International Journal of Research In Science & Engineering
Volume: 1 Special Issue: 2
e-ISSN: 2394-8299
p-ISSN: 2394-8280
RECOVERING HDR IMAGE USING DISCRETE WAVELET
TRANSFOR
Swetha S 1 , Dr .Vivek Maik 2
Dept. of ECE, Oxford College of Engineering, [email protected]
2
Dept. of ECE, Oxford College of Engineering, [email protected]
________________________________________________________________________________________________
1
ABSTRACT
Recently visual representation using high dynamic range (HDR) images become increasingly popular with
advancement of technologies for increasing the dynamic range of image. HDR image is expected to be used in wide
ranging applications such as digital cinema, digital photography because of its high quality and its power full
expression capability. In this paper we represent a method of recovering high dynamic range image using discrete
wavelet transform (DWT) like Haar wavelet. The main objective is to enhance the dynamic range of the images
using wavelet theory. This is implemented using 2D-DWT technique.
Keywords—high dynamic range, wavelet, discrete wavelet transform,Haar wave let.
----------------------------------------------------------------------------------------------------------------------------- -------I.
INTRODUCTION
High dynamic range imaging is a branch of computational photography aiming at enlarging the range of intensities
represented in images between the smallest and the largest illumination value (also called dynamic range).dynamic
range in photography describes the ratio between the maximum and minimum measurable light intensities. For
recovering HDR image various methods have been used .In this paper we used a method to recover the HDR image by
making use of wavelet called discrete wavelet transform (DWT).
Wavelets have been used by quite frequently in image processing. Wavelet transform [12][13] is capable of
providing the time and frequency information simultaneously. The frequency and time information of a signal .But
sometimes we cannot know what spectral component exists at any given time instant. The best we can do is to
investigate that what spectral components exist at any given interval of time.
Higher frequencies are better resolved in time, and lower frequencies are better resolved in frequency. This means
that, a certain high frequency component can be located better in time (with less relative error) than a low frequency
component & low frequency component can be located better in frequency compared to high frequency component.
Wavelet transform technique is based on 2D-Discrete wavelet transform (2DDWT).A discrete wavelet transform
(DWT) is another wavelet transform for which the wavelets are discretely sampled for numerical analysis and
functional analysis. The advantage of DWT is, it captures both frequency and time information.
Discrete wavelet transform (DWT) decompose signals into sub-bands with smaller bandwidths and slower sample
rates namely Low-Low (LL), Low-High (LH), High-Low (HL), and High-High (HH). With this we get four sub-bands
from one level of transform – first low-pass sub-band having the coarse approximation of the source image called LL
sub-band, and three high pass sub-bands that exploit image details across different directions – HL for horizontal, LH
for vertical and
HH for diagonal details. After decompose these bands we can obtain high frequency components
using these sub bands. So it will help to enhance the images.
II. RELATED WORKS
We know that HDR images have a major inconvenience in application, that is, they cannot be displaye d correctly on
ordinary display devices such as printers or monitors. That is why tone mapping methods are proposed, which is related
to recovering HDR image methods mentioned in our paper. Tone mapping methods can be broadly classified by spatial
processing techniques into two categories: global and local methods [1]. For global methods, they usually compress the
dynamic range using gamma function, sigmoid function or histogram equalization. Each pixel is mapped based on
global image characteristics regardless of its spatial location in a bright or dark area. The global methods are easier to
implement and faster to perform. However, when the dynamic range of the scene is particularly high, these methods
tend to result in either graying out or losing visible details. For local method, different operations are applied to
different pixels. In this case, one input value can produce more than one output values, which depends on the pixel
value and the surrounding pixel’s values. The local methods can scale the image’s dynamic range to the output device’s
dynamic range while increasing the local contrast. However, they tend to produce ringing artifacts. Since the local
methods are capable of compressing quite large dynamic range and also modeling the local adaptation of the human
visual system, more emphasis is recently put on developing this type of metho d. A brief of the local method is given
below. Reinhard et al. [2] propose a tone mapping method for HDR rendering by modeling dodging and burning in
traditional photography. iCAM06 [3] is an image appearance model that has been extended to render HDR images fo r
displaying on common devices. Meylan et al. [4] propose a center/surround retinex model for displaying HDR images.
In that paper, the weights of surrounding pixels are computed with an adaptive filter, which
IJRISE| www.ijrise.org|[email protected][207-210]
International Journal of Research In Science & Engineering
Volume: 1 Special Issue: 2
e-ISSN: 2394-8299
p-ISSN: 2394-8280
can adjust the shape of the filter to the high contrast edges in images. In 2007 years, Meylan presents another
tone mapping method [5] that is derived from a model of retinal processing.
A method in gradient domain [6] is proposed by Fattal et al., by attenuating the magnitudes of large gradients, they
operate on the gradient field of an image. Durand et al.[7] use a bilateral filter to reduce the overall contrast while
preserving local details in an image. Here we have explored a simple technique to recover HDR image with discrete
wavelet transform like Haar wavelet discrete transform. The discrete wavelet transform technique section provides an
idea used in our paper, result section shows some examples and we end with our conclusion.
III. DISCRETE WAVELET TRANSFORM.
DWT (Discrete Wavelet Transform) is an application of subband coding [11]; thus, before introducing DWT, we
briefly describe the theory of subband coding.
