![Fig. 11. Quantitative performance results on 500 colour images from Berkeley dataset [21]: the first, second, third, fourth, and fifth rows correspond respectively to WTHE, FHSABP, HMF, CEBGA and CVC. The measurements from the original images are coded in red, while thosefrom the images enhanced using different algorithms are coded in black.](/figures/fig-11-quantitative-performance-results-on-500-colour-images-wsznnx5v.webp)
![Fig. 13. (a) Contrast enhanced images resulted from applying different algorithms on sample images from ORL face database [24]: the first, second, third, fourth, fifth, and sixth rows correspond respectively to theoriginal images and images enhanced by WTHE, FHSABP, HMF, CEBGA and CVC. (b) Face recognition on ORL face database [24] using 2DPCA [25] on images enhanced by different algorithms.](/figures/fig-13-a-contrast-enhanced-images-resulted-from-applying-pp7ejpjp.webp)
University of Warwick institutional repository: http://go.warwick.ac.uk/wrap
This paper is made available online in accordance with
publisher policies. Please scroll down to view the document
itself. Please refer to the repository record for this item and our
policy information available from the repository home page for
further information.
To see the final version of this paper please visit the publisher’s website.
Access to the published version may require a subscription.
Author(s): Celik, T. and Tjahjadi, T.
Article Title: Contextual and Variational Contrast Enhancement
Year of publication: 2011
Link to published article:
http://dx.doi.org/10.1109/TIP.2011.2157513
Publisher statement:” © 2011 IEEE. Personal use of this material is
permitted. Permission from IEEE must be obtained for all other uses, in
any current or future media, including reprinting/republishing this
material for advertising or promotional purposes, creating new
collective works, for resale or redistribution to servers or lists, or reuse
of any copyrighted component of this work in other works.”
1
Contextual and Variational Contrast Enhancement
Turgay Celik and Tardi Tjahjadi Senior Member, IEEE
Abstract
This paper proposes an algorithm which enhances the contrast of an input image using inter-pixel contextual information.
The algorithm uses a two-dimensional (2D) histogram of the input image constructed using mutual relationship between each
pixel and its neighbouring pixels. A smooth 2D target histogram is obtained by minimizing the sum of Frobenius norms of the
differences from the input histogram, and the uniformly distributed histogram. The enhancement is achieved by mapping the
diagonal elements of the input histogram to the diagonal elements of the target histogram. Experimental results show that the
algorithm produces better or comparable enhanced images than four state-of-the-art algorithms.
Index Terms
Contrast enhancement, histogram equalization, image quality enhancement, face recognition.
I. INTRODUCTION
Contrast enhancement is used to either increase the contrast of an image with low dynamic range or to bring out image
details that would otherwise be hidden [1]. The enhanced image looks subjectively better than the original image as the grey
level differences (i.e., the contrast) among objects and background are increased.
The conventional approach to enhance the contrast in an image is to manipulate the grey-level of individual pixels. Global
histogram equalization (GHE) [1] uses an input-to-output mapping derived from the cumulative distribution function (CDF) of
the image histogram. Although GHE utilizes the available grey scale of the image, it tends to over-enhance the image if there
are large peaks in the histogram, resulting in a harsh and noisy appearance of the enhanced image. It does not always produce
satisfactory enhancement for images with large spatial variation in contrast. Local histogram equalization (LHE) algorithms
have been developed, e.g., [2], [3], to address the aforementioned problems. These algorithms use a small window that slides
over every image pixel sequentially and the histogram of pixels within the current position of the window is equalized. LHE
sometimes over-enhances some portion of the image and any noise, and may produce undesirable checkerboard effects.
Other algorithms that focus on improving GHE [4]–[9] can achieve satisfactory contrast enhancement, but the variation in
the grey-level distribution may result in image degradation [10]. Dynamic histogram specification (DHS) [10] uses the desired
histogram, generated dynamically from the input image, to modify the input image histogram. In order to retain the features
in the input image histogram, DHS extracts the differential information from the input image histogram and incorporates
additional parameters to control the enhancement such as the image original and the resultant gain control values. However,
the degree of enhancement that can be achieved is not significant. In order to address the artefacts due to over-enhancement
and saturation of grey levels of GHE, the original image histogram is modified by weighting and thresholding before the
histogram equalization in [9]. The weighting and thresholding are performed by clamping the original image histogram at an
This work was supported by Warwick University Vice Chancellor Scholarship.
