We present a method for the fast selection of a region on a 3D mesh using geometric information.
This is done using a weighted arc length minimization with a conformal factor based on the mean
curvature of the 3D surface. A careful analysis of the geometric estimation process enables our
geometric curve shortening to use a reliable smooth estimate of curvature and its gradient. The result
is a robust way for a user to easily interact with particular regions of a 3D mesh construced from
In this study, we focus on building a robust and semi-automatic method for extracting selected
folds on the cortical surface, specifically for isolating gyri by drawing a curve along the surrounding
sulci. It is desirable to make this process semi-automatic because manually drawing a curve through
the complex 3D mesh is extremely tedious, while automatic methods cannot realistically be expected
to select the exact closed contour a user desires for a given dataset. In the technique described here, a
user places a handful of seed points surrounding the gyri of interest; an initial curve is made from these
points which then evolves to capture the region. We refer to this user-driven procedure as targeting
or selection interchangeably. To illustrate the applicability of these methods to other medical data,
we also give an example of bone fracture CT surface parcellation.
This paper presents a novel analytic technique to perform shape-driven segmentation. In our approach, shapes
are represented using binary maps, and linear PCA is utilized to provide shape priors for segmentation. Intensity
based probability distributions are then employed to convert a given test volume into a binary map representation,
and a novel energy functional is proposed whose minimum can be analytically computed to obtain the desired
segmentation in the shape space. We compare the proposed method with the log-likelihood based energy to
elucidate some key differences. Our algorithm is applied to the segmentation of brain caudate nucleus and
hippocampus from MRI data, which is of interest in the study of schizophrenia and Alzheimer's disease. Our
validation (we compute the Hausdorff distance and the DICE coefficient between the automatic segmentation
and ground-truth) shows that the proposed algorithm is very fast, requires no initialization and outperforms the
log-likelihood based energy.
The level set method is a popular technique used in medical image segmentation; however, the numerics involved
make its use cumbersome. This paper proposes an approximate level set scheme that removes much of the
computational burden while maintaining accuracy.
Abandoning a floating point representation for the signed distance function, we use integral values to represent
the signed distance function. For the cases of 2D and 3D, we detail rules governing the evolution and maintenance
of these three regions. Arbitrary energies can be implemented in the framework.
This scheme has several desirable properties: computations are only performed along the zero level set;
the approximate distance function requires only a few simple integer comparisons for maintenance; smoothness
regularization involves only a few integer calculations and may be handled apart from the energy itself; the zero
level set is represented exactly removing the need for interpolation off the interface; and evolutions proceed on
the order of milliseconds per iteration on conventional uniprocessor workstations.
To highlight its accuracy, flexibility and speed, we demonstrate the technique on intensity-based segmentations
under various statistical metrics. Results for 3D imagery show the technique is fast even for image volumes.
The level set method for curve evolution is a popular technique used in image processing applications. However,
the numerics involved make its use in high performance systems computationally prohibitive. This paper proposes
an approximate level set scheme that removes much of the computational burden while maintaining accuracy.
Abandoning a floating point representation for the signed distance function, we use the integral values to
represent the interior, zero level set, and exterior. We detail rules governing the evolution and maintenance of
these three regions. Arbitrary energies can be implemented with the definition of three operations: initialize
iteration, move points in, move points out.
This scheme has several nice properties. First, computations are only performed along the zero level set.
Second, this approximate distance function representation requires only a few simple integer comparisons for
maintenance. Third, smoothness regularization involves only a few integer calculations and may be handled apart
from the energy itself. Fourth, the zero level set is represented exactly removing the need for interpolation off the
interface. Lastly, evolution proceeds on the order of milliseconds per iteration using conventional uniprocessor
To highlight its accuracy, flexibility and speed, we demonstrate the technique on standard intensity tracking
and stand alone segmentation.