A Retinex-Based Local Tone Mapping Algorithm Using L0 Smoothing Filter - Advances in Image and Graphics Technologies - page 43

3

Proposed Method

The classic retinex algorithm has some drawbacks as described in section 2. These
drawbacks are overcome if the proposed method is used. The input data for our
algorithm are RGBE images. We need to convert from the RGBE image to the RGB
image, and then convert from the RGB image to the HSV image. Luminance is
obtained from the HSV image to perform the tone mapping process. Tone mapping
consists of global tone mapping and local tone mapping. First, a global histogram
adjustment method is a pplied for the initial global tone mapping. After that, a
retinex-based local tone mapping is applied, which uses L 0 smoothing filter as the
surround function to reduce halo artifacts. Finally, the result image is obtained from
the tone-mapped luminance and the original RGB image through color correction.
The following are the details of the proposed method.

3.1 Global Tone Mapping

The global tone mapping that is applied to luminance image performs a first
compression of the dynamic range. It is like the early stage of the human visual
system where a global adaptation takes place [7]. In the HDR image, since the
luminance of bright area is too high, we firstly compress the high-luminance areas
using this formula:

Lxy (, )

Lxy (, ) =

w

(5)

1( , + Lxy )

w

in which,

w Lxy is the luminance of original image for pixel (, )

(, ) xy , scaled to 0 and

100, while L is the initial compressed image.
With formula (5), the mapped image appears with low contrast, so it needs further
processing. A method called histogram adjustment based linear to equalized quantizer
(HALEQ) [8] is applied to enhance the contrast of image. Linear mapping divides
luminance range into N=256 equal length intervals, and l is the cutting points.
Histogram equalized mapping divides luminance range into N intervals such that the
number of pixels falling into each interval is the same, and e is the cutting points.
HALEQ strikes a balance between the linear mapping and the histogram equalized
mapping, and the cutting points le is defined as this formula:

(

n

le =+ − (6) l

ʲ

e l )

n n n n

in which, 0

≤≤ is parameter to control the global contrast. If 1 ʲ = 0

, HALEQ is

the linear mapping,

ʲ = , then HALEQ is the histogram equalized mapping. Pixels
falling into the same interval are mapped to the same integer display level. We can
express the whole process as

1

g Lxy

(, ) HALEQ( (, )) = Lxy

(7)

In the above formula, L is the result of global tone mapping.