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Image Magnification based on directed linear interpolation

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Image Magnification based on Directed Linear Interpolation
T. Romen Singh
1
, O. Imocha Singh
1
, Kh. Manglem Singh
2
, Th. Rupachandra Singh
1
and Tejmani Sinam
1
1
Department of Computer Science, Manipur University, Canchipur, India
2
DOEACC Centre, Imphal, Manipur, India.
Abstract
The technology of computer graphics and digital cameras
are prevalent. High-resolution display and printer are
available. High-resolution images are needed in order to
produce high quality display images and high quality prints
for use in desktop publishing, large artistic printing, mobile
phone etc. However, since high-resolution images are not
usually provided, there is a need to magnify the original
images. This paper proposes an algorithm for image
magnification by linear interpolation, which is better than
some of the prevalent methods such as pixel replication,
bilinear interpolation and bicubic interpolation. The
proposed algorithm uses linear interpolation method to
magnify pixels that lie in the perimeter, whereas it uses
directed bilinear interpolation method to magnify the
interior region inside the magnified blocks. Determination
of the right direction for interpolation is the key for
achieving better performance of the proposed algorithm.
1. Introduction
Image magnification is a process of obtaining an image at
resolution higher than taken from the image sensor. Image
magnification synonyms are interpolation, enlargement,
zooming, etc. Until now, a large number of interpolation
techniques for magnifying images have been proposed. The
simplest method to magnify images is the pixel replication,
where the color of the nearest pixel of the original image is
replicated, resulting the magnified images with aliasing
effect in the form of jagged edges to the new image. The
color of the pixel in the nearest neighbor method is the
color of the nearest pixel in the image [1]. Most editing
software uses nearest neighbor method. It increases the
visibility of jaggies in the magnified images, however it
does not introduce aliasing effect. Bilinear Interpolation
determines the value of a new pixel based on a weighted
average of the 4 pixels in the nearest 2 × 2 neighborhood of
the pixel in the original image [1]. It gives less jaggies with
relatively smooth edges and the weighted average has an
antialiasing effect. Bicubic interpolation method is
commonly used by editing software, printer drivers and
many digital cameras for resampling images. It is more
sophisticated and produces smoother edges than bilinear
interpolation method. A new image magnification
technique is bicubic function that uses sixteen pixels in the
nearest 4 × 4 neighboring pixels in the original image [1,2].
Other methods such as B-spline interpolators [3,4] and the
cubic convolution methods [5] have also been proposed.
However, these methods tend to blur the edges and cause
them to be jagged.
Allebach and Wong [6] proposed a method that searches for
edges in the image so that the interpolation does not cross
them. The main difficulty is to find out the important edges.
Other edge-adaptive methods have been proposed by
Jensen and Anastassious [7], Li and Orchard [8] and
Muresan and Parks [9]. The methods presented in [8] and
[9] are the most widely used known edge-adaptive methods.
They can avoid jagged edges, but these methods introduce
visible artifacts in the magnified images. Yu et. al proposed
triangulation method [10], however this method fails to
give curved edges specially at large scaling factor. Morse
and Schwartzwald [11] proposed a level-set reconstruction
method to solve the problem of jagged edges. This method
does not overcome the problem of blurring effect in the
bicubic interpolation method. Hertzmann et al [12] and
Freeman et al [13] proposed methods that learn the
correspondences between low and high resolution images
from a set of training data. The main drawback of these
methods is that they fail if the input image is different from
the training data and the computational cost is also very
high. Malgouyres and Guichard [14] proposed variation
based approach for image magnification. Their method
gives better-magnified images than the bicubic interpolation
method, but the computational cost is very high. Johan and
Nishita proposed progressive refinement approach for
image magnification. Their method gives sharp magnified
image without generating distinct artifacts, however it
produces sometimes jaggies in the magnified images.
Muneeb et al [16] proposed an adaptive approach for image
magnification, which produces a high quality magnified
image while preserving the content of the original image.
Their method has some defect.
