26-02-2013, 11:13 AM
Image Registration Using Adaptive Polar Transform
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Abstract
Image registration is an essential step in many image
processing applications that need visual information from multiple
images for comparison, integration, or analysis. Recently,
researchers have introduced image registration techniques using
the log-polar transform (LPT) for its rotation and scale invariant
properties. However, it suffers from nonuniform sampling which
makes it not suitable for applications in which the registered images
are altered or occluded. Inspired by LPT, this paper presents
a new registration algorithm that addresses the problems of the
conventional LPT while maintaining the robustness to scale and
rotation. We introduce a novel adaptive polar transform (APT)
technique that evenly and effectively samples the image in the
Cartesian coordinates. Combining APT with an innovative projection
transform along with a matching mechanism, the proposed
method yields less computational load and more accurate registration
than that of the conventional LPT. Translation between the
registered images is recovered with the new search scheme using
Gabor feature extraction to accelerate the localization procedure.
Moreover an image comparison scheme is proposed for locating
the area where the image pairs differ.
INTRODUCTION
I MAGE registration is a process of aligning two images that
share common visual information such as images of the
same object or images of the same scene taken at different geometric
viewpoints, different time, or by different image sensors.
Image registration is an essential step in many image processing
applications that involve multiple images for comparison, integration
or analysis such as image fusion, image mosaics, image
or scene change detection, and medical imaging. The main objective
of image registration is to find the geometric transformations
of the model image, , in the target image.
ADAPTIVE POLAR TRANSFORM APPROACH
Inspired by the scale and rotation invariance properties of the
conventional LPT approach, we propose a novel image transformation
scheme, APT, that is designed to address the two major
problems of LPT: the high computational cost in the transformation
procedure and the bias matching due to the nonuniform
sampling, while maintaining all the advantages. Section II-A
briefly introduces LPT and its advantages for image registration.
Section II-B presents the motivation of the proposed APT
approach. Sections II-C and II-D present the proposed APT and
the projection transform, respectively.
Motivation of the Proposed Approach
Although LPT has been widely used in many image processing
applications, it suffers from nonuniform sampling. As
shown in Fig. 1(a), as the radius of the mapping increases, pixels
in the Cartesian coordinates are sampled with less number of
times. This nonuniform sampling would cause image pixels that
are far away from the center point to be missed. This phenomenon
yields losses in image information which will eventually
decrease the accuracy of the registration system. To prevent any
image pixel from being missed in the mapping process, large
numbers of samples are required in both the log-radius and the
angular directions. We denotes and as numbers of samples
in the log-radius and the angular directions, respectively.
Proposed APT Approach
The objective of our proposed APT is to address the two
major problems of the conventional LPT: the uneven sampling
to the entire transformed image, and the computational waste
due to the oversampling at the fovea. It can be seen that the cause
of the problems comes from the fact that the number of samples
of the conventional LPT increases exponentially from the peripheral
to the fovea. Hence, when the transformed image is used
for matching, more consideration is given to the fovea than to the
other area of the image. To address these problems, we propose
a novel APT approach that yields robustness in registering images
that subjects to occlusion and alteration, while maintaining
sufficiently low computational cost during the transformation.
Projection Transform
As shown in Fig. 5(b) and (d), the result from adaptive
sampling is a series of sample bins arranged in the step-like
manner which do not show coordinate shifts for scaled and
rotated image as in LPT any longer. To maintain the advantages
of scale and rotation invariance in LPT, we use an innovative
projection transform method which projects the 2-D image
on the radius and angular coordinates, respectively. From the
two projections, we can accurately calculate the scale and
rotation parameters, for which the details will be elaborated in
Section III. For now we define the projection transform for the
APT transformed image.
Image Comparison
This work extends the use of image registration to the environment
where images contain occlusion or alteration. Hence,
it is important to be able to locate the area such changes take
place in the target image, which will be useful for many applications
such as medical image registration and scene change
detection. Using the advantages of APT, we propose a fast and
simple image comparison scheme that can effectively and automatically
locate the altered area or the area where the registered
image pair differs without scarifying additional computational
cost.
EXPERIMENTAL RESULTS
To evaluate the effectiveness of the proposed image registration
approach, we apply twelve different sets of test images.
In Section IV-A, we present the registration of images that are
rotated and scaled. We use five sets of test images in the experiment.
Different rotation and scale parameters are applied
to three sets of test images: squirrel, statue of liberty and bird
using Matlab. Another two sets of test images consisting of images
of objects: speed limit sign, and syrup bottle taken at different
locations and at different illuminations are also presented
in this section. In Section IV-B, we present the registration of
images that are subjected to occlusion and alteration. We use
seven sets of test images for the experiment. The first two sets
of test images: Dreese building and flower are rotated and scaled
using Matlab. Occlusions artificially generated using random
number are included in the test images. The next five sets of
test images are nonartificial including the medical images of the
human brain, and human lung taken before and after the medical
therapy, and occluded images of objects: cereal box, stop sign,
and OSU tower. To compare the performance of the proposed
approach, we repeat the experiments with the conventional LPT
based image registration approach (as proposed in [4]).
CONCLUSION
Although LPT has been widely used in many image processing
applications, it suffers from nonuniform sampling.
Hence, there are two major problems of the conventional LPT:
the high computational cost in the transformation process,
which comes from the oversampling at the fovea in the spatial
domain, and the bias matching, in which the matching
mechanism focuses only on the fovea or central area while
the peripheral area is given less consideration. Previous works
on image registration using the conventional LPT indicate
successful results in the ideal conditions as when registering
images with different orientations and scales. In reality, however,
occlusions and alterations between the two images need
to be taken into consideration. Inspired by this fact, this paper
presents a new image registration algorithm based on the novel
APT approach. By evenly and effectively sampling the image
in the Cartesian coordinates and using the innovative projection
transform to reduce the dimensions, the proposed APT yields
faster sampling than that of the conventional LPT and provides
more effective and unbias matching.