Turgay Celik and Tardi Tjahjadi are with the School of Engineering, University of Warwick, Coventry, CV4 7AL, United Kingdom. e-mail: Turgay Celik
(celikturgay@gmail.com), Tardi Tjahjadi (t.tjahjadi@warwick.ac.uk).
2
upper threshold and at a lower threshold, and transforming all the values between these thresholds using a normalized power
law function with an index. We refer the algorithm as weighted thresholded histogram equalization (WTHE). WTHE provides
satisfactory enhancement with the carefully selected default parameter setting.
One group of algorithms decompose an input image into different subbands so as to modify, globally or locally, the magnitude
of the desired frequency components of the image data using multiscale analysis [11]–[14]. These algorithms enable the
simultaneous global and local contrast enhancement by transforming the appropriate subbands and in the appropriate scales.
For example, the centre-surround Retinex algorithm [11] achieves lightness and colour constancy in images. However, the
enhanced image may include “halo” artefacts, especially along boundaries between large uniform regions. A “greying out” can
also occur resulting in the image of the scene tending to middle grey.
Optimisation methods have also been used for contrast enhancement. Convex optimisation is used in flattest histogram
specification with accurate brightness preservation (FHSABP) [15] to transform the input image histogram into the flattest
histogram, subject to a mean brightness constraint. This is followed by applying an exact histogram specification algorithm
to preserve the image brightness. FHSABP behaves very similar to GHE when the grey levels of the input image are equally
distributed. Since it is designed to preserve the average brightness, FHSABP may produce low contrast results when the average
brightness is either too low or too high. Contrast enhancement in histogram modification framework (HMF) [16] minimizes a
cost function to compute a target histogram. The cost function is composed of penalty terms of minimum histogram deviation
from the original and uniform histograms, and histogram smoothness. Furthermore, the edge information is embedded into the
cost function to weight pixels around region boundaries to address noise and black/white stretching [16]. In order to design a
parameter free contrast enhancement algorithm, genetic algorithm (GA) is employed in [17] to find a target histogram which
maximizes a contrast measure based on edge information. We refer this algorithm as contrast enhancement based on GA
(CEBGA). CEBGA suffers from the drawbacks of GA based algorithms, namely dependency on initialization and convergence
to a local optimum. Furthermore, the convergence time is proportional to the number of distinct grey levels in the input image.
All the above approaches use a 1-dimensional (1D) histogram. Other than HMF [16], they do not take into account the
contextual information content in the image. HMF [16] uses the image edge information to weight the 1D histogram.
We propose a contextual and variational contrast enhancement algorithm (CVC) to improve the visual quality of input images
as follows. Images with low-contrast are improved in terms of an increase in dynamic range. Images with sufficiently high
contrast are also improved but not as much. The colour quality are improved in terms of colour consistency, higher contrast
between foreground and background objects, larger dynamic range and more image details are visible. The enhancement process
is based on the observation that contrast can be improved by increasing the grey-level differences between the pixels of an
input image and their neighbours. Furthermore, for the purpose of image equalization, grey-level differences should be equally
distributed over the entire input image. To realise these observations, a 2D histogram of the input image is constructed and
modified with a priori probability which assigns higher probability to the high grey-level differences, and vice versa. In 2D
histogram, for each grey-level in the input image, the distribution of other grey-levels in the neighbourhood of the corresponding
pixel is computed. A smooth 2D target histogram is obtained by minimizing the sum of Frobenius norms of the differences
from the 2D input histogram, and the 2D uniformly distributed histogram. The contrast enhancement is achieved by mapping
the diagonal elements of the 2D input histogram to the diagonal elements of the 2D target histogram.
The paper is organized as follows. Section II presents the proposed CVC. Section III presents the subjective and quantitative
comparisons of CVC with four state-of-the-art enhancement techniques. Section IV concludes the paper.
3
(a) (b)
Fig. 1. The input image (a) and its 2D histogram (b) using 7 × 7 neighbourhood. For display purpose, h
x
(m, n) is shown in logarithmic scale.
II. PROPOSED ALGORITHM (CVC)
A. Grey-Scale Image Enhancement
Consider an input image, X = {x (i, j)
1 ≤ i ≤ H, 1 ≤ j ≤ W } , of size H × W pixels, where x (i, j) ∈ [0, Z
+
] and
assume that X has a dynamic range of [x
d
, x
u
] where x (i, j) ∈ [x
d
, x
u
]. The objective of CVC is to generate an enhanced
image, Y = {y (i, j)
1 ≤ i ≤ H, 1 ≤ j ≤ W }, which has a better visual quality than X. The dynamic range of Y can be
stretched or compressed into the interval [y
d
, y
u
], where y (i, j) ∈ [y
d
, y
u
], y
d
< y
u
and {y
d
, y
u
} ∈ [0, Z
+
]. In this work, the
enhanced image utilizes the entire dynamic range, e.g., for an 8-bit image y
d
= 0, and y
u
= 2
8
− 1 = 255.
