Three-Dimensional Spine Reconstruction from Radiographs - Spinal Imaging and Image Analysis - page 164

determine the 2D-3D relationship of the radiographic scene by self-calibration [ 27 ].
Hence, two distinct correspondence features were developed for the discrete non-
linear optimization procedure and are described below.

3.3.1 Visual Hull Reconstruction

This section exposes an approach which has been extensively investigated in visual
robotics, by adapting an algorithm derived from the shape-from-silhouette principle
for a visual hull reconstruction of medical images. First, the spine shapes are rst

segmented on the images using a prior knowledge Bayesian framework [ 32 ]to
capture vertebral contour, width, and rotation information in the frontal and sagittal
planes. This facilitates the partitioning problem for complex pathological defor-
mations. The silhouettes of the segmented anterior portion of the spine on the
biplanar images are then used for the visual hull reconstruction of the global shape
of the spine as illustrated in Fig. 6 . A visual hull depends both on the spine
silhouettes si i with i and on the camera viewing parameters P i ¼ f 1 ; 2 g such as

P i : <

3

!<

2

;

which remain to be determined. Once the silhouettes are obtained
from the images [ 32 ], the reconstruction is based on the concept of visual hulls.
Formally, the visual hull of the 3D spine S with respect to the viewing plane X ,
denoted by VH ð S ; XÞ , is a volume in space such that for each point P in VH ð S ; XÞ
and each camera viewpoint Vi i in X , the half-line from Vi i

through P contains at least

one point of S [ 39 ]. This de nition states that the visual hull consists of all points in

space whose images lie within all silhouettes viewed from the viewing region.

Fig. 6 Principal of the visual hull 3D reconstruction of the global spine shape based on the
projected silhouette s PA and s LAT on the biplanar radiographic views. The shape of the object S is
estimated by the intersection of both visual cones issued from viewpoints V, offering a sparse and
approximate representation of the global spine shape