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incorporate additional mathematical constraints (e.g. Kruppa
s equations and epi-
polar geometry [
21
] which are mathematical constructs frequently used for camera
self-calibration from a sequence of images). Additional constraints allow the
reduction of the number of degrees of freedom in the system of equations without
additional data. Using corresponding high-order geometrical primitives (line seg-
ments, ellipses, curves, etc.) instead of only point correspondences for the resolu-
tion of the self-calibration problem can drastically increase the quantity of data fed
into the algorithm. Geometric parameters such as the rotation and translation
components of the camera con
'
guration can be determined based on shape infor-
mation taken from the biplanar projection views, such as with mathematical high
level geometrical primitives (lines or ellipses) [
52
] or with intrinsic properties such
as tangent vectors and maximal curvature points to [
16
]. Although these properties
have yet to be used for orthopaedic imaging, properties such as geometrical torsion
which describes the 3D phenomena in AIS [
51
] can be used in the context of
calibrating an X-ray scene to establish the 2D-3D relationships for tangential and
curvature characteristics extracted from 3D spinal curves [
40
]. Thus by determining
the 3D parameters of a Frenet-Serret frame for example, based on the 2D infor-
mation collected from the projection images, this set of information can be
exploited in a 2D-3D correspondence framework.
3.3 Image-Based Self-calibration
Progressing towards an automated calibration technique therefore involves seg-
menting anatomical shapes or high level geometrical primitives which can be
accurately matched on the X-ray images. Segmentation of bony anatomical struc-
tures remains however a challenging problem due to overlapping organs in the
thoracic region and low image signal-to-noise ratio. Automatic spine segmentation
approaches have been sparsely explored by using machine learning approaches
based on localized texture parameters, morphological descriptions in dynamic
programming [
19
] or from Active Shape Models (ASM) using templates from
learning data [
57
]. Based on the work of Cheng et al. [
6
] which presented a
Bayesian approach that uses manually labelled data for parcellation applications,
spatial relationships can be used, where the segmentation of the spine shape relied
mostly on prior anatomical knowledge information taken from an atlas prior [
32
].
The core idea of using a manual training set for incorporation of prior statistics and
class conditional densities can be transposed in such a work to model the variation
distribution of vertebral boundaries by constraining image intensities. This
approach is motivated from the fact that segmenting spine contour silhouettes from
the biplanar images would offer high level geometrical primitives which could be
used to establish 2D-3D correspondence metrics in the self-calibration optimization
scheme. Hence, visual reconstructions can be exploited as high-level anatomical
primitives, which are subsequently matched between the biplanar X-rays to
