Help for SHADOW

PURPOSE:

Shadow enhancement for non-uniform illumination images. The program
will brighten the shadows, and preserve details of the image. The program
is implemented based on retinex theory. For detailed algorithm, please 
see METHOD section. 

The program currently supports only grayscale format. The input images
to the program must be 1-band in HALF format.

EXECUTION:
The program provides adaptive or global gamma brightness correction modes.
Adaptive gamma brightness correction mode will brighten shadows automatically
based on input image statistics. Global gamma brightness correction mode
uses a constant gamma value. Depending on the constant gamma value, global
gamma correction may brighten shadow more, but it may also over brighten
the non-shadow areas.

  1) SHADOW INP=input.img OUT=output.img
The above command will enable adaptive gamma brightness correction mode.
The program will brighten shadows more than it will brighten non-shadow 
areas.

  2) SHADOW INP=input.img OUT=output.img GAMMA=0.5
The above command will enable global gamma brightness correciton mode. 
In general cases, gamma needs to be in range of 0 to 1 (exclude 0 and 1).
Using global gamma correction mode, the non-shadow areas may be over
brightened. 

METHOD:
The SHADOW program consists of the following steps:
  
  1) Decompose input image into illumination image and reflectance image
     based on retinex theory.
  2) Gamma brightness correction on illumination image.
  3) Contrast enhancement on illumination image using probability density 
     function.
  4) Combine illumination image and reflectance image to generate the 
     final output.

Retinex theory in short indicates that scenes presented to a digital camera
or human eye can be decomposed into illumination and reflectance components.
In this program, the illumination image is estimated using Gaussian kernel 
convolves with the input image. 

Estimate illumination image using Gaussian kernel sometimes causes 
problems including halo artifacts around big edges. In order to suppress
the halo artifacts, a weighted map is computed based on the following
equations:

    high_freq_image(x,y) = |input_image(x,y) - illumination_image(x,y)|
    weight_map(x,y) = convolution(high_freq_image(x,y), gaussian_kernel(x,y))
    
x and y are line and samp in the images respectively. Next, the weight map 
is used as in the equation below to compute the modified illumination image. 
The halo atrifacts in the original illumination image will be removed from 
this step.

    mod_illu_image(x,y) = weight_map(x,y) * input_image(x,y) + (1 - weight_map(x,y)) * illumination_image(x,y)

x and y are line and samp in the images respectively, and weight_map(x,y) 
was normalized to [0, 1]. The reflectance image is then decomposed using 
the modified illumination image based on the equation below.

    reflectance_image(x,y) = input_image(x,y) / mod_illu_image(x,y)

The reflectance image contains high frequency information, which in other 
words, it contains detailed information of the input image.
    
Apply gamma correction to the modified illumination image. The program
provides two modes of gamma correction: (1) global gamma correction, 
(2) adaptive gamma correction. Gamma correction is defined by the equation
below:

    result(x,y) = input(x,y)^gamma(x,y).

input(x,y) should be normalized to [0, 1] prior to the computation. If 
gamma(x,y) is smaller than 1, then result(x,y) will be brighter than
input(x,y). If gamma(x,y) is larger than 1, then result(x,y) will be
darker than input(x,y).

In global gamma correction mode, gamma(x,y) will be set to a user defined
constant value. In order to brighten the image, gamma value needs to be
in range of 0 to 1 (exculde 0 and 1). The smaller the gamma value, the 
brighter the result will be. 

In adaptive gamma correction mode, gamma(x,y) will be a function defined
by the equation below:

                  2 * mod_illu_image(x,y) + 1
    gamma(x,y) = -----------------------------
                    2 + mod_illu_image(x,y)

The adaptive gamma correction mode will brighten the dark areas more than
it brightens the areas that are already bright enough to see the details.
Adaptive gamma correction mode is enabled by default. If the parameter
GAMMA is defined, the program will switch to global gamma correction mode.

Note that in the following steps, histogram will be modified for the purpose 
of enhancing contrast, so the brightness of the result from this step won't 
be directly reflected in the final resultant image. 

Gamma correction usually decreases the contrast of the image, so at this 
step a probablity density function based adjustment will be performed to
enhance the contrast of the image. Firstly, the histogram of modified 
illumination image is computed, then the histogram is used to compute the 
probability density function. Secondly, in order to remove the spikes of the 
computed probability density function, the moving average of the probability 
density function is computed. Next, the final cumulative density function
(CDF) is computed based on the despiked probability density function. Finally,
the contrast enhancement mapping curve is defined by the equation below:

     mapping_curve(l) = round_off(l_max * CDF(l) + 0.5)

where l_max is the maximum intensity value in the input image, and l belongs
to the range of [0, l_max - 1]. Once the mapping_curve is obtained, it is
used to generate final illumination image.

    final_illu_image(x,y) = mapping_curve(gamma_illu_image(x,y))

Where gamma_illu_image is the illumination image after gamma correction. The
final illumination image reflects the enhancement both in brightness and 
contrast, and it preserves the naturalness of the input image because the
shape of the new histogram is similar with the original histogram.

The final step of this program is to combine the final illumination image
with the reflectance image.

    final_image(x,y) = reflectance_image(x,y) * final_illu_image(x,y)


REFERENCE:
1. Efficient naturalness restoration for non-uniform illumination images.
   Authors: Yonghun Shin, Soowoong Jeong, Sangkeun Lee.
2. A Histogram Modification Framework and Its Application for Image
   Contrast Enhancement.
   Authors: Tarik Arici, Salih Dikbas, Yucel Altunbasak.

HISTORY:
2016-05-04 Steven Lu Initial gammacorrection by Steven Lu.
COGNIZANT PROGRAMMER: Steven Lu