Summary:

The field of view of a camera determines how robustly we can estimate the 3D Motion of this camera. For example, the estimation for a small FOV camera is ill-posed which manifests itself in ambiguities that are explained and demonstrated. These ambiguities disappear when we increase the field of view.

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INFLUENCE OF FIELD OF VIEW

Accurate 3D Motion Estimation is Necessary to Build Accurate 3D Models .

Accurate ego-motion estimation is essential if one wants to build accurate models of the world from video. As can be seen in the following movie (AVI, 3,2Mb) .

Effect of Motion Estimation Error on Reconstruction Accuracy

that demonstrates how small changes in the localization of the feature points and camera positions and orientations can have dramatic effects on the accuracy of the reconstruction. The maximum localization error in this movie was 5 pixels for the correspondendence and two percent relative error for the camera position relative to the object distance.

Stability of 3D motion estimation depends on the field of view.

It is a well known fact that the stability of 3D motion estimation for a pinhole camera strongly depends on the size of the field of view. To demonstrate the effect, please take a look at the following movie (AVI, 5,2Mb) that illustrates the confusion of rotation and translation for a small field of view camera.

Confusion of Rotation and Translation for Small Field of View

On the left the camera is undergoing translational motion, on the right rotational motion. While the movie is playing, examine the top and side views of the cameras and try to decide only based on the image information which views are from the translating camera and which views are from the rotating camera.

We see that if we have only access to the top view then the estimation is very ambiguous. In contrast, if we have also access to a side view, the confusion between rotation and translation disappears.

Solution of motion estimation for small field of view is under constrained.

The reason for the sensitivity can easily be explained. If we examine the following two illustrations, we see that the measurements in the images, here we show image gradients, but they might as well be optical flow vectors or feature tracks, can only be made in the plane perpendicular to the image location vector (left illustration below).

Measurements are only made in the image plane

Ambiguity in recovery of motion parameters

Usually the rigid motion parameters are determined by fitting a parameterized instantaneous motion model to the observed measurements. That means we are trying to the find the motion parameters that explain the image measurements most accurately according to some error criteria. In the illustration to the right above, we see that we cannot determine the component of motion parameter vectors that are parallel to r. If we have a small field of view, that means that the vectors r span only a small part of the sphere of directions, then the motion estimation will be subject to the so called line ambiguity.

Comparison of small FOV vs Spherical FOV Cameras.

The line ambiguity can be seen in the following example where we compare the motion estimation for the individual cameras of the Argus Eye with the estimation that uses information from all the cameras simultaneously and thus is a large field of view camera.

Residuals over all translation directions for single cameras.

Residual over all translation directions when combination infomation from all six cameras.

There is a noticable valley in the error surface for the individual cameras due to the line ambiguity, while the ambiguity vanishes when we use all the cameras.

More information:

For more detailed information please read the accompanying paper about the Argus Eye and the papers about camera hierarchies in the publications section.