Abstract: This paper presents an improved image segmentation
model with edge preserving regularization based on the
piecewise-smooth Mumford-Shah functional. A level set formulation
is considered for the Mumford-Shah functional minimization in
segmentation, and the corresponding partial difference equations are
solved by the backward Euler discretization. Aiming at encouraging
edge preserving regularization, a new edge indicator function is
introduced at level set frame. In which all the grid points which is used
to locate the level set curve are considered to avoid blurring the edges
and a nonlinear smooth constraint function as regularization term is
applied to smooth the image in the isophote direction instead of the
gradient direction. In implementation, some strategies such as a new
scheme for extension of u+ and u- computation of the grid points and
speedup of the convergence are studied to improve the efficacy of the
algorithm. The resulting algorithm has been implemented and
compared with the previous methods, and has been proved efficiently
by several cases.
Abstract: This paper presents an application of level sets for the segmentation of abdominal and thoracic aortic aneurysms in CTA
datasets. An important challenge in reliably detecting aortic is the
need to overcome problems associated with intensity
inhomogeneities. Level sets are part of an important class of methods
that utilize partial differential equations (PDEs) and have been extensively applied in image segmentation. A kernel function in the
level set formulation aids the suppression of noise in the extracted
regions of interest and then guides the motion of the evolving contour
for the detection of weak boundaries. The speed of curve evolution
has been significantly improved with a resulting decrease in segmentation time compared with previous implementations of level
sets, and are shown to be more effective than other approaches in
coping with intensity inhomogeneities. We have applied the Courant
Friedrichs Levy (CFL) condition as stability criterion for our algorithm.
Abstract: Segmentation techniques based on Active Contour
Models have been strongly benefited from the use of prior information
during their evolution. Shape prior information is captured from
a training set and is introduced in the optimization procedure to
restrict the evolution into allowable shapes. In this way, the evolution
converges onto regions even with weak boundaries. Although
significant effort has been devoted on different ways of capturing
and analyzing prior information, very little thought has been devoted
on the way of combining image information with prior information.
This paper focuses on a more natural way of incorporating the
prior information in the level set framework. For proof of concept
the method is applied on hippocampus segmentation in T1-MR
images. Hippocampus segmentation is a very challenging task, due
to the multivariate surrounding region and the missing boundary
with the neighboring amygdala, whose intensities are identical. The
proposed method, mimics the human segmentation way and thus
shows enhancements in the segmentation accuracy.
Abstract: A one-step conservative level set method, combined with a global mass correction method, is developed in this study to simulate the incompressible two-phase flows. The present framework do not need to solve the conservative level set scheme at two separated steps, and the global mass can be exactly conserved. The present method is then more efficient than two-step conservative level set scheme. The dispersion-relation-preserving schemes are utilized for the advection terms. The pressure Poisson equation solver is applied to GPU computation using the pCDR library developed by National Center for High-Performance Computing, Taiwan. The SMP parallelization is used to accelerate the rest of calculations. Three benchmark problems were done for the performance evaluation. Good agreements with the referenced solutions are demonstrated for all the investigated problems.
Abstract: This paper is concerned with an improved algorithm
based on the piecewise-smooth Mumford and Shah (MS) functional
for an efficient and reliable segmentation. In order to speed up
convergence, an additional force, at each time step, is introduced
further to drive the evolution of the curves instead of only driven by
the extensions of the complementary functions u + and u - . In our
scheme, furthermore, the piecewise-constant MS functional is
integrated to generate the extra force based on a temporary image that
is dynamically created by computing the union of u + and u - during
segmenting. Therefore, some drawbacks of the original algorithm,
such as smaller objects generated by noise and local minimal problem
also are eliminated or improved. The resulting algorithm has been
implemented in Matlab and Visual Cµ, and demonstrated efficiently
by several cases.