The main contribution of this paper is to produce a
magnified image that produces high visual quality of the
original image with linear interpolation, which is very
simple as compared with other techniques such as bilinear,
bicubic, B-spline etc. The basic idea of the proposed
technique is to select the direction of linear interpolation
method based on the 2×2 pixel values, and then the
interpolator assigns proper intensity values to the
undefined pixels along the directed line.
The paper is organized as follows. Section 2 is on the proposed
algorithm., Section 3 explains various methods of interpolation.
Section 4 gives experimental results followed by Section 5 on
conclusions.
2.
Proposed Algorithm
Intensity surface can be viewed as a landscape with hills
and hollows, rides and valleys and curve surfaces. Any
NCC 2009, January 16-18, IIT Guwahati 367
three-dimensional (3-D) surface, with some approximation
can be created from directed linear interpolation like the
triangular plane, which is very similar with the triangular
based image magnification, square plane and twisted curve
surface based on the pixel intensities of 2×2 block. Look at
the image intensity as 3-D surface built from directed linear
interpolation, where vertices are image pixels with intensity
along z-axis as shown in Fig. 1.
To magnify an image, new image must be complemented
with new pixels, added necessary columns and rows of
pixels, and calculated new pixels intensity. In this work
assumption is made that new pixels intensity is situated on
suitable line along the diagonals, horizontal, or vertical
according to the direction chosen. During image
magnification, edges are blurred because of reduction in
slope sharpness. This is the main problem for all known
magnification methods. So edges must be located at
distinctive points on intensity surface for different
magnification algorithm applied. There are two things that
must be solved: choose the best arrangement of the pixel by
selecting the right direction of interpolation and interpolate
the new pixel intensity.
This proposed system called as directed linear interpolation
(DLI) proceeds in three phases for magnification of the
original image.
Phase I:
The image of M×N size is divided into many non-
overlapping and square blocks of equal dimension, each of
2×2 size. We consider one block at a time for magnification
of the original image and pixel values from a block are
assigned as corner pixel values in the magnified block as
shown in Fig. 2(a). The coordinates (x, y) of pixels in the
magnified image in the term of top-left pixel coordinates
(i,j) in the square block of unmagnified image and
magnified block of p×p size, where p is the magnification
factor is given by Eq. (1) below.
( 1)
( 1)
x p i m
y p j n
= − +
 
 
= − +
 
(1)
where (m, n) is the coordinates of pixel in the magnified
block such that m=1, 2,…, p and n=1,2,…, p.
The size of the magnified image is (pM p + 1) × (pNp +
1), short by (p 1)×(p – 1) size from pM×pN size, the
apparent size of the magnified image.
After assigning pixel values at the four corners that are top-
left, top-right, bottom-left and bottom-right locations in the
magnified blocks with the respective pixel values from the
unmagnified block of the original image, the unfilled
perimeter pixel values of the square block are interpolated
linearly using the filled corner pixel values as shown in
Fig.2(b) by using Eq. (2).
( )( ( ,
1 2 1) ( , )
1 1
1 1 1 2 1
( )( ( ,
1 2 2) ( , )
1 2
2 1 2 2 1
( )( ( ,
1 1 2) ( , )
1 1
1 1 1 2 1
(
2 2 1
( , ) ( , ) for left edge
( , ) ( , ) for right edge
( , ) ( , ) for top edge
( , ) ( , )
x x I x y I x y
x x
x x I x y I x y
x x
y y I x y I x y
y y
y
I x y I x y
I x y I x y
I x y I x y
I x y I x y
= +
= +
= +
= +
)( ( ,
1 2 2) ( , )
2 1
2 1
for bottom edge
y I x y I x y
y y
(2)
where
1 1 1 2 2 1 2 2
I x y I x y I x y I x y
are the
pixel values at top-left, top-right, bottom-left and bottom-
right corners respectively of the magnified blocks.
Phase II:
In this phase, interpolation direction is determined. Detail is
discussed in the next sub-section.
