JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
COMPUTER ENGINEERING
IMAGE MOSAICING USING EUCLIDEAN WARPING
1 SONIYA
1, 2
HINGU,
2
ASST.PROF. NARENDRA .M.PATEL
Department of Computer Engineering, Birla Vishvakarma Vidyalaya,
CVM, V.V.Nagar
[email protected],[email protected]
ABSTRACT : Image Mosaicing is a technique of stitching series of images together to produce a single
panoramic image. The field of view (FOV) of the commercial camera is much smaller than that of humans.
Thus, large objects cannot be seen completely in one image. Mosaicing is a computer-vision-based approach to
attain high field of view without compromising the image quality. It is the process of generating a single, large,
integrated image by combining the visual clues from multiple images .Image mosaics are collection of
overlapping images together with coordinate transformations that relate the different image coordinate systems.
By applying the appropriate transformations via a warping operation and merging the overlapping regions of
warped images, it is possible to construct a single image covering the entire visible area of the scene. The
proposed algorithm for Image Mosaicing using Euclidean Warp and Bilinear Interpolation has been discussed.
The implementation aspect of the algorithm is discussed along with test results. The merits and demerits of the
algorithms have been analyzed. We have used our own image datasets for experimenting.
Key Words : Image Mosaicing, Manual Image Registration, Control Points, Transformation Matrix,
Bilinear
Interpolation, Euclidean Warping.
I. INTRODUCTION
Because the human brain mosaics the split images of
a large object that are automatically captured through
eyes. Each eye functions as a camera lens. But, it is
impossible to cover very large area with the help of
an eye than a pair of eyes. Keeping this in mind, one
can infer that two eyes capture the two split images
of a large object which are later mosaiced into a
single complete large image. Similarly, even in the
real world the concept of mosaicing is essential
because it may not be possible to capture a large
document with a given camera in a single exposure.
Image mosaics are collection of overlapping images
together with coordinate transformations that relate
the different image coordinate systems.
Mosaicing process comes under two main processes.
1) Image registration
2) Image stitching.
By applying the appropriate transformations via a
warping operation and merging the overlapping
regions of warped images, it is possible to construct a
single image covering the entire visible area of the
scene. This merged single image is the motivation for
the term “mosaic”. Image mosaicing can be done in a
variety of ways. There are many algorithms to do
image mosaicing. The algorithm does require
effective corner matching. Usually, the algorithms
differ in the Image registration process.
The proposed algorithm using “Euclidean Warp and
Bilinear Interpolation” is discussed. This is very
simple and works by using Euclidean warping, using
which the image registration parameters are extracted
[2]. Once the transformation matrix is formulated, the
nearest neighbor interpolation technique is used.
The basic goal of the program is to stitch a series of
flat images together to produce a continuous
panoramic image (a mosaic) [2]. The difficulty here
is that in order for the images to fit together some of
the images must be warped (transformed) to adjust
for the difference of perspective in the images. The
initial estimate of the transformation is usually very
imprecise and results in a very sloppy match between
two images.
II. REGISTRATION PROCESS
IMAGE registration is a classical problem
encountered in many image processing applications
where it is necessary to perform joint analysis of two
or more images of the same scene acquired by
different sensors, or images taken by the same sensor
but at different times[3]. Given two images, I1
(defined as a reference image) and I2 (defined as a
sensed image) to match the reference image, the goal
of image registration is to align the sensed image into
the coordinate system of the reference image and to
make corresponding coordinate points in the two
images fit the same geographical location. These
unregistered images may have relative translation,
rotation, and scale between them.
Image Registration method can be done in two ways:
1) Manual Image Registration
2) Automatic Image Registration
In, this paper we have used approach for manual
image registration. The overall registration process
carried out in the following steps:
Step 1) Feature detection: Unique Features such as
(closed-boundary regions, edges, contours, line
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JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
COMPUTER ENGINEERING
intersections, corners, etc.) are manually or,
preferably, automatically detected in the reference
image. For further processing, these features can be
represented by their point representatives (centers of
gravity, line endings, distinctive points), which are
called control points (CPs) in the literature [3].
Step 2) Feature matching: In this step, the
