Information Technology Reference
In-Depth Information
A clique is a set of sites in which all pairs of sites are neighbors. The clique
potentials can be de
ned by
Þ
¼
c
c
if all sites on c have the same label
V
c
ð
ð
Þ
f
11
c
c
;
otherwise
where
c
c
is the potential for type-c cliques. In this proposed method, the Potts
model [
22
] which is similar to Derin-Elliot model [
23
] is used. This model uses the
potentials of the Potts model describing the spatial pairwise interaction between two
neighboring pixels. The MGRF with the second order (8-pixel) neighborhood
depends only on the whether the nearest pairs of pixel labels are equal or not. In this
method,
c
c
is estimated using the method proposed by Ali et al. in [
24
].
Human anatomical structures such as spine bones, kidneys, livers, hearts, and
eyes may have similar shapes. These shapes usually do not differ greatly from one
individual to another. There are many works which analyze the shape variability.
Cootes et al. [
25
] proposed effective approach using principle component analysis
(PCA). Abdelmumin [
26
] proposed another shape based segmentation method
using the Level sets algorithm. Tsai et al. [
27
] proposed a shape model which is
obtained using a signed distance function of the training data. Eigenmodes of
implicit shape representations are used to model the shape variability. Their method
does not require point correspondences. Their shape model is obtained using a
coef
cient of each training shape. Cremers et al. [
28
] proposed a simultaneous
kernel shape based segmentation algorithm with a dissimilarity measure and sta-
tistical shape priors. This method is validated using various image sets in which
objects are tracked successfully. Most published works are theoretically valuable.
However, parameter optimization of the shape priors may take high execution time
if the training set is large. Also, the optimization methods used in shape registration,
such as the gradient descent, takes high execution time.
For the shape de
All
the geometrical information that remains when location, scale, and rotational effects
are
nition, mathematician and statistician D.G. Kendall writes:
“
Hence, the shape information is modeled after the
sample shapes are transformed into the reference space. Finally, the shape variability
is modeled using the occurrences of the transformed shapes. In the proposed work,
the vertebral body shape variability is analyzed using a probabilistic model.
In the next sections, each step is described in detail.
filtered out from an object.
”
2.4.1 Shape Model Construction (Training)
Registration is the important method for shape-based segmentation, shape recog-
nition, tracking, feature extraction, image measurements, and image display. Shape
registration can be de
ned as the process of aligning two images of a scene. Image
registration requires transformations, which are mappings of points from the source
(reference) image to the target (sensed) image. The registration problem is for-
mulated such that a transformation that moves a point from a given source image to