Phase III:
In this phase, interpolation is performed along the
determined direction to fill up the unfilled inner pixel
values of the square block other than the perimeter, which
is filled during Phase I. The possible directions are along
left diagonal, right diagonal, horizontal or vertical direction.
More detail is discussed in the next section. After
completely filling up of all the pixel values of the square
block, then comes to the next
2 2
×
block of the original
image for next mapping to the magnified image. The
processing from Phase I to Phase III is repeated until the
last block of the original image is processed.
The proposed algorithm can be applied the proposed
algorithm both in gray-scale and color images. In the case
of color images, the process is performed for each color
channel separately.
2.1 Determination of interpolation direction
The selection of right interpolation direction will result the
high quality magnified images. To determine the direction,
the absolutes of the diagonal pixel differences of two
diagonals are used. In Fig.2 white small square marks are
new pixel values that are inserted to magnify the image
while gray-circled marks are the original pixel value. The
unfilled intensity of the new pixels is calculated from the
four original pixel values at the corners of the magnified
block by interpolating along the suitable direction linearly.
There will be two cases to determine directions of
interpolation.
Case I
Unequal absolute diagonal intensity differences: If
the absolute differences of the diagonal pixel intensities are
not equal, and there is no two pixels having same intensity
in the 2×2 block, either along horizontal or vertical line
with the nearest intensity outside the 2×2 block, along the
line, the direction of the linear interpolation is along the
diagonal having less intensity difference. Otherwise it will
Fig 1: Image intensity surface.
NCC 2009, January 16-18, IIT Guwahati 368
be along vertical/horizontal direction. Its possible states are
shown in the Fig.8 and Fig.9.
All possible states of vertical and horizontal edges that have
equal intensity with the adjacent blocks are shown in Fig. 8.
To identify whether any three pixel intensities are equal or
not, we can take standard deviation of the three pixel
intensities. If the standard deviation is 0, it can be
concluded that the three pixels are of same intensity value.
We can check for presence of edge within the 2×2 pixel
block by taking standard deviation of the relevant
consecutive three pixels along vertical and horizontal
directions with other pixels other than the pixels in the 2×2
block, or within the 2×2 block itself. Fig 9 shows the
presence of three equal intensity pixels within the 2×2
block. In this case, interpolation is along diagonal and it is
considered even for three pixels along vertical or horizontal
having the same intensity. The method of interpolation is
shown in Fig.3 and Fig.4 according to the determined
direction. Diagonal directed interpolation gives two
triangular planes joining at the selected diagonal, where
vertical and horizontal directed interpolations give either
square plane or twisted curve.
Case II
Equal absolute differences:
In this case, the equal
absolute differences condition is considered and all possible
conditions are shown in Fig.5. We can consider two sub-
conditions here such as:
(a) Equal absolute differences and average diagonal pixel
values (Fig. 5(a)): The interpolation technique will be linear
along horizontal/vertical direction by using either Eq. (3) or
(4), resulting a square plane surface, being four diagonal
pixels as vertices. Its surface looks like roof as shown in
Fig. 4(a).
(b) Equal absolute differences, but different average
diagonal pixel values: This condition is shown in Fig.5(b).
If the averages of the diagonal pixels are not equal, it is
further required to determine the direction of interpolation.
It may be along vertical/horizontal or diagonal direction. It
is not sufficient to determine the direction by the current
concerned block C shown in Fig.6(a). Neighboring blocks
such as T (top), R (right) and B (bottom) are required to
support the determination of interpolation direction. Their
individual direction is determined and if one of the three
blocks gives the direction, then the interpolation takes place
along the determined direction, say right diagonal direction
in the Fig.6(b). If it still fails to determine the direction
even with the help of the three blocks, its direction should
be same as condition I, that is, linear along
vertical/horizontal resulting a twisted curve surface, which
is shown in Fig. 4(b).
