Biomedical Engineering Reference
In-Depth Information
interpolation techniques are required to enlarge these
images to a proper display size. A common interpolation
technique, bilinear interpolation, refers to linear in-
terpolation along the horizontal and vertical direction.
The pixel value at any display point is computed based
on a weighted sum of pixel values at the corner locations
of the smallest rectangular cell in the image that sur-
rounds the point. The weighting factor is the ratio of the
area the diagonally opposite corner forms with the con-
sidered display point to the area of the rectangular cell
formed by the pixel image. Although bilinear inter-
polation may provide satisfactory results for many ap-
plications, more elaborate interpolation techniques may
also be required.
were developed, but they did not lead to a general so-
lution. Subsequently, isosurfaces were developed and
used for this purpose, as described later. Because of the
drawback of dealing with a large number of triangles to
represent the branch, other approaches based on an im-
plicit analytical representation were investigated and
used in a limited number of applications. New tech-
niques under investigation show promise, especially
model-based approaches where a model representing the
Y branch can be appropriately parameterized to adapt to
points in the contour lines.
2D texture mapping and parametrizing images
Texture mapping is a concept introduced in computer
graphics for providing high visual realism in a scene
[28]
.
Painting the elements of a drawing with realistic effects
each time they appear in the scene may be an un-
warranted intensive task, especially when the purpose is
to provide only a visual context, such as the background
field in a game. In those cases, an image piece repre-
senting the elements, such as its photograph, could be
used to create the illusion that the elements appear as if
they were drawn into the scene. The simplicity and
popularity of this technique enabled both graphics soft-
ware developers and graphics hardware manufacturers to
use it widely. The technology of texture mapping rapidly
advanced and became inexpensive. In the scientific vi-
sualization field texture mapping contributes to realism
and speed, but more importantly it provides a geometric
representation for the image, separating the spatial in-
formation from its image-pixel fragments. This sub-
stantially simplifies the tasks involved in visualization
problems. By solving the problem in its geometric for-
mulation, which in many cases would be more straight-
forward, and letting the texture mapping technique take
care of the pixel association with the geometry, more
ingenious visualization systems could be built.
2D contours and deformable models
Manipulation of the entire 2D image appeared to be
a cumbersome approach when the feature of interest
could be represented as contour lines delineating struc-
tures of interest. Besides, such contours could provide
quantitative information such as area and perimeter, and
they could also be used to build 3D models. Considering
such benefits, both manual (supervised) and automatic
approaches were developed. Earlier automatic contour
extraction techniques suffered setbacks due to the in-
sufficient quality of the image. Later, deformable models
were developed to preserve the continuity of the contour
and its topology. The user would provide an initial simple
contour line that served as an initial reference. The
deformable model would then shrink or expand the
contour to minimize a cost function associated with its
shape evaluated at each iterative step as the contour
progressively approached the boundary of interest. By
defining appropriate penalty values to prevent irregular-
ities in the contour, the continuity around poor image
boundaries was preserved. This approach, also called
snakes or active contours, created considerable technical
interest in the field.
6.6.2.3 Third generation systems
Contour models
In early systems, contours from a stack of serial slices
could be arranged to display a topographic view of the 3D
form representing the boundary of structures. Later,
''contour stitching'' techniques were developed to sew
the contours and provide a 3D surface model view of the
contour stacks. Although simple in appearance, these
techniques required significant attention, especially
when the contour shapes changed considerably and led to
aliasing problems in the rendered surface. A case of
particular interest was the Y branch frequently encoun-
tered in vascular or airway trees. In these cases, one
contour in a slice had to be stitched to two contours in
the adjoining slice to produce the Y branch. Several ap-
proaches that could solve the problem in special cases
With the arrival of 3D images in the biomedical
field, researchers developed various methods to display
volume information
[17]
. The effectiveness of a tech-
nique depends primarily on the source of the image.
Probably the most important factor in the development
of volume visualization is the fact that the data had one
dimension more than the computer display. Thus, in
some sense, every technique ultimately had to project
the 3D information to form a 2D image, a process where
information could be potentially lost or occluded. Al-
though stereo display may have eliminated some of these
problems, the fundamental problem of presenting a 3D
volume of information in a form that the user can quickly
interpret still remains an elusive visualization problem. In