correspondence between the features detected in the
sensed image and those detected in the reference
image is established. Various feature descriptors and
similarity measures along with spatial relationships
among the features are used for that purpose[3].
Step 3) Transform model estimation: The type and
parameters of the so-called mapping functions,
aligning the sensed image with the reference image,
are estimated. The parameters of the mapping
functions are computed by means of the established
feature correspondence [3].
III. IMAGE MOSAICING USING EUCLIDEAN
WARP AND
BILINEAR INTERPOLATION
After observing the problem domain that is the
specifications of the area on which we are working,
as simulation of these basic fundamentals is essential
for thorough understanding of the algorithm[2]. We
chose Euclidean warp of transformation and Bilinear
Interpolation in estimating the missing values.
A. Euclidean image warp
In case of the image mosaicing, the images specified
need not to be necessary that they are aligned as per
the images provided. For this fact the proper
transformation is performed on each and every image
to make it properly aligned as per the first image.
Mainly in dealing with this kind of implementation of
algorithm, a common VECTOR is found out.So that
the multiplication of that vector with the image aligns
it perfectly. IMAGE WARPING is vector technique
used in these algorithms.
Warping is a pair of two-dimensional functions, u(x;
y) and v(x; y), which map a position (x; y) in one
image, where x denotes column number and y
denotes row number, to position (u; v) in another
image (see Figure 2.2) [10].
Figure 1: Notation used for image warping [9]
In mosaicing, the transformation between images is
often not known before hand. In this example, two
images are merged and we will estimate the
transformation by letting the user give points of
correspondence (also called control points or
landmarks etc.)[1] In each of the images. In order to
recover transformation warping parameters are
calculated.
Image warping is in essence a transformation that
changes the spatial configuration of an image. Using
this definition, a simple displacement of an image by
few pixels in the x-direction would be considered a
warp. The Euclidean warp is also called Euclidean
similarity transform involving four parameters as in
equation 1[2].
P = [s; α; tx; ty] ----------------------------------------- (1)
Where
s= Scaling Factor,
α= Rotation angle,
tx and ty The translation in x and y direction
respectively.
Now Let p = (x; y; 1) denote a position in the original
image, I and p0 = (x0; y0; 1) denote the corresponding
position in the warped image, I0 (both in
homogeneous coordinates). Looking at one pixel, we
can write a simple linear transformation, equation
2.Where T denotes the composite transformation
matrix [2].
p0 = T × p ------------------------ (2)
Instead of warping a single point we could warp the
whole image of n points, equation 3.this can be
expressed as follows [2]:
x1 x2………xn
y1 y2 ………yn
p=
1
1 ………1
.………… (3)
Due the discrete nature of raster images, one is in no
way ensured that each input pixel exactly maps to an
out pixel. Consequently backward warping is mostly
performed i.e. from the output image to the input
image. Since T is square and has full rank we can
easily compute the inverse transformation as in
equation 4[2].
P = T-1x PꞋ
---------------------------------- (4)
In mosaicing, the transformation between images is
often not known beforehand. Approximate estimation
of the transformation required between two images to
be merged is done. The estimated transformation is
done by providing the points of correspondence in
each of the images. In order to recover the
transformation we rearrange the warping equation 2
so that the warping parameter is the vector t in
equations 5 and 6[2].
PꞋ = Z x t………………… (5)
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COMPUTER ENGINEERING
x y 1 0 0
Xꞌ = y–x 0 1 0 x s.sinα
0 0 0 0 1
tx
1
s.cosα
YꞋ
ty
1
------------------------------ (6)
The warping parameters are now obtained by solving
the linear system equation 6. Therefore at least two
points are required for solving [2]. Therefore
matching points on each image is to be estimated.
B. Bilinear Interpolation Technique
Interpolation is defined as estimation of a missing
value by taking an average of known values at
neighboring points. The more adjacent pixels
included while interpolating, more accurate in
estimation. But this comes at the expense of
computational time. In bilinear interpolation, the
intensity at a point is determined from the weighted
sum of intensities at four pixels closest to it.
Therefore, given location (X,Y ) and assuming u is
the integer part of X and v is the integer part of Y ,
the intensity at (X,Y ) is estimated from the
intensities at (u, v), (u +1,v), (u, v +1), (u +1,v +1).
Bilinear interpolation includes best of both worlds; it
is accurate as well as fast. Hence, Bilinear
Interpolation is used here. For bilinear interpolation,
weighted average of two translated pixel values for
each output pixel value is used [1].
Some of the assumptions made are:
The camera conforms to the pinhole model camera.