Fig. 2: 2×2 pixel mapped to magnified image
(a). 6x6 mapped square block
1 1
( , )
x y
2 2
( , )
x y
1 2
( , )
x y
2 1
( , )
x y
2x2
(b). 6x6 perimeter filled square block
1 1
( , )
x y
2 2
( , )
x y
1 2
( , )
x y
2 1
( , )
x y
(i,j)
(a)
I(x
1
,y
1
)
I(x
1
,y
2
)
I(x
2
,y
1
)
I(x
2
,y
2
)
2x2 pixel
(b)
Fig.3: Diagonal interpolation –
(a) Left linear diagonal interpolation
and (b) Right linear diagonal interpolation.
Fig.4.: Linear interpolation –
(a) Linear plane surface (b) Linear
twisted curved surface
f
(i,j)
f
(i,j+1)
f
(i+1,j
)
f
(I+1,j+1)
I
(x1,y1)
I
(x1,y2)
I
(x2,y1)
I
(x2,y2)
I
(x1,y1)
I
(x1,y2)
I
(x2,y1)
I
(x2,y2)
f
(i,j)
f
(i,j+1)
f
(i+1,j
)
f
(I+1,j+1)
(a) 4x4 magnified square plane surface
(b) 4x4 magnified square twisted surface
(a) Equal absolute difference and average
diagonal pixels
Fig. 5: Equal absolute diagonal pixel differences
(b) Equal absolute difference but
unequal average diagonal pixels
Fig.6: Direction determination: (a) 2x2 pixel block
C
with
neighboring pixels (b) Interpolated along right diagonal.
(a) (b)
(a) (b)
Fig.7: Diagonal interpolation. (a). Right diagonal directional
interpolation. (b). Left diagonal directional interpolation.
NCC 2009, January 16-18, IIT Guwahati 369
3. Methods of interpolation
3.1 Boundary interpolation:
Magnification is done by taking blocks sequentially from
the original image. The four pixel values from a block are
assigned to the magnified block as shown in Fig.2(a). The
unfilled pixels along the perimeter of the square block in
the magnified image are filled by interpolating between two
corresponding intensities at the vertices of the coordinates
from (x
1
, y
1
), (x
2
, y
1
), (x
1
, y
2
) and (x
2
, y
2
) by using Eq. (2).
3.2. Inner pixels interpolation
3.2.1 Vertical/Horizontal linear interpolation
In Phase II,
C
ase II, Condition (a), unfilled pixels are filled
by interpolating linearly by using Eq. (3) or Eq. (4) along
horizontal/vertical direction as follows.
1 2 2 1
2 1
( , ) ( ) ( , )( )
( , ) ( )
I x y y y I x y y y
I x y y y
− +
=
(3)
1 2 2 1
2 1
( , ) ( ) ( , ) ( )
( , ) ( )
I x y x x I x y x x
I x y x x
− +
=
(4)
3.2.2. Diagonal directed interpolation
In diagonal direction interpolation, there are a pair of
equations for the upper and lower triangular regions of the
square block. Each triangular region is filled separately
during filling up of unfilled pixels diagonally. Direction
may be either left or right direction as shown in Fig.7.
Equations for right diagonal interpolation are given below:
1 1 1
1
1
( ( , ) ( , ))( )
( , ) ( , )
I x q I p y y y
I x y I p y p x
− −
= +
1 1 1 1
1
( , )( ) ( , )( )
I p y x x I x q y y
p x
− +
=
(5)
where p= x+y-y
1
and q= x+y-x
1
for x
1
+y-x
1
y
2
2 2 2
2
2
( ( , ) ( , ))( )
( , ) ( , )
I x q I p y y y
I x y I p y x p
− −
= +
2 2 2 2
2
( , )( ) ( , )( )
I p y x x I x q y y
x p
− +
=
(6)
where
p= x+y-y
2
and q =x+y-x
2
for x+y-x
1
> y
2
Equations for left diagonal interpolation are given below:
2 1 1
1
2
( ( , ) ( , ))( )
( , ) ( , )
I x q I p y y y
I x y I p y x p
− −
= +
1 2 2 1
2
( , )( ) ( , )( )
I p y x x I x q y y
x p
− +
=
(7)
where p= x-y+y
1
and q= x
2
-x+y for x
2
+y-x
y
2
2
1
( ( 1, ) ( , 2))( )
( , ) ( , 2)
I x q I p y y y
I x y I p y p x
− −
= +
2 1 1 2
1
( , )( ) ( , )( )
I p y x x I x q y y
p x
− +
=
(8)
where p= x+y+y
2
and q= x
1
-x+y for x
2
+y-x>y
2
(a) Right diagonal direction:
In Right diagonal direction, unfilled pixels can be
interpolated by using Eqs. (5) and (6). Eq (5) is for upper
triangular region and Eq. (6) is for lower triangular region.
