Foreword
You created a stunning portrait flip picture of a couple, but you noticed unsightly black spots on the woman's face upon closer inspection. After examining the photo more closely, you realized the spots were traces of the man's black beard shown in the other image. Despite all the effort to create a perfect picture, it can be frustrating to encounter issues like this.
Many of us consider ghosting to be a "force of destiny." The contrary is true: ghosting can be significantly reduced and even fully eliminated in most cases. And there is even more good news: the treatment involves only image processing, which is implemented by software.
The ghosting phenomenon
When a lenticular flip picture is viewed from a proper angle, it should display only one of the images in the sequence. In reality, it also displays weak traces of other images in the sequence. This effect is caused by fundamental optical mechanisms that prevail in the lenticular picture. These mechanisms can be decreased by special means like anti-reflection coatings, but such means are very expensive and impractical for the lenticular print application. Here, we will propose other means that are based on pure image processing techniques and can be implemented without any cost.
Let us illustrate the ghosting phenomenon with a simple, though artificial pair of images shown in Fig. 1.
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Figure 1: Pair of images for ghosting illustration
When a lenticular flip picture is made from these images, the displayed images will be as shown in Fig. 2:
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Figure 2: The displayed images showing the ghosting effect
The grey circles manifest the ghosting effect. A similar effect occurs in images containing bright features on a dark background. Such images are shown in Fig. 3:
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Figure 3: Pair of images with white features on a dark background
A lenticular picture with these images will display the following images instead:
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Figure 4: Ghosted version of the images of Fig. 3
These ghosting features in both cases are absent in the original images and are considered visual defects.
"Line" images
To simplify the discussion, we will represent images by lines. The images that we have used for illustrations (Figs. 1 and 3) will be represented by lines as follows:
Figure 5: Line representation of images
The ghosted versions of these images will be represented as follows:
Figure 6: Ghosted versions of the images of Fig. 5
We can now represent the ghosting phenomenon schematically by the diagram shown in Fig. 7:
Figure 7: Scheme of the ghosting mechanism
The compensation method for ghosting treatment
The simplest way to eliminate ghosting is to compensate for it. This requires a simple modification of the original images.
Let us reconsider the scheme shown in Figure 7. Suppose we replace the original images with those shown in Figure 8. These images contain compensating features to eliminate ghosting.
Figure 8: Compensated versions of the original images
Applying the ghosting mechanism to the images in Fig. 8, we obtain
Figure 9: Ghosting elimination by compensation
The compensating features are designed as the negatives of the ghosting features. Therefore, when ghosting is applied, the compensating features nullify the ghosting features, and a ghost-free display is obtained. The same principle can also be applied to images with a bright feature on a dark background.
The clipping error in the compensation method
The compensation method is a simple and effective solution to the ghosting problem. Unfortunately, this method cannot be applied universally. To explain why this method fails, we have to introduce basic quantitative measures to our discussion.
Fig. 10 shows the bottom image pair of Fig. 5 together with a grey-level scale. The range of this scale is chosen to be between 0 to 255, as in 8-bit images. It was also assumed that the dark features are black and the bright backgrounds are white. The grey levels of these image elements are 0 and 255, respectively.
Figure 10: Line images with the grey-level scale
The compensated versions of the images in Fig. 10 are shown in Fig. 11. It is evident that these images require grey-level values exceeding 255. Such compensation is impossible. We call this a "clipping error."
Figure 11: Compensated images with clipping error
Compensation application to images with white features on a black background will require negative grey-level values, which is equally impossible.
Clipping error occurs often in cases when ghosting is strongest. To make the compensation method practical, one must find a way to avoid the clipping error.
Clipping error workaround by image mapping
Clipping errors can be overcome by image color mapping. Suppose that we reduce the white level of the images in Fig 10 to a certain level, as shown in the figure below.
Figure 12: Images with a reduced white level ("mapped") to allow compensation
The images can now be compensated. This two-step compensation process is illustrated in Fig. 13.
Figure 13: Two-step compensation to avoid clipping
The compensated images can be used now for the lenticular picture print, which will be ghost-free.
This work around allows the application of the compensation method universally, but it involves a penalty: the image color space is reduced, and the picture contrast will decrease. This creates a trade-off between the picture contrast and the ghosting level. One may opt for partial compensation to reduce the impact on the picture contrast. In some cases, it may be preferable to give up ghosting treatment altogether to leave the picture contrast untouched.
Summary
Ghosting is an acute problem in lenticular flip pictures. In extreme cases, it may reduce the picture's visual quality to an unacceptable level.
Ghosting can be alleviated by the method of compensation, which is implemented by relatively simple image processing. There is no cost involved and no significant increase in computing resources.
In many cases, compensation application requires reducing the picture color space. This creates a trade-off between visual quality and ghosting treatment. It is possible to choose the trade-off point in between so that both effects are balanced to produce an optimal picture.
Manually implementing the compensation method is possible, but it will require a significant amount of effort. Developing a custom software tool to make ghost treatment practical is necessary.