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A Robust, Feature-based Algorithm for Aerial

Image Registration

Mohamed S. Yasein

Department of Electrical and Computer Engineering,

University of Victoria

Victoria, B.C., Canada, V8W 3P6

Email: [email protected]

Pan Agathoklis

Department of Electrical and Computer Engineering,

University of Victoria

Victoria, B.C., Canada, V8W 3P6

Email: [email protected]

Abstract— In this paper an algorithm for aerial image reg-istration is proposed. The objective of this algorithm is toregister aerial images having only partial overlap, which are alsogeometrically distorted due to the different sensing conditions andin addition they may be contaminated with noise, may be blurred,etc. The geometric distortions considered in the registrationprocess are rotation, translation and scaling. The proposedalgorithm consists of three main steps: feature point extractionusing a feature point extractor based on scale-interaction of Mexican-hat wavelets, obtaining the correspondence between thefeature points of the first (reference) and the second image basedon Zernike moments of neighborhoods centered on the featurepoints, and estimating the transformation parameters betweenthe first and the second images using an iterative weighted leastsquares algorithm. Experimental results illustrate the accuracy of image registration for images with partial overlap in the presenceof additional image distortions, such as noise contamination andimage blurring.

I. INTRODUCTION

Image registration has found applications in numerous real-

life applications such as remote sensing, medical image analy-sis, computer vision and pattern recognition [1]. Given two, or

more, images to be registered, image registration estimates the

parameters of the geometric transformation model that maps

a given image to the reference one.

Many image registration techniques have been proposed in

the literature. In general, existing image registration techniques

can be categorized into two classes. The first class utilizes im-

age intensity to estimate the parameters of the transformation

between two images using an approach involving all pixels of

the image, such as [2], [3]. On the other hand, the second class

extracts a set of feature points from the image and uses only

these points to obtain the parameters of the transformation,

such as [4], instead of using all pixels. Extensive surveys of image registration techniques can be found in [1], [5].

One of the applications of image registration is in remote

sensing where several aerial images are being used to obtain

coverage of a region. These individual images usually do

not cover the same area and may be sensed under different

conditions. A typical situation is when images have only

partial overlap and because of different sensing conditions,

they appear distorted. Further, due to environmental condi-

tions, some of them may be noisy or they may not be well

focused. The registration of such images has been extensively

considered in the literature due to the potential applications.

Earlier techniques used manual markers or GPS locations

for registration. Recently, techniques have been developed

for automatic registration of aerial images. Some of these

techniques rely on image contours, such as [6], [7], [8], others

rely on feature points of the image , such as [9], and othersrely on lines and feature points of the image, such as [10]. The

performance of such techniques depends on several factors,

such as the area of overlap between images and to what extent

it is possible to model the different orientation between images

with simple geometric transformations. Further, image quality,

affected by distortions such as noise contamination and blur-

ring, as well as, image characteristics such as smooth/textured

areas or similarity of different areas, play also a role in the

techniques’ performance.

Feature point-based techniques rely on locating feature

points in both images and using these feature points to obtain

the transformation parameters for registering the two images.

They tend to give good results, but their performance dependson the accuracy of the feature point extractor. In order to

improve the performance, robust estimation techniques have

been used in [9], [10], [11].

In this paper, an algorithm for aerial image registration is

proposed. The main objective of the proposed algorithm is

accurately registering aerial images, which are distorted due

to different sensing conditions. The images may have partial

overlap and are further geometrically distorted. The possible

geometric distortions considered are rotation, scaling and

translation. The algorithm proposed here is an extension of the

one presented in [12] and can deal with images having partial

overlap using an adaptive weighted least squares technique.

The proposed algorithm involves three stages: feature pointextraction, obtaining the correspondence between the feature

points of the two images, and transformation parameters

estimation. An enhanced efficient feature point extractor that is

based on scale-interaction of Mexican-hat wavelets [13], [12]

is utilized to extract two sets of feature points from the first and

the second images respectively. The correspondence between

these two sets of points is evaluated using Zernike moments

invariants of circular neighborhoods that are centered on the

feature points. Zernike moments have proved to be superior in

17311-4244-0755-9/07/$20.00 '2007 IEEE



terms of information redundancy, low sensitivity to noise [14],

and their rotation invariance property [15]. The transformation

parameters are estimated using an adaptive weighted least

squares technique with an objective function that depends

on the weighted difference between the locations of a set of

feature points in the first image and another set in the second

image. Experimental results show that the proposed algorithm

leads to accurate registration and robustness against several

distortions types, e.g., image blurring and noise contamination.