It is also shown in Fig.3(b) and Fig. 7(a).
(b) Left diagonal direction
Here in this case, it is almost similar to right diagonal
direction and the only difference is its direction. It can be
interpolated using Eqs. (7) and (8) for the upper and lower
triangular region. Fig.3(a) and Fig.7(b) show the way of
interpolation.
4. Experimental Results
Proposed Interpolation technique was tested and compared
with several common magnification techniques like Pixel
Replication (PR), Bilinear Interpolation (BL), and Bicubic
Interpolation (BC). Qualitative analysis provides a set of
image comparisons to the readers for visual analysis. A
quantitative analysis is done by utilizing root mean squared
error (RMSE), peak-signal-to-noise-ratio (PSNR) in dB,
cross-correlation coefficient (CCC) and. These are given in
Eqs. (9), (10) and (11).
2
1
1 1
( ( , ) ( , ))
M N
M N
i j
R M S E F i j I i j
= =
= −
∑ ∑
(9)
2
1
1 0 g 1 0P S N R lo
R M S E
 
=
 
 
(10)
1 1
2 2 2
1 1 1 1
( , ) ( , )
( , ) ( , )
M N
i j
M N M N
i j i j
I i j F i j MNab
CCC
I i j MNa F i j MNb
= =
= = = =
 
 
 
 
=
 
 
− −
 
 
∑ ∑∑
(11)
where I is the magnified image, F is the original image, M
and N
are the image dimension, a and b are the
corresponding average pixel values in each image.
Fig.8: Unequal pixel difference, but horizontal/vertical edge presence
states of concerned 2x2 ma
rked block. (a) & (c) are left and right
vertical edge where (b) & (d) are top and bottom horizontal edge
presence state .
Fig.9: Unequal diagonal pixel difference and no horizontal/vertical
edge presence stat
es of concerned 2x2 marked block. (a) No edge
presence right directed. (b) Right directed diagonal edge presence
state. (c) Left directed, one pixel contrast (d No edge presence right
directed . They will be interpolated along diagonal direction.
NCC 2009, January 16-18, IIT Guwahati 370
Three different quantitative analysis measurements were
used on ten images such as camera stand (CS) of 41×36,
Arial view (AV) of 72×55, Lena (LN) of 100×100, Lena
eye (LE) of 61×47, Flower (FL) of 348×376, Mandrill (CP)
of 295×297, Rose (RS) of 132×135, Human eye (HE) of
110×44, Veronam (VM) of 242×141 and Moon (MN) of
267×471 size respectively.
Table 1 gives numerical results in PSNR (dB) on various
images under consideration for comparison of different
techniques. It was found from Table 1 that the values of
PSNR of the proposed algorithm were the largest. Fig. 10
shows the comparison of the proposed algorithm for a
magnification factor p = 4. The result of the proposed
algorithm contains no jag at all and it gives very smooth
regions, where there are no edge.
5. Conclusions
The paper proposes a new technique for image
magnification. The experimental results show the
effectiveness of the algorithm in comparison with pixel
replication, bilinear and bicubic interpolation methods.
Conventional linear interpolation is used to magnify the
pixels that lie at the perimeter of the square block of the
magnified blocks and directed bilinear interpolation is used
to magnify pixels for the pixels in the interior region of the
magnified blocks. Magnification direction is decided for
horizontal, vertical and diagonal directions and it even
considers pixels from adjacent blocks when necessary.
