Automatic registration of vestibular systems with exact
landmark correspondence
Minqi Zhang
a
, Fang Li
a
, Xingce Wang
b
, Zhongke Wu
b
, Shi-Qing Xin
c
, Lok-Ming Lui
d
, Lin Shi
e
,
Defeng Wang
e
, Ying He
a,
⇑
a
School of Computer Engineering, Nanyang Technological University, Singapore
b
College of Information Science and Technology, Beijing Normal University, Beijing, China
c
Faculty of Information Science and Engineering, Ningbo University, Zhejiang, China
d
Department of Mathematics, Chinese University of Hong Kong, Hong Kong, China
e
Department of Imaging and Interventional Radiology, Chinese University of Hong Kong, Hong Kong, China
article info
Article history:
Received 2 March 2014
Received in revised form 27 March 2014
Accepted 2 April 2014
Available online 18 April 2014
Keywords:
Registration
Landmark matching
Vestibular system
Discrete geodesic
Harmonic map
Holomorphic 1-form
abstract
Shape registration has a wide range of applications in geometric modeling, medical imag-
ing, and computer vision. This paper focuses on the registration of the genus-3 vestibular
systems and studies the geometric differences between the normal and Adolescent Idio-
pathic Scoliosis (AIS) groups. The non-trivial topology of the VS poses great technical chal-
lenges to the geometric analysis. To tackle these challenges, we present an effective and
practical solution to register the vestibular systems. We first extract six geodesic land-
marks for the VS, which are stable, intrinsic, and insensitive to the VS’s resolution and tes-
sellation. Moreover, they are highly consistent regardless of the AIS and normal groups. The
detected geodesic landmarks partition the VS into three patches, a topological annulus and
two topological disks. For each pair of patches of the AIS subject and the control, we com-
pute a bijective map using the holomorphic 1-form and harmonic map techniques. With a
carefully designed boundary condition, the three individual maps can be glued in a seam-
less manner so that the resulting registration is a homeomorphism with exact landmark
matching. Our method is robust, automatic and efficient. It takes only a few seconds on
a low-end PC, which significantly outperforms the non-rigid ICP algorithm. We conducted
a student’s t-test on the test data. Computational results show that using the mean curva-
ture measure E
H
, our method can distinguish the AIS subjects and the normal subjects.
Ó 2014 Elsevier Inc. All rights reserved.
1. Introduction
Surface registration is the process that aligns a source
3D surface to a target. It has a wide range of applications
in geometric modeling, medical imaging, and computer
vision. This paper focuses on registration of the vestibular
systems (VS) and studies the geometric differences
between the normal and Adolescent Idiopathic Scoliosis
(AIS) groups. The vestibular system is the sensory system
situated in the inner ear, which contributes to balance
and the sense of spatial orientation. The VS is a genus-3
structure with three semicircular canals (see Fig. 1)) and
the morphometry of VS plays an important role in the anal-
ysis of various diseases such as the AIS disease, which is a
3D spinal deformity affecting about 4% school children
worldwide. The etiology of AIS is still unclear but believed
http://dx.doi.org/10.1016/j.gmod.2014.04.010
1524-0703/Ó 2014 Elsevier Inc. All rights reserved.
⇑
Corresponding author.
E-mail addresses: mzhang1@e.ntu.edu.sg (M. Zhang), asfli@ntu.edu.sg
(F. Li), wangxingce@bnu.edu.cn (X. Wang), zwu@bnu.edu.cn (Z. Wu),
xinshiqing@nbu.edu.cn (S.-Q. Xin), lmlui@math.cuhk.edu.hk (L.-M. Lui),
shilin@cuhk.edu.hk (L. Shi), dfwang@cuhk.edu.hk (D. Wang), yhe@ntu.
edu.sg (Y. He).
Graphical Models 76 (2014) 532–541
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Graphical Models
journal homepage: www.elsevier.com/locate/gmod