The paper is organized as follows. Section II describes

the proposed registration algorithm in detail. In Section III,

experimental results are presented and the performance of

the proposed algorithm is discussed. Finally, conclusions are

drawn in Section IV.

I I . THE PROPOSED REGISTRATION ALGORITHM

A geometric distortion of an image can take many forms,

from relatively simple transformations to complex geometric

distortions. The types of distortions considered here are ro-

tation, translation, and scaling (RTS) transformations. Suchtransformations are rigid in the sense that shapes and angles

are preserved. A combined transformation of these types

typically has four parameters: translation parameters in

and¡

directions (¢ £

and¢ ¥

respectively ), rotation angle¦

,

and scaling parameter § . This transformation maps a point¨ © ! of the first image

#to a point ¨ $ © $

$

! of

the transformed image #

$ as follows:

¨

$

©

f ¨ 0 ! © 4

¢£

¢¥

! 7

§ 9

¦

! ¨ (1)

where f is the transformation function, 0 © C

¢ £ ¢ ¥ ¦ § H is the

transformation parameters vector, 4 and 9 represent transla-

tion and rotation operations respectively, and#

¨ ! represents

a pixel value at location¨ ©

!

.The problem of image registration is to estimate the trans-

formation parameters in the above equation using the first and

the second images. The images may be further distorted, for

example, by noise contamination or the two images may have

only partial overlap between them. The approach used in this

paper is based on estimating the transformation parameters

using an adaptive weighted least squares technique with an

objective function that depends on the weighted difference

between the locations of a set of feature points in the first

image # and another set in the second image #

$ . In order

to obtain the transformation parameters, three main steps are

performed in the proposed algorithm: feature extraction, find-

ing correspondence between feature points, and transformationparameters estimation. Typically, the feature extraction process

and obtaining the correspondence between feature points are

carried out on gray scale images or the luminance component

of color images.

A. Feature Point Extraction

A set of feature points are extracted from the image using

an enhanced efficient feature point extractor that is based on

scale-interaction of Mexican-hat wavelets [13], [12]. This step

involves two stages. In the first stage, the response of the image

to a feature detection operation is obtained and in the second

stage, the feature points are localized by finding the local

maxima in the response. Obtaining the responseS

¨

§

§

!

in the first stage can be represented as

S

¨

§

§

! © T V ¨

§

! X V ¨

§

! T (2)

whereV ¨

§ `

! ©

#

¨ ! b b e f ¨

§ `

!

denotes the 2-D convolution of the image#

with the Mex-

ican hat wavelet and #

¨ ! represents the intensity of the

image at location ¨ © P D ! . In the spatial domain, the

Mexican hat wavelet can be expressed as

e fa h ¨

§`

! © r

t

u v

X

7

t

y

f

(4)

where t

©

v

,§

` is the scale of the function, and are the vertical and horizontal coordinates respectively.

The second stage localizes the feature points of the imageby finding the local maxima of the responseS

. A local

maximum of S is a point with maximum value in a disk-

shaped neighborhood of radius

. An example showing the

process of feature point extraction from an image is illustrated

in Fig. 1.

(a) (b)

(c) (d)

Fig. 1. Feature point extraction process: (a) The feature points superimposedon the input image, (b) Response of applying Mexican hat wavelet with scale

, (c) Response of applying Mexican hat wavelet with scale , (d) Absolutedifference of the two responses and the locations of the obtained local maxima.

B. Correspondence between Points

Applying the feature extraction process on the first and the

second images results in two sets of feature points,

and

$ respectively. The number of the feature points in the first

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image is and the corresponding number of the second image

is

$ . The objective of this step is to pair feature points of

the first image with the corresponding ones of the second

image. This is done using circular neighborhoods of radius

centered on each feature point

in the first image and each

point

$

in the second image. The similarity measure used is

based on computing Zernike moments-based descriptors [14]

using these circular neighborhoods. One important feature of

the magnitude of the complex Zernike moments is that they

are rotational invariant [16] and this is the reason for using

circular neighborhoods. If the image (or regions of interest,

i.e., the circular neighborhoods) is rotated by an angle S , then

the Zernike moment

of the rotated image can be obtained

as

$

©

f

(5)

Thus, the magnitudes of the Zernike moments can be used as

rotationally invariant image features. Translation invariance is

achieved by taking the locations of the image feature points

as the centers of the neighborhoods.