Determination of the right direction for interpolation is
critical for achieving better performance of the proposed
algorithm.
PSNR
Algorithms
Images
PR BL BC DLI
CS 19.9023 21.115 21.743 24.2505
AV 18.5428 20.809 21.54 23.8827
LN 22.2941 24.748 25.692 27.6253
LE 19.6902 22.384 22.819 24.8637
FL 42.7779 33.706 33.739 48.7289
CP 31.0924 33.548 34.576 39.2707
RS 24.4595 27.19 28.315 29.2844
HE 15.8697 18.572 18.723 18.7702
VM 20.6525 22.901 23.714 23.7745
MN 29.9477 35.579 37.741 37.289
References
[1] ‘Digital Photography Review’ http://www.dpreview.com/
[2] Adobe Photoshop. Adobe Systems.
[3] K. Jensen and D. Anastassiou. Subpixel edge localization and
the interpolation of still images. IEEE Transactions on Image
Processing, 4(3):285–295, 1995.
[4] S. W. Lee and J. K. Paik. Image interpolation using adaptive
fast Bspline filtering. In Proceedings of IEEE International
Conference onAcoustics, Speech, and Signal Processing Vol. 5,
pages 177–179, 1993.
[5] R. Keys. Cubic convolution interpolation for digital image
processing. IEEE Transactions on Acoustics, Speech, Signal
Processing, 29(6):1153–1160, 1981.
[6] J. Allebach and P.W. Wong, Edge-directed interpolation, Proc.
IEEE ICIP, Vol. 3, pp. 707-710, 1996.
[6] V. Vyšniauskas. Triangle based Image Magnification.
Electronics and Electrical Engineering, ISSN 1392-1215- 2006.
Nr. 6(70) elektronika ir elektrotechnika
[7] K. Jenson and D. Anastassiou, Subpixel edge localization and
the interpolation of still images, IEEE Trans. on Image Processing,
4(3), pp. 285-295, 1995.
[8] X. Li and M.T. Orchard, New edge-directed interpolation,
IEEE Trans. on Image Processing, 10(10), pp. 1521-1527, 2001.
[9] D.D. Muresan and T.W. Parks, Aaptive quadratic (AQUA)
image interpolation, IEEE Trans. on Image Processing, 13(5), pp.
690-698, 2004.
[10] X. Yu, B.S. Morse, and T.W. Sederberg, Image
reconstruction using data-dependent triangulation, IEEE Computer
Graphics and Applications, 21(3), pp. 62-68, 2001.
[11] B.S. Morse and D. Schwatzwald, Image magnification using
level-set reconstruction, Proc. IEEE on Computer Vision, pp. 333-
341, 2001.
[12] A. Hertzmann, C.E. Jacobs, N. Oliver, B. Curless and D.H.
Salesin, Image Analysis, Proc. SIGGRAPH, pp. 327-340, 2001.
[13] W.T. Freeman, T.R. Jones, E.C. pasztor, Example based
superresolution, IEEE Computer Graphics and Applications,
22(2), pp. 56-65, 2002.
[14] F. Malgouyres and F. Guichard, Edge direction preserving
image zooming:A mathematical and numerical analysis, SIAM
Journal on Computer Analysis, 39(1), 1-37, 2001.
[15] H. Johan and T. Nishita, A progressive refinement approach
for image magnification, IEEE Proc. 12
th
Pacific Conference
Graphics and Applications, 1550-4085/04.
[16] Muneeb and N. Khattak, An edge preserving locally adaptive
antialiasing zooming algorithm with diffused interpolation, IEEE
Proc, CRN, Vol. 00, p. 49, F1 33189-23-24, March 2006.
Fig.10: Result comparison on the 4
×
Lena image: : (a) Original image,
(b), (c), (d) and (e) are results of PR, BL, BC and proposed method.
(a)
(b)
(c)
(d)
(e)
NCC 2009, January 16-18, IIT Guwahati 371
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