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2.1 Image-Registration
The proposed approach is based on the selection of a
significant set of matching points, i.e. key-points,
between a selected base image and an image to be
registered and subsequently using them to calculate
the transformation matrix for image registration.
2.1.1 SIFT based Key-point Selection
SIFT (Lowe, 2004) is an algorithm that is capable of
detecting and describing local features of an image.
It’s invariance to rotation, scale and translation has
made it a popular algorithm in many areas of
computer vision. It is also invariant to illumination
changes and robust to local geometric distortion.
In the proposed approach to image registration we
select a base image from amongst the set of multi-
exposure images and an image to be registered to it
and use SIFT to find significant key-points in both
images. Due to large number of feature points that
may be selected by SIFT in execution the matching
of key-points between two images to be registered; it
is likely that two non-corresponding points may
match as they result in the minimum distance.
Therefore reducing keypoint outliers prior to the
matching key-points will improve the reliability of
matching and hence the outcome of the final task.
2.1.2 Using RANSAC to Remove Matching
Point Outliers
RANSAC (Fischler and Bolles, 1981) algorithm is
an iterative method to approximate factors of a
mathematical form, from a set of experimental data
which include outliers. RANSAC is able to do
robust estimations of the model factors; it can
estimate the parameters with a high degree of
accuracy even when a significant amount of outliers
are present in the data set.
In our approach all SIFT key-points points
resulting from the stage described in section 2.1.1
from the base image and the image being registered
are fed to RANSAC algorithm. It fits a model to
these inlier points and tests the points from the
image being registered against the fitted model, and
if a point fits to the model it will be regarded as
inlier. The model is recalculated from all inliers and
then the error is estimated relative to the model. The
outlier key-points are finally removed from the key-
points of the image.
2.1.3 CPD Algorithm for Registration
In this section we describe the use of the CPD
(Myronenko, 2010) algorithm to register the images,
accordingly preparing them to be fused in the
subsequent stage of the proposed approach. CPD is
based on ‘Point Set Registration’ and aims to form
links between two given sets of points to find the
corresponding features and the necessary
transformation of these features that will allow the
images to be registered.
There are two methods for registering an image
in CPD, rigid and non-rigid point set approaches,
based on the transformation model principal. The
key characteristic of a rigid transformation is
“distance between points are preserved”, which
means it just can be used in the presence of
translation, rotation, and scaling, but not under
scaling and skew. Affine, the transformation we
have used in our work is a non rigid transformation,
which provides the opportunity of registering under
non-uniform scaling and skew.
2.2 Multi-Exposure Image Fusion
Once all images are registered to the base image we
use WBCT to identify regions of maximum energy
from within the multiple exposure images, with the
idea of combining these to form the perceptually
best quality fused image.
2.2.1 Multi-exposure Image Fusion
The basic idea of the fusion algorithm is to compare
the corresponding sub-bands of the WBCT
decomposition of each multi-exposure image set and
to determine the one with the highest energy, i.e.
most detailed. We propose the use of different fusion
rules depending on the frequency band of each sub-
band being fused, as follows:
Fusion of High Frequency Contourlet Sub-bands
:
The high frequency sub-bands contain details of an
image such as texture and edges where as the low
frequency sub-bands contains details of more
spread-out nature or fuzzy, such as background
information. By calculating the absolute energy of
high-frequency coefficients, the energy of a region
can be obtained. A higher value means sharper
changes. Region energy E of a high frequency sub-
band E
H
(where H = (l,m,n), l-level of wavelet
decomposition, m-LH, HL and HH bands of wavelet
decomposition, n-directional Contourlet sub-band)
of an image X can be obtained as follows:
E
(
)
=
(
)
(
,
)
∈
(
x,
)
(1)
f
H
(x,y) is the coefficient at location (x,y) of the
CONTOURLET BASED MULTI-EXPOSURE IMAGE FUSION WITH COMPENSATION FOR
MULTI-DIMENSIONAL CAMERA SHAKE
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