hand, z axis is not considered in Equation (4) . Such constraint can be interpreted geometrically
as an infinite length cylinder with radius given by radius, whose length is aligned parallel to
the z axis.
Once the graph is constructed, the segmentation is given by the minimum cut where the re-
gion of interest is extracted.