1574 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 24, NO. 12, DECEMBER 2005
A Novel Local Thresholding Algorithm for
Trabecular Bone Volume Fraction Mapping in the
Limited Spatial Resolution Regime of In Vivo MRI
Branimir Vasilic* and Felix W. Wehrli
Abstract—Recent advances in micro-magnetic resonance
imaging have shown the possibility of in vivo assessment of
trabecular bone architecture. However, the small feature size
and relatively low signal-to-noise ratio (SNR) achievable in vivo
cause the intensity histogram to be unimodal. The critical first
step in the processing of these images is the extraction of bone
volume fraction for each voxel. Here, we propose a local threshold
algorithm (LTA) that determines the marrow intensity value in
the neighborhood of each voxel based on nearest-neighbor statis-
tics. Using the local marrow intensities we threshold the image
and scale the intensities of voxels partially occupied by bone to
produce a marrow volume fraction map of the trabecular bone
region. We show that structural parameters derived with the LTA
are highly correlated with those obtained with the previously
published histogram deconvolution algorithm (HDA) and that
the LTA is robust to image noise corruption. The LTA is found to
correctly identify trabeculae with a significantly higher reliability
than HDA. Finally, we demonstrate that the LTA is superior in
preserving connectivity by showing for 75 in vivo images that the
genus of the trabecular bone surface is always higher than when
processed with the HDA.
Index Terms—Image segmentation, local, threshold, trabecular
bone.
I. INTRODUCTION
L
ONG, load bearing bones adapt a structure that is optimal
[1] to carry the maximum load at a given mass of bone.
Long bones have an outer shell of cortical bone that encloses
the marrow and the trabecular bone, an intricate network of
struts and plates. Trabecular bone is concentrated mostly at the
ends of long bones where it serves to distribute the applied
loads with a minimum of bone material. Similarly, trabecular
bone is predominant in the vertebrae. While a significant part
of bone’s strength % comes from bone density alone, the
microstructure of trabecular bone also plays a very important
role. In a healthy person bone is dynamically resorbed and re-
built [2], [3] through the process of remodeling for the purpose
of repairing microdamage and adapting its structure to changing
Manuscript received April 1, 2005; revised August 23, 2005. This work was
supported in part by the National Institutes of Health (NIH) under Grant R01
AR49553, Grant R01 AR41443, and Grant T32 EB00814. The Associate Ed-
itor responsible for coordinating the review of this paper and recommending its
publication was W. Niessen. Asterisk indicates corresponding author.
*B. Vasilic is with the Department of Radiology, the University of Pennsyl-
vania Medical Center, 3400 Spruce Street, 1st Floor Founders, MRI Learning
Center, Philadelphia, PA 19104 USA (e-mail: brana7@comcast.net).
F. W. Wehrli is with the Department of Radiology, the University of Pennsyl-
vania Medical Center, Philadelphia, PA 19104 USA.
Digital Object Identifier 10.1109/TMI.2005.859192
loads. The balance of bone remodeling can be affected by var-
ious diseases, the most common being osteoporosis [4], leading
to a deterioration in bone competence. An ideal way to deter-
mine bone quality would be an in vivo measurement capable of
detection and quantification of changes in bone microstructure.
Advances in magnetic resonance microscopy ( MRI) [5], [6]
have made this noninvasive imaging modality a promissing tool
that could potentially be used for longitudinal monitoring of tra-
becular bone changes in patients.
Since MRI pushes the limits of magnetic resonance imaging
(MRI) in both resolution and signal-to-noise ratios (SNRs) [7],
adequate image processing is crucial in extracting relevant in-
formation from acquired images. Fundamental to the analysis of
MR images of trabecular bone is to correctly classify voxels
as bone or marrow. All subsequent analysis of microstructure
depends on the proper voxel classification and it is, therefore,
critical to preserve all available information on bone occupancy
of voxels. This task is complicated by the following factors: a)
Noise leads to misclassification of voxels and has to be dealt
with, b) Partial volume effects are always present in MR im-
ages of bone since the resolution is often too low to cover trabec-
ulae with more than a single voxel, and finally c) Coil shading,
especially important with surface coils, modulates signal inten-
sities across the image which has to be accounted for by the
algorithm used. Coil shading can be corrected before bone oc-
cupancy analysis or can be incorporated into the algorithm used
for bone volume fraction (BVF) mapping.
Bone appears dark in MR images while marrow is bright due
to the intense fat signal. However, noise and partial volume ef-
fects make the image histograms unimodal, thus hiding the dis-
tinction in intensities between bone and marrow. The absence of
bimodality in the histogram causes simple thresholding methods
to give very poor results so other, more sophisticated methods
have to be employed. To this end we have used [8] a histogram
deconvolution algorithm (HDA) that identifies voxels partially
occupied by bone and iteratively removes the noise in those
voxels producing a noiseless BVF map. However, we have ob-
served that in low SNR images the HDA often fails to correctly
identify thin or weakly connected trabeculae so we explored al-
ternative solutions to the problem.
In this work we introduce a statistical method which calcu-
lates a local intensity threshold value that distinguishes voxels
containing pure marrow from those partially occupied by bone.
In the local threshold algorithm (LTA) we determine a condi-
tional probability that relates the intensity of a voxel with the
probability that it has a certain value of the discrete Laplacian.
0278-0062/$20.00 © 2005 IEEE