global mapping is learned from ground-truth exposure
data in the training dataset [16,17]. The advantage of
global exposure correction is their simplicity and compu-
tational efficiency. However, with global mapping, pixel
values are mapped uniformly regardless of their spatial
and local properties, which may reduce local contrast and
cause detail loss. Moreover, global mapping is usually
image-dependent. Users are required to tune the para-
meters of the mapping to produce the best results.
Local exposure correction [7,8,10,11,18,9] takes local
spatial context into account when mapping a pixel. In
particular, two pixels with the same luminance value may
be mapped to two different luminance values. This flex-
ibility during the mapping may help to better preserve
local contrast. Retinex [10,11,19] corrects the exposure by
compressing large and undesirable contrast while preser-
ving or enhancing small contrast. The Gradient-based
method [7] computes a gain map for gradients of the
image, reduces large gradient relative to small ones and
then recover an exposure corrected image from the
manipulated gradients. While Li et al. [8] use a pyramidal
image decomposition and attenuate the coefficients at
each level to adjust the exposure. Duan et al. [18] propose
a local histogram adjustment method to map high
dynamic range images, which tunes the log-average lumi-
nance of a local patche to a key value adaptively. Exposure
fusion [9] combines multi-exposed images together to
produce an image with good exposure, wherein the
weights for combining the images are calculated based
on luminance, contrast and saturation at each pixel of the
input images. The problem with existing local exposure
correction methods is that luminance, contrast, gradient or
saturation is not an appropriate measure of exposure,
since a large contrast or gradient between pixels unne-
cessarily comes from a large exposure difference. As a
result, these local mapping methods may undesirably
reduce contrast as well as lead to detail loss and unrealistic
exposure. Therefore, we propose the use of bright channel,
which can better reflect the exposure in local image
regions.
Our bright channel prior is inspired by the dark channel
prior proposed in [20]. But the dark channel and bright
channel have different physical representations. The dark
channel is used to estimate the haze's transmission, while
we use the bright channel to measure the local exposure of
an image. Furthermore, we utilize the bright channel prior
on a totally different application—exposure correction. An
over-exposure correction method is proposed in [21] to
recover the lost intensity and color information in over-
exposed image regions. However, we do not take over-
exposure into account in this paper; our goal is to lighten
the under-exposed regions locally.
3. Image exposure model
Given an input image I, we first transform it to HSV
color space. In order to avoid color shift, we only adjust the
luminance channel (V) of the input image I
v
, while the
color channels (H and S) are unchanged and directly
copied to the corrected result. The image exposure model
can be represented as
I
v
ðxÞ¼
1
αðxÞ
J
v
ðxÞþnðxÞ; ð1Þ
where J and J
v
are the ideal well-exposed image and its
luminance channel respectively, and n is the additive
image noise. The pixel-wise coefficient α represents the
relative exposure between the ideal well-exposed image
and the input image. Under this model, α is greater than 1
in under-exposed regions, equal to 1 in well-exposed
regions, and less than 1 in over-exposed regions.
Our aim is to correct the exposure of the input image I
and recover the well-exposed and noise-free image J.
Multiplied by the relative exposure α, Eq. (1) becomes
J
v
n
ðxÞ¼J
v
ðxÞþαðxÞnðxÞ¼αðxÞI
v
ðxÞ: ð2Þ
Here, we note that the noise in the under-exposed regions
will be amplified after the exposure correction. Hence, we
use J
v
n
to represent the noisy well-exposed image. After the
correction, a spatial-variant image denoising is applied to
reduce the amplified noise.
To recover the well-exposed image, we need to first
estimate the pixel-wise relative exposure α. In the next
section, we will propose a novel measure of local exposure
and introduce a novel image prior to estimate the relative
exposure.
4. Bright channel prior
We find that most patches of a well-exposed image
contain some pixels which have high intensities in at least
one channel, unless the patches are in dark shadows or
covered by big black colored objects. Specifically, the
maximum intensity in each well-exposed image patch
should have a large value. We call this the bright channel
prior and define the bright channel of image J as
J
bright
ðxÞ¼max
y∈ΩðxÞ
max
c∈fr;g;bg
J
c
ðyÞ
¼ max
y∈ΩðxÞ
J
v
ðyÞ; ð3Þ
where J
c
is one of the RGB channel of image J and ΩðxÞ
denotes a local patch centered at pixel x. According to the
definition of HSV color space, J
v
¼ maxðJ
r
; J
g
; J
b
Þ.IfJ
bright
of
the whole image has high intensities, we can say that the
image is well-exposed.
The bright channel of a well-exposed image always has
high intensity mainly due to three factors: (a) strong light
sources. e.g., the sun, lamps, light reflected from water or
mirror, etc, (b) colorful objects or surfaces. e.g., grass,
flowers, sea, etc. They will form saturated pixels in an
image with one or two channels having high intensities
and (c) bright objects or surfaces. e.g., snow, white color
clothes, white walls, etc. These objects themselves will
have high intensity in an image. These three kinds of
conditions are widely available in many scenes. Hence the
bright channel prior is feasible.
We perform a statistical experiment to verify the bright
channel prior. We collect a large set of natural images from
the image sharing website (e.g., flickr.com) using 47
popular keywords (e.g., “landscape”, “travel”, “nature”,
etc). We remove the images containing large black objects
and manually select 6000 well-exposed images from the
Y. Wang et al. / Signal Processing 93 (2013) 3227–3238 3229