Should I worry about the keystone distortion?

Introduction

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Keystone distortion (aka "perspective distortion") arises when a 3D sequence is photographed with the camera pointing at a fixed ("pivot") point, usually chosen near the scene center. This distortion grows with the camera angular deviation. In lenticular applications, the angular deviation is typically ~5 degrees, and in such a case, the keystone distortion is slight, even hardly noticeable, and is often neglected.

As long as the angular deviation is small, one can wonder whether keystone correction is worth the effort. The answer is yes; not because the keystone spoils the picture, but because there is hardly any effort required to apply the correction, if one has the appropriate software.

To discuss the keystone distortion, one must dive deep into optical imaging and projective geometry, both complex mathematical subjects. In this post, we will demonstrate the keystone distortion with an intuitive, straightforward example. This will not explain how the distortion is created or corrected. These questions are left to the mathematicians, but our illustration will give you sufficient insight to understand what it is about and what damage it can inflict on your art.

3D photography of a flat object

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The title of this paragraph sounds like nonsense, and, in fact, it is. Our interest in this absurd stems not from artistic needs but from it being an excellent demonstration of the keystone distortion.

Figure 1 shows the scenario of 3D pivot photography of a flat object. In this example, the pivot point is at the object center. Five cameras will produce a five-image sequence, shown in Figure 2.

Figure 1: Pivot 3D photography of a flat object

Figure 2: The photographed sequence

When this sequence is interlaced and printed, the object will appear in the picture's plane. This happens because the pivot point in this example is on the object plane. Object points located at the picture plane have zero parallax, and therefore must be static; in other words, they must be located in the same position in all sequene images. Since in this example all object points lie in the picture plane, all sequence images should be identical.

It is evident from Figure 2 that this is not the case. To further emphasize this point, we present in Figure 3 a superposition of all five images. The malicious parallax possesses a vertical component, which is taboo in proper 3D sequences.

Figure 3: The sequence images superimposed

Figures 2 and 3 demonstrate the keystone distortion in flat objects. There is no reason to believe that the keystone distortion does not affect 3D objects too. In fact, it can be shown that the distortion increases with the deviation from the picture plane.

Keystone distortion in a 3D object

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In Figure 4, the flat image is replaced by a 3D object. The pivot point lies inside the cube and is hidden, but it also lies on the green rectangle plane.

Figure 4: Photography of a 3D object

The sequence produced in the scenario of Figure 4 is shown in Figure 5. Since the green rectangle lies in the picture plane, it must be identical in all sequence images. This is not the case, due to the keystone distortion.

Figure 5: The raw sequence

The corrected sequence is shown in Figure 6. In this sequence, the green rectangle is static, as it should be. This sequence will produce a 3D image with better visual quality.

Figure 6: The corrected sequence

A keystone correction tool is included in our Grape 10 software.