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5 Spatial decomposition by patch-wise computation

 

A straightforward way of expanding the scale expansion of information into a decomposition in both scale and spatial coordinates is to evaluate the Kullback contrast patch-wise over the image, letting the patch size vary with the resolution.

This can be implemented at almost no extra cost by noting that the normalization of the two distributions tex2html_wrap_inline657 and tex2html_wrap_inline659 in the Kullback contrast can be delayed. Thus an efficient algorithm is:

  1. Compute the Kullback contrast pointwise,

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  2. Compute moving averages (ma) of the same window size for Qma = ma(k) , tex2html_wrap_inline667 and tex2html_wrap_inline669 .
  3. The local (computed over the window size) Kullback contrast is:

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   figure129
Figure 10: Scale and spatial distribution of the information in the Group image.

In Figure 10 we show such a spatial decomposition for the Group image. Each image has been normalized to the same range for printing. To compare total contrast between different scales use Fig. 8.

At the very shortest scales this method draw the most attention to the sharp lines on the spatula, toy shovel and butter dish. The spray bottle has softer edges, and does not stand out as much. The clutter near the upper and lower edges of the image comes from low amplitude high frequency noise, generated by the camera in those otherwise signal-less areas.

In the longer scales other features start popping out, in an order according to their physical sizes. First we see the slotted spatula, its high contrast handle and the small top of the spray bottle. The narrow shaft of the shovel also comes early.

Notice that the contrast operator can respond to both a step edge as well as a whole object, so large objects with sharp edges will pop out first because of the edges, and later because of the whole object dimensions. Comparing the total contrast in the images using the data in Fig. 8 we see that the absolute information value our measure assigns to the edges is much lower than to that of the whole objects. (Around 0.01 for the edge responses for the 2 and 4 pixel observer compared to 0.05 to 0.1 for the object responses at 16 pixels and up.)

At 128 pixel resolution we get another phenomenon. Our information measure has no way of knowing what is object or what is background (anti object) in the image. At this resolution we start responding to the background around the group of objects and the fairly large patch of background enclosed by the shovel, spatula and butter dish.


next up previous
Next: 6 A Different Measure: Up: Inform. theory approach to Previous: 4 Comparison to Other