The objects in the images are sufficiently far
away to be approximated by planar surfaces.

When defining the points of correspondence,
two corresponding points are selected in exactly the
same order in both images. If it is not accurately
matched then the output will get distorted [2].
IV. IMPLEMENTATION METHODOLOGY
A Modules of the System
The entire system basically comprises of modules to
execute the given algorithms. No further sub division
of these modules is possible. These are:
1)
Input Images.(may be more than 2).
2)
Selection of algorithm for processing.
3)
Output mosaiced image.
4)
Comparison of the results based on various
algorithms applied
B. Euclidian Warp and Bilinear Interpolation
Algorithm
The algorithm can be summarized in the following
steps [2].
1)
Load two input images (color/grayscale).
2)
Show input images and prompt for
correspondence.
3)
Choose two matching points in both the
images in the same order.

Manually select two control points to
established feature correspondence between two
images. When defining the points of correspondence,
two corresponding points are selected in exactly the
same order in both images. Failure to comply with
this assumption will result in unpredictable warping.
4) Estimate parameter vector t using Euclidean
Warping.
5) Construct the transformation matrix.
6) Warp incoming corners to determine the size of
the output image (in to out).

Using Transformation matrix we can
determine the warped (output) image size using
corner detection of the second image.
7) Do backwards transform (from out to in).

Backward warping is also performed for the
proper alignment of input and output pixels.
8) Re-sample pixel values with bilinear interpolation.

Interpolation is an estimate made for the
missing pixel by taking the average value of the
neighboring pixels.
9) Offset and copy original image into the warped
image.
10) Show the result.
V. CONCLUSION
We have concluded that the points of reference in
both the images, which help to identify similar points
in the chosen image, must be selected very carefully
with great accuracy. Any minor change in the
selection of those points will lead to distortion in the
output image.
In the extension of this method, we can implement a
technique which can do automatic image registration
by automatically detecting and selecting control
points in the reference image as well as in the sensed
image.
VI.
PERFORMANCE
RESULTS
AND
ANALYSIS
1.
Result of Euclidean warp and bilinear
interpolation (For two images in case of rotation)
Figure 2: (a) input image 1[2]
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COMPUTER ENGINEERING
Figure 7: control points are manually selected in first
two images.
Figure 3: (b) input image 2[2]
(c) Mosaic image
Figure 4: Resultant mosaic image
2. Result for mosaicing 3 images:
Figure 5: (a) input image 1
Figure 8: Mosaic image of two images
REFERENCES
[1] M. B. Stegmann, “Image Mosaicing Using
Euclidean Warping
and Bilinear interpolation
technique”, Informatics and Mathematical Modeling,
Technical University of Denmark Richard Petersens
Plads, Building 321, DK-2800 Kgs. Lyngby,
Denmark.
[2] A. R. Bhat, ShivaPrakash M. And Vinod
D.S.(2007) “Intensity Based Image Mosaicing”,
International Journal Of Education And Information
Technologies,(Issue 2, Volume 1, 2007).
[3] B. Zitova´*, J. Flusser,( 2003,August) “Image
registration methods: a survey”
Department of
Image Processing, Institute of Information Theory
and Automation, Academy of Sciences of the Czech
Republic.
[4] Richard Szeliski Image Alignment and Stitching:
A Tutorial Foundationsand Trends in Computer
Graphics and Vision Vol. 2, No 1 (2006)pages 1104
[5] Getian Ye Image Registration and Superresolution Mosaicing Doctoral thesis School of
Information Technology and Electrical Engineering,
Australian Defence Force Academy University
College, The University of New South Wales
September 2005
[6] Mikkel B Stegmann, (October 2001), Image
Warping Informatics and Mathematical Modelling,
Technical University of Denmark, DTU
[7] Soo-Hyun Cho, Yun-koo Chung, Jae Yeon Lee,
Automatic
Image Mosaic System Using Image
Feature Detection a nd Taylor Series Proceeding
VIIth Digital Image Computing: Techniques and
Application Sun C., Talbot H., Ourselin S. and
Adriaansen T. (Eds.), 10-12 Dec. 2003.
Figure 6: (b) Input image 2
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