home   |<<    <--    -->    >>|

Worst case scenario: ellipsoids.

And here's how bad it can get with the ellipsoids. Here's a set of tensors with varying shapes, but the orientation is really unfortunate, so that in image space, they look pretty similar.

From another viewpoint, we can see how different they are. The subtle shading cues are doing a poor job of showing the different aspect ratios among the ellipsoids.