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fluoroscopic
image(s) is a challenging task. A priori information is often required to handle this
otherwise ill-posed problem. Previously, kriging-based methods [
6
Constructing a 3D surface model of the vertebra from 2D calibrated
fl
11
] as well as
-
statistical shape model (SSM)-based methods [
12
14
] have been proposed. Unlike
the methods in the former category, where one generic object is used as the prior
information, the methods in the latter category use statistical shape models obtained
from statistical shape analysis. Statistical shape analysis is an important tool for
understanding anatomical structures from medical images [
15
-
17
,
32
,
33
]. Statis-
-
tical shape models give ef
cient parameterization of the shape variations found in a
collection of sample models of a given population. Model-based approaches are
popular due to their ability to robustly represent objects [
18
,
19
]. In Benameur et al.
[
12
,
13
], a SSM of scoliotic vertebrae was
fitted to two radiographic views by
simultaneously optimizing both shape and pose parameters. The optimal estimation
was obtained by iteratively minimizing a combined energy function, which is the
sum of a likelihood energy term measured from an edge potential
field on the
images and a prior energy term measured from the statistical shape model. Boisvert
et al. [
14
] used a statistical articulated model of the spine for 3D reconstruction
from partial radiographic data. Previously, we proposed a 2D-3D reconstruction
scheme combining statistical instantiation and regularized shape deformation with
an iterative image-to-model correspondence establishing algorithm, and showed its
application to reconstruct a surface model of the proximal femur [
20
,
21
].
Common to all these previous works is that at least two images are used as the
input. Recently, we proposed a technique that could reconstruct a scaled, patient-
speci
c 3D surface model from a standard X-ray radiograph and showed its appli-
cation to reconstruct a surface model of the pelvis [
22
]. Based on this work, this paper
presents an improved technique that combines a landmark-to-ray registration with a
statistical shape model-based 2D/3D reconstruction scheme for reconstructing a
scaled, patient-speci
c 3D surface model of the lumbar vertebra from a single
fl
uo-
roscopic image. The landmark-to-ray registration is used to
find an initial scale and an
initial rigid transformation between the
fluoroscopic image and the statistical shape
model. The estimated scale and rigid transformation are then used to initialize the
statistical shape model-based 2D/3D reconstruction scheme.
This chapter is organized as follows. Section
2
brie
fl
y presents the construction
of the statistical shape model. Section
3
describes the statistically deformable 2D/
3D reconstruction approach. Section
4
describes the experimental design and
results, followed by the discussion and conclusions in Sect.
5
.
fl
2 Construction of a Statistical Shape Model of the Lumber
Vertebrae
In this step, our goal was to construct a statistical shape model of the lumbar
vertebrae, simultaneously considering shape information from all
five lumbar
levels, and thereby to determine the principal modes of shape variation. We chose
