# Exposure Bracketing Techniques for Camera Document Image Enhancement
## 3 HDR Document Image Generation  
### Document Image Registration  
The image registration problem has been intensively studied in remote sensing images, medical images, and camera images and very rarely, research can be found for document image registration. The most popular registration in the context of exposure bracketing is from [3], where a translational geometric model was employed to account for the geometric disparity between two images. However, we found that the translational model is not suitable for general camera document images. Figure 4 shows two pseudo color image patches that are composed of two LDR images that are already illustrated in Figure 1. The green band and blue band come from the corresponding bands in the well-exposed image while the red band is from the corresponding band in the over-exposed image. If there are no geometric disparities between these two images, the foreground (textual part) of the image should overlap. In Figure 4, we can clearly see that geometric difference exists as the foreground texts do not overlap. On top of it, we can clearly see that the global translational model cannot account for the geometric disparity between these two images. For example, Figure 4a is the left central image patch and we can see that the geometric difference between the well-exposed image and over-exposed image in this region is around 10 pixels (half the size of the lowercase letter \"a\") in the vertical direction. However, in Figure 4b, the right central image patch, we can see that the geometric difference between the well-exposed image and over-exposed image in this region is around 20 pixels (the size of the lowercase letter \"a\") in the vertical direction. This is obvious evidence that the geometric disparity between LDR images cannot be translational and that it must follow a more complicated geometric model. Figure 4: Pseudo color image composed of Figure 1a,c. The green and blue bands come from the green and blue bands of Figure 1b, while the red band is from the red band of Figure 1c. (**a**) The small image patch from the bottom-left part of the pseudo color image. (**b**) The small image patch from the bottom-right part of the pseudo color image. Among all the geometric models, such as the affine model, translational model, rotation model, and so on, we ended up selecting the planar homograph model [6] to represent the geometric disparity between LDR images. Under this model, points in two different images can be mapped as:  
\[\left( \begin{array}{c}x^{\prime}\\ y^{\prime}\\ z^{\prime}\end{array} \right)=\left[ \begin{array}{ccc}a&b&c\\ d&e&f\\ g&h&1\end{array} \right]\left( \begin{array}{c}x\\ y\\ z\end{array} \right) \tag{1}\]  
where points are represented by homogeneous coordinates and so point (\(x\), \(y\), \(z\)) is the same as (\(x\)/\(z\), \(y\)/\(z\)) in the inhomogeneous coordinate. We selected this model because during the bracketing stage, hand-shake is inevitably introduced, leading to different imaging angles for the same document object, and the planar homograph model is suitable for the situation where the imaging object is put on a planar surface and is captured from different view-angles. When the planar homograph model is selected, we have to estimate this model's eight parameters. Basically, there are two methods [7]. The first method is called the area-based method. Using this method to estimate the planar homograph model involves two steps: in the first step, a moving window is defined in the reference image and the image patch within the window is regarded as the template. We used the template to search for a corresponding image patch in the sensed image (an image that was registered). The centers of matched image templates are used as control points (CPs). There are many ways of finding a matching template, and one of the most popular criteria is cross correlation. When multiple CPs are generated, we then use these CPs to estimate the planar homograph model.