Gradated Histogram Fitting

Another artifact of the histogram fitting that was not addressed by Phillips and Vardi [33] was the sudden discontinuity in illumination as we switch from the left side of the face to the right side. This is induced by the switch from mapping function $f_{H_l \rightarrow G}$ to $f_{H_r \rightarrow G}$. We overcome this sudden transition by ``averaging'' the effects of $f_{H_l \rightarrow G}$ and $f_{H_r \rightarrow G}$ with a linear weighting that slowly favors one for the other as we move from the left side to the right side of the face. This ``gradual'' application of the mappings is implemented with the mapping function $f_{H_{total} \rightarrow G}$ shown in Equation , which uses a mixture of $f_{H_l \rightarrow G}$ and $f_{H_r \rightarrow G}$ and reduces discontinuities in histogram fitting:

$$f_{H_{total} \rightarrow G}(i) = leftness \times f_{H_l \rightarrow G}(i) + (1-leftness) \times f_{H_r \rightarrow G}(i)$$ (4.23)

The parameter, leftness is varied as we travel across the image from left to right as displayed in Figure .

  

Figure 4.20: The mixture of histogram mappings from the left to the right side of the face.