Let X = {x
1
, x
2
, . . . , x
K
} be the sorted set of all possible K grey-levels that can occur in an input image X where
x
1
< x
2
< . . . < x
K
, where K = 256 for an 8-bit image. The 2D histogram of the input image X is computed as
H
x
=
h
x
(m, n)
1 ≤ m ≤ K, 1 ≤ n ≤ K
, (1)
where h
x
(m, n) ∈ [0, Z
+
] is the number of occurrences of the n
th
grey-level (x
n
) in the neighbourhood of the m
th
grey-level
(x
m
). Different types of neighbourhood can be employed, however for a typical implementation of CVC w × w neighbourhood
around each pixel is considered. For example, Fig. 1 shows the input image and its 2D histogram using 7 × 7 neighbourhood.
The image has more bright regions than dark regions, thus its histogram has larger values located at higher grey-values. In
homogeneous regions, the neighbours of each pixel have very similar grey-levels which result in higher peaks at diagonal or
near-diagonal elements of the histogram.
For an improved contrast there should be larger grey-level differences between the pixel under consideration and its
neighbours. Thus, the 2D histogram is modified according to
h
x
(m, n) = h
x
(m, n) h
p
(x
m
, x
n
) (2)
and
h
p
(x
m
, x
n
) = (|x
m
− x
n
| + 1) / (x
K
− x
1
+ 1) , (3)
where h
p
(x
m
, x
n
) ∈ [0, 1] assigns a weight to the occurrences of (x
m
, x
n
) which is proportional to the modulus of the
grey-level difference between x
m
and x
n
. The 2D histogram shown in Fig. 1(b) is updated as shown in Fig. 2(b) using the
h
p
(x
m
, x
n
) shown in Fig. 2(a). It is clear from Fig. 2(a) that h
p
(x
m
, x
n
) assigns higher weights to the components according
to their distance from the diagonal elements. Thus, h
p
(x
m
, x
n
) enhances larger differences which results in greater contrast
in the overall image.
4
(a) (b)
Fig. 2. Updating the 2D histogram shown in Fig. 1(b): (a) h
p
(x
m
, x
n
) computed using Eq. (3); and (b) Updated 2D histogram h
x
(m, n) using Eq. (2).
For display purpose, h
x
(m, n) is shown in logarithmic scale.
The updated 2D histogram H
x
is normalized according to
h
x
(m, n) = h
x
(m, n)
.
K
X
i=1
K
X
j=1
h
x
(i, j) (4)
to give a CDF
P
x
=
P
x
(m) =
m
X
i=1
m
X
j=1
h
x
(i, j)
m = 1, . . . , K
. (5)
Let Y = {y
1
, y
2
, . . . , y
K
} be the sorted set of all possible K grey-levels that can occur in output image Y where y
1
< y
2
<
. . . < y
K
. In order to map the elements of X to the elements of Y, it is necessary to determine a K × K target histogram
H
t
and its CDF P
t
. In order to equally enhance every possible occurrence of grey-levels of the input image pixels and their
neighbours, H
t
can be selected as a 2D uniformly distributed histogram
H
u
=
h
u
(m
′
, n
′
) =
1
K
2
1 ≤ m
′
≤ K, 1 ≤ n
′
≤ K
. (6)
However, such a selection does not consider the contribution of the 2D input histogram. Instead, H
t
should have a minimum
distance from the input histogram, i.e.,
H
t
= argmin
H
kH − H
x
k, (7)
where k·k computes the norm. Motivated by the maximum entropy principle, H
t
should also have a minimum distance from
the uniformly distributed histogram, i.e.,
H
t
= argmin
H
kH − H
u
k. (8)
Furthermore, in order to satisfy a smooth mapping, H
t
should have minimum deviations between its components, i.e.,
H
t
= argmin
H
kHDk, (9)
where D ∈ R
K×K
is a K × K bidiagonal difference matrix
D =
d −d 0 · · · 0 0 0
0 d −d · · · 0 0 0
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
0 0 0 · · · 0 d −d
0 0 0 · · · 0 0 d
, (10)
where d is a constant which is set to 1. The matrix multiplication in Eq. (9) results in a matrix which holds differences between
the horizontal elements of the matrix H. The vertical elements can also be considered, however the enhancement result will
not change significantly.