matching methods of nonrigid points, such as optimal
processing of the energy function could get trapped in bad
local minima, the topology of the neighboring feature points
are not always preserved well and so on. Most importantly,
the pixel intensity, texture information being not utilized in
above matching methods of nonrigid points, is very useful
and significant in the point matching of deformation
measurement.
In our previous work, a deformation field measurement
method based on the feature point tracking and Delaunay TIN
(Triangular Irregular Network) was presented. But in the
experiment results of this method, a certain number of
incorrectly matched points that have negative effect on
measurement accuracy cannot be eliminated automatically
[5], [6], [7].
In this paper, we propose an integrated matching approach
TSSC, in which TPS, SURF, and the proposed Spatial
Associate Correspondence information (SAC) are utilized to
obtain the global information of MR images, local
neighborhood information of feature points, and spatial
associate correspondence information among the points in
one neighborhood. In this method, the Fast-Hessian and
Harris detector are utilized to extract a number of feature
points distributing on the flat region, boundaries of the tissues.
Then TPS transformation model is adopted to identify the
matching region of the query point in the deformed MR image,
thus avoiding the ambiguities that may occur when an images
has multiple similar regions. To improve the correct ratio of
matching the proposed SAC method is combined with SURF
descriptor to match the feature points. Finally the TPS
clustering method is proposed to eliminate the mismatching
of the feature points. Matching and mismatching elimination
are iterative processed, and with the iterative of the process,
TPS transformation model becomes more accurate, and more
correctly matched points are obtained. When we
experimentally compared our proposed method with the SIFT
and SURF methods, we found that our method was feasible
and effective.
2. OERVIEW OF THE PROPOSED APPROACH
The flow chart of TSSC is shown in Fig. 1. In order to extract
a number of feature points distributing on the flat region,
boundaries of the tissues, Fast-Hessian and Harris operator is
utilized in this paper. SURF descriptor lacks global
information on images, making it prone to mismatching when
there are multiple similar local regions in the image. However,
similar local regions usually occur in the MR images of
nonrigid biological tissue. To overcome this drawback of
SURF, we utilized the TPS transformation model to
determine the small matching region in the deformed image
for every query point in the initial image. Even in the matched
region, mismatches would still occur if the feature points are
matched only by the SURF descriptor. We therefore propose
SAC and combine it with SURF descriptor during the
matching process. The details of TPS-SURF-SAC matching
are described in Section 3.
After TPS-SURF-SAC matching of the feature points, the
TPS clustering method is adopted to eliminate the residual
mismatching points. We introduce a difference vector,
consisting of the coordinate differences between the points
matched by TPS and TPS-SURF-SAC. This is followed by
use of the clustering method of difference vectors to identify
the correctly matched points, which are determined by the
maximum cluster of difference vectors. The details of the TPS
clustering method are described in Section 4.
The elimination of mismatches of TPS clustering is
dependent on the TPS transformation. Since the initial TPS
model determined by several landmarks is not accurate, only
a small number of correctly matched points could be
identified after clustering based on the initial TPS model. To
solve this problem, we repeated the processes of matching
and elimination of mismatches, such that TPS and feature
point matching reinforce each other. After every iterative
matching and elimination of mismatching, we obtained more
correctly matched points to improve the TPS model, making
it closer to the real deformation of tissues. In addition, the
matched regions determined by TPS model would be more
accurate, and the results of mismatching elimination by TPS
clustering should also be improved, until the processing is
stable.
Fig. 1. The flow chart of proposed TSSC method
3. MATCHING
3.1. Identification of the Matching Region
Thin Plate Spline is an interpolation method that finds a
"minimally bended" smooth surface that passes through all
given points [50], [51]. It is particularly popular in
representing shape transformations, such as image morphing
or shape detection and matching. TPS maps any location x=[x,
y]
T
to a new location x=[x’, y’]
T
as follows:
3