The correspondence between feature points in the two

images is obtained using the following algorithm:

1) For each point of

and

$ in images#

and#

$ ,

respectively, take a circular neighborhood of radius

and construct a descriptor vector

[15] as

© T

j T m m m T

j

T m m m T

n j nT ! (6)

where T

j

T is the magnitude of Zernike moment of

a non-negative integer order

,

X T T is even, andT T

. When computing the Zernike moments of a

circular neighborhood located around a feature point, the

feature point is taken as the origin and the coordinates

of each pixel inside the neighborhood are mapped to the

range inside a unit circle, i.e.,

7

(

r

. Zernike

moments of order

are given by

©

7

r

!

z

£

z

£

{ }

¦

!

! (7)

where

©

7

¦

©

!

and

! represents the intensity at a pixel inside

the circular neighborhood. In the above equation,{

}

denotes the complex conjugate of the Zernike polyno-mial of order and repetition which can be defined

as

{

¦

! ©

9

! f

(8)

where9

! is a real-valued radial polynomial defined

as

9

! ©

n

X

r

!

X

§

!

§

(9)

where

©

r

v

m m m ; T T

; and

X T T is

even. While higher order moments contain information

about fine details in the image, they are more sensitive

to noise than lower order moments [14]. Therefore, the

highest moment order used in the descriptor vector

(r

in the algorithm) is chosen to achieve a compromise

between noise sensitivity and the information content of

the moments.

2) Construct the distance matrix

, where each entry

of this matrix is given by

©

X

$

!

©

`

T

! X

$

! T (10)

where

! and

$

! are the entries of

and

$

, respectively,

©

r

v

m m m

and

©

r

v

m m m

$ .

In other words, each entry represents the

X

of the difference between the two descriptor vectors of

the feature points

and

$

in the first and the secondimages, respectively. In the distance matrix , find the

minimum distance coefficients along rows and along

columns. A correspondence between two points and

$

is established if, and only if, the minimum distance

coefficient in a row is also the minimum distance coef-

ficient in the associated column of

. This results in

paired points, where

ª

$ ! .

C. Transformation Parameters Estimation

The transformation parameters, required to transform the

distorted image to its appropriate size, orientation and position,

will be estimated by solving an iterative weighted least squares

minimization problem where the objective function depends on

the distance between the feature point pairs in the two images.

The objective function is defined in terms of the

X

of

the weighted errors

®

0 ! ©

±

f

$

0 ! X

! !

©

z

²

³

´

´

´

f

$

0 ! X

´

´

´

(11)

where ± © C

³

m m m

³

m m m

³

z

²

H ,³

is the weight associated

with the distance between the feature points pairs

and

$

) and0 © C

¢£

¢¥

¦ § H

is a vector of the transformationparameters. The transformation parameters can be obtained

then by solving the optimization problem

ª

·

®

0 ! (12)

The solution of this optimization problem would give the

correct transformation parameters provided that the correspon-

dence obtained in the previous sub-section is correct for all

feature points pairs. This will not be the case if, for example,

the two images have only partial overlap between them. It

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(a)

(b)

(c)

Example 1 (d) Example 2

Fig. 2. Examples of registering aerial images: (a) First images, (b) Second images, (c) Correspondence between the feature points of the first images,represented by crosses, and the feature points of transformed distorted images, represented by squares , and (d) The transformed distorted images are overlaidon the corresponding reference images

1735



between images, in the presence of additional distortions, such

as image blurring and noise contamination. Results indicate

that the use of the iterative weighted lease squares algorithm

is very effective in eliminating feature points that have false

correspondence and that the proposed algorithm leads to an

accurate estimation of the transformation parameters.

ACKNOWLEDGMENT

This work has been supported by the Natural Sciences and

Engineering Research Council of Canada (NSERC).

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