Night color image enhancement via statistical law and retinex - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 205

(2)
The radius ( r ) of the circular arc can be expressed as follows:
(3)
The circular arc can be expressed as follows:
(4)
Using Equation (4) , we can get the illumination image directly and quickly. The circular arc
is shown in Figure 2 .
FIGURE 2 Fitting circular arc.
According to Equation (4) , we can know that the circular arc takes two parameters called x 0
and λ . The smaller x 0 is, the more obvious the brightness enhancement is. The greater λ is, the
more obvious the brightness enhancement is. It can be seen that the darker the input image
is, the smaller x 0 is and the greater λ is, and vice versa. Therefore, we assign the average pixel
value of the source image to λ . x 0 is represented by the following formula: