We motivate the practical usefulness of the Kullback based information theoretic contrast showing the resulting scale space information distribution for several real images.
Figure 2: Information distribution in scale-space for the checkers image.
The first image (Fig. 1) shows a tilted checker board. This image has two dominating elements, the tiles on the checkerboard, and the checker pieces on the board, both having almost the same dimensions. Looking at how the information is distributed in scale-space (Fig. 2) we find a very sharp peak at 32 pixels. This indeed corresponds very well to the actual dimensions of the checkerboard squares in the image. Contributions at larger scales can be attributed to the dimension of the whole board. We can also see in the scale-space pyramid (Fig. 3) that most detail disappears at resolution lengths longer than 32 pixels.
Figure 3: Scale-space expansion of the checkers image.
Figure 4: The Peanut image, and its information distribution.
Our second picture (Fig. 4) of densely packed peanuts has a random distribution of peanut sizes within an interval of approximately 30-60 pixels. (Note that both the long and short cross sections give contributions.) Correspondingly we find a broader peak in the information-scale expansion centered around 45 pixels.
Figure 5: The Robotlab image, and its information distribution.
The third picture, Fig. 5, from our robot laboratory, has a much wider range of scales in it, which is also evident from the information-scale plot.
In the Tinytown (Fig. 6) example we can see structure on the macroscopic level (cars, trees, houses etc...), but there is also structure at a much smaller scale, corresponding to the textures of the ground and trees. (This is perhaps hard to see in the printouts, but much more evident on a grey scale monitor.)
Figure 7: Log plot of Information distribution in the Tinytown image.
The bimodal structure of the scale-space information expansion accurately tells us about these two scales present in the image. It is easy to see in the log plot in Fig. 7.
Last we show an image of a group of household items against a uniform black background (Fig. 8). As expected this image has virtually no information content at smaller scales, while we see a wide peak between 50 and 150 pixels, corresponding to the typical lengths represented in the objects, such as the narrow handles, and spatula slots accounting for the low end and the overall dimensions accounting for the high end.