A. Subband coding
In subband coding, the spectrum of the input is decomposed into a set of band limited components, which is called
subbands. Ideally, the subbands can be assembled back to reconstruct the original spectrum without any error. Fig ure. 1.
shows the block diagram of two-band filter bank. At first, the input signal will be filtered into lowpass and highpass
components through analysis filters. After filtering, the data amount of the lowpass and highpass components will
become twice that of the original signal; therefore, the lowpass and highpass components must be down sampled to
reduce the data quantity. At the receiver, the received data must be upsampled to approximate the original signal.
Finally, the upsampled signal passes the synthesis filters and is added to form the reconstructed approximation signal.
2
h0(n)
X(n)
2
Synthesis
Analysis
h1(n)
g0(n)
2
2
+
X’(n)
g1(n)
Figure .1.Two-band filter bank.
Now back to the discussion on the DWT. In two dimensional wavelet , transform, a two-dimensional scaling
function, 
 x, y  and three two-dimensional wavelet function  H  x, y  , V  x, y  and D  x, y 
are required.
Each is the product of a one-dimensional scaling function f(x) and corresponding wavelet function 
  x, y     x    y 
 H  x, y     x    y 
(1)
 V  x, y     x   x   D  x, y     x   x 
Where 
H
 x .
measures variations along columns (like horizontal edges),
V
responds to variations along rows (like
vertical edges), and  corresponds to variations along diagonals.
Similar to the one-dimensional discrete wavelet transform, the two-dimensional DWT can be implemented using
digital filters and samplers. With separable two-dimensional scaling and wavelet functions, we simply take the onedimensional DWT of the rows of f (x, y), followed by the one-dimensional DWT of the resulting columns. Fig.2.Shows
the block diagram of two-dimensional DWT.
D
Rows
Columns
hψ(-n)
hψ(-m)
2
WDψ(j,m,n)
hϕ(-m)
2
WVψ(j,m,n)
hψ(-m)
2
WHψ(j,m,n)
hϕ(-m)
2
WHϕ(j,m,n)
2
WΦ(j+1,m,n)
hϕ(-n)
2
Figure.2.The analysis filter bank of the two -dimensional DWT
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International Journal of Research In Science & Engineering
Volume: 1 Special Issue: 2
e-ISSN: 2394-8299
p-ISSN: 2394-8280
As in the one-dimensional case, image f (x, y) is used as the first scale input, and output four quarter-size
H
sub-images W
,WH ,WV ,WD as shown in the middle of figure 3. The approximation output WH  j, m, n  of the
filter banks in figure.2.can be tied to other input analysis filter bank to obtain more sub images, producing the two-scale
decomposition as shown in the left of Figure. 3. Figure. 4. Shows the synthesis filter bank that reverses the process
described above.
WHϕ(j,m,n) WHψ(j,m,n)
WΦ(j+1,m,n)
WVψ(j,m,n) WDψ(j,m,n)
Figure.3.Two-scale of two-dimensional decomposition
Rows
WDψ(j,m,n)
2
hψ(-m)
Columns
+
WVψ(j,m,n)
2
hϕ(-m)
WVψ(j,m,n)
2
hψ(-m)
WHϕ(j,m,n)
2
hϕ(-m)
2
hψ(-n)
+
+
2
WΦ(j+1,m,n)
hϕ(-n)
Figure.4.The synthesis filter bank of the two-dimensional DWT
IV.HAAR WAVELET TRANSFORM
Haar functions have been used from 1910 when they were introduced by the Hungarian mathematician Alfred Haar
[8]. Haar wavelet is discontinuous, and resembles a step function.
For an input represented by a list of numbers, the Haar wavelet transform may be considered to simply pair up input
values, storing the difference and passing the sum. This process is repeated recursively, pairing up the sums to provide
the next scale, finally resulting in differences and one final sum. The Haar Wa velet Transformation involves averaging
and differencing terms, storing detail coefficients, eliminating data, and reconstructing the matrix such that the resulting
matrix is similar to the initial matrix.[9-10].
A Haar wavelet is the simplest type of wavelet. In discrete form, Haar wavelets are related to a mathematical
operation called the Haar transform. The Haar transform serves as a prototype for all other wavelet transforms. Like all
wavelet transforms, the Haar transform decomposes a discrete signal into two sub -signals of half its length. One subsignal is a running average or trend; the other sub-signal is a running difference or fluctuation.
V.RESULT
In this paper we have successfully applied our proposed algorithm to a number of low dynamic range images and
recovered HDR images. This proposed method is using for enhancing the dynamic range of the images. In our paper we
used two dimensional Haar wavelet of discrete wavelet transform to perform the above defined operation and have
obtained the dynamic range enhanced images with good quality of image. Figure 5(a),(b),(c).represents the input
images and figure (d),(e),(f) represents corresponding resultant recovered HDR image with two dimensional Haar
DWT.
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International Journal of Research In Science & Engineering
Volume: 1 Special Issue: 2
e-ISSN: 2394-8299
p-ISSN: 2394-8280
(a)
(d)
(b)
(e)
(c)
(f)
Figure.5.Recovered HDR results.
(i).input images(a-c) (ii).Recovered HDR images with DWT(d-f)
CONCLUSION
This paper proposed a method of recovering HDR image based upon an enhancement technique using discrete
wavelet transform. This technique enhances the lower and higher contrast area of an image both in spatial and
frequency domain. Here Haar discrete wavelet transform enhanced the dynamic range of the image, so we can say that
the algorithm is mainly using for denoising.The proposed method is easy to implement and understand. Result of this
experiment shows that algorithm not only enhancing the image contrast, range but can preserve the original image
quality.
REFERENCES
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[3] J. Kuang, G. M. Johnson, and M. D. Fairchild, “iCAM06: A refined image appearancemodel for HDR image
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[1]
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