IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 12, NO. 5, SEPTEMBER/OCTOBER 2006
Lines of Curvature for Polyp Detection in Virtual Colonoscopy
Lingxiao Zhao, Charl P. Botha, Member, IEEE, Javier O. Bescos, Roel Truyen, Frans M. Vos, and Frits H. Post
Abstract— Computer-aided diagnosis (CAD) is a helpful addition to laborious visual inspection for preselection of suspected colonic
polyps in virtual colonoscopy. Most of the previous work on automatic polyp detection makes use of indicators based on the scalar
curvature of the colon wall and can result in many false-positive detections. Our work tries to reduce the number of false-positive
detections in the preselection of polyp candidates.
Polyp surface shape can be characterized and visualized using lines of curvature. In this paper, we describe techniques for generating
and rendering lines of curvature on surfaces and we show that these lines can be used as part of a polyp detection approach. We have
adapted existing approaches on explicit triangular surface meshes, and developed a new algorithm on implicit surfaces embedded in
3D volume data. The visualization of shaded colonic surfaces can be enhanced by rendering the derived lines of curvature on these
surfaces.
Features strongly correlated with true-positive detections were calculated on lines of curvature and used for the polyp candidate
selection. We studied the performance of these features on 5 data sets that included 331 pre-detected candidates, of which 50 sites
were true polyps. The winding angle had a significant discriminating power for true-positive detections, which was demonstrated by
a Wilcoxon rank sum test with p < 0.001. The median winding angle and inter-quartile range (IQR) for true polyps were 7.817 and
6.770−9.288 compared to 2.954 and 1.995−3.749 for false-positive detections.
Index Terms—Medical visualization, virtual colonoscopy, polyp detection, line of curvature, implicit surface.
F
1 INTRODUCTION
Colonic polyps are an important precursor of colon cancer, which is
among the leading causes of cancer deaths in the western world [24].
A polyp is a benign growth of the colon lining. It typically presents as
a sphere protruding from the colon wall. Early detection and removal
of polyps significantly decrease the incidence of colon cancer. For
this purpose, virtual colonoscopy has been developed as a procedure
to inspect the interior wall of the human colon by using CT or MRI-
scans.
Virtual colonoscopy is a minimally-invasive technique, which
causes much less discomfort to the patient than traditional optical
colonoscopy [3, 22]. The CT or MRI-scans are processed by iso-
surface extraction or by direct volume rendering (DVR) to allow for
visual inspection by a radiologist. However, a thorough, visual exam-
ination of the complete colon wall is rather time consuming, which
makes the method unattractive for large-scale screening. Therefore,
computer-aided techniques have been proposed to pre-detect and high-
light colonic polyps in order to reduce the examination time and cost,
especially in mass screening of low-incidence populations [26].
A considerable amount of work has been done in the field of auto-
matic polyp detection; many schemes make use of curvature. Curva-
ture is an important quantity from differential geometry [6], which is
widely used in computer vision and visualization applications to char-
acterize the shape of 3D surfaces. It can be represented by a scalar
• Lingxiao Zhao is with Data Visualization Group, Delft University of
Technology, E-mail: zlx@graphics.tudelft.nl.
• Charl P. Botha is with Data Visualization Group, Delft University of
Technology, E-mail: c.p.botha@tudelft.nl.
• Javier O. Bescos is with Philips Medical Systems Nederland BV, Best,
E-mail: javier.olivan.bescos@philips.com.
• Roel Truyen is with Philips Medical Systems Nederland BV, Best, E-mail:
roel.truyen@philips.com.
• Frans M. Vos is with Quantitative Imaging Group, Delft University of
Technology and Dept. of Radiology, Academic Medical Centre,
Amsterdam, E-mail: f.m.vos@tudelft.nl.
• Frits H. Post is with Data Visualization Group, Delft University of
Technology, E-mail: frits.post@ewi.tudelft.nl.
Manuscript received 31 March 2006; accepted 1 August 2006; posted online 6
November 2006.
For information on obtaining reprints of this article, please send e-mail to:
tvcg@computer.org.
(e.g. mean or Gaussian curvature), and by two vectors, indicating the
directions of principal curvatures at a given point.
Indicators based on scalar curvature values have been frequently
used in previous work for computer-aided diagnosis (CAD) of colonic
polyps. Yoshida et al. [33] made use of 3D geometric features called
the volumetric shape index and curvedness to develop a CAD scheme
for polyp detection. Na¨ppi and Yoshida [18] proposed to use feature-
guided analysis for achieving high sensitivity and a low false positive
rate in their CAD scheme. Huang et al. [8] developed a two-stage
curvature estimation method on triangular surface meshes and per-
formed a filtering based on the sphericity index to identify potential
polyps. Van Wijk et al. [31] introduced the technique of normalized
convolution to measure curvature features in 3D volume data for au-
tomatic polyp detection. Accurate and noise-insensitive curvature cal-
culation is essential for any such scheme. Representations based on
point-sampling will in general be more sensitive to noise, whereas ag-
gregation within a region of interest will enhance the robustness at the
cost of some sensitivity. Using scalar curvature by itself for polyp
detection can result in a large number of false-positive detections.
The potential of principal curvature direction fields has not yet been
explored in current polyp detection techniques. On a surface, the two
principal curvature directions define two orthogonal vector fields, and
these can be visualized by lines of curvature, which are lines every-
where tangent to one of these vector fields. We will call these curves
streamlines of curvature. They have also been used for surface shape
analysis in engineering design [4]. However, to the best of our knowl-
edge, no attempt has been made to apply streamlines of curvature for
colonic polyp characterization in medical visualization. We hypothe-
size that the patterns in streamlines of curvature are a good indicator
of specific features to detect polyps, both visually and automatically.
In our work, the proposed CAD process proceeds in three steps:
pre-detection of polyp candidates, candidate selection, and finally en-
hanced visualization. Polyp candidates are pre-detected using an ex-
isting polyp detection scheme. These polyp candidates include many
false-positive detections. The main contribution of our work is to pro-
pose a new additional polyp candidate selection approach based on
a use of streamlines of curvature, which helps to reduce the number
of false-positive detections. We will present methods to generate pat-
terns of streamlines of curvature on the colon wall. We have improved
existing algorithms for explicit triangle mesh surfaces, and developed
a new method for implicit surfaces embedded in a 3D volume data
representation. The basis of our work is a robust technique for the
computation of principal curvature directions so that the streamlines
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