Moving blocks

Figure 1

This being preliminary to a post about the way that images in the brain might degrade with movement and how that relates to the frames of consciousness of LWS-N.

Figure 2

Let us suppose we have an input area called A, a rectangle made up of one million pixels, evenly arranged in rows and columns, and an output area called B, another, identical rectangle, containing the same number of pixels. The value of one of these pixels is either null or some colour, perhaps in the RGB way of Microsoft’s Powerpoint, snapped in the figure above. Noting in passing, that a pixel is not the same as a neuron and it is not at all clear that a single neuron can do the job of such a pixel, its seemingly large information content notwithstanding.

We suppose that A is being continuously updated and that for present purposes it may be taken to be a true and fair representation of some part of the world of interest.

There is a smaller rectangle, of contrasting colour to help the detection of movement, traversing A from left to right at a constant speed, with the speed S being measured in pixel columns per millisecond.

The pixels in B decay discretely. That is to say if the value of some pixel has been set to some non-null value at time T, in the absence of further action, that value will be reset to null at T+M milliseconds.

The task is to copy A to B, on the basis of a random but uniform sample of pixels of A. At the rate of N pixels per second. At the time a pixel is sampled, the value of the corresponding pixel on B is set to its value in A. There is no random noise in this simple system. This sampling is done in parallel, quite independently, of the continuous update of A already mentioned.

Such sampling is apt to be with replacement, but we neglect in what follows the possibility that a pixel may well be sampled more than once.

The present post is about what sort of an image there might be on B at some particular point T in time.

Figure 3

We will talk of the background and of the foreground object.

The right hand version of the foreground object indicates the real position at time T. The left hand version of the foreground object indicates the real position at time T-M. The two versions together span the area from which sample points from the foreground object will have been copied to B.

Given S, the ambiguous areas left and right will both be S × M pixel columns wide, which we suppose for the moment to be a lot less than the width of the foreground object. They are the areas for which the values of the sample points on B available at time T will sometimes be drawn from the background, sometimes from the foreground. To be more precise, half the sample points will be from the background and the other half will be from the foreground, giving a sense of transparency in the corresponding parts of the image of the foreground object on the target rectangle B. This image will also appear to have stretched slightly along the horizontal axis.

Areas to the left and right of this central area will have been reproduced satisfactorily on B.

Figure 4

We now add a bit more information to the foreground object. Under option 1 we have vertical stripes, while under option 2 we have horizontal stripes.

Under option 2, the horizontal stripes are reproduced satisfactorily on rectangle B, some degradation in the ambiguous areas left and right apart.

Figure 5

Figure 6

However, under option 1, things are more complicated, and in this example, the narrow bars are spread over an area which spans a number of other bars, the pale pink rectangle in the figure above, with the probable result that all that is left is a blur, possibly involving obscure oscillations of colour across the image of the foreground figure. It all depends on the numbers, on the parameters to the system.

At the limit, when the vertical bars are just lines, there will always be significant blurring.

A blurring which does arise under option 2.


Other examples

Figure 7

And it seems likely that the jittering of the horizontal stripes of Figure 4 above when I scroll (vertically) down that part of the original Word document is caused by some mechanism of the same sort. And when I have a narrow window for Word and scroll across (horizontally), something similar happens to the vertical stripes of the same figure.

With a more organic version being to display Figure 7 above full screen and turn the head rapidly from side to side, when I think, it being hard to be sure, something of the same sort is happening. Up and down is not so easy, given that all my computer screens are a lot wider than they are high.

Figure 8

A familiar example of what might be something of the same sort, being the way that the sequence of identical signs on the platform saying what station one is at become progressively harder to read as the train pulls out of the station, usually to the point of illegibility, although blinking sometimes produces something that can be read. One might think that it would be easier if they were arranged across the platforms, rather than along them, thus reducing the amount of movement in the words on the sign, as seen from the train, but the railway station furnishers never seem to do that.

From where I associate, probably wrongly, to the waggon wheels in Westerns appearing to go around backwards.

Conclusions

All of which is suggests that, under horizontal movement, horizontal features will tend to be preserved, while vertical features will tend to be destroyed.

But it all depends. We have suggested one method of copying rectangle A to rectangle B, but there are lots of other ways that that something of the sort could be done. One might, for example have a scanning process rather than a sampling process. There are lots of models waiting to be written down – and some of them might have something to do with the ways in which eyes work.

Furthermore, it all depends on the assumption that the copying from one place to another involves some serial processing, the duration of which is dependant on the size of whatever it is that is being copied, on the number of pixels. Serial processing which gives rise to an integration time, during which something changes, during which our foreground object moves slightly to the right. If, contrariwise, we assume some kind of parallel connections between all the pixels of the two rectangles, the copying is more or less instantaneous and there is no blurring. Maybe the brain can afford such wideband connections some of the time, but not all of the time?

References

Reference 1: https://www.frc.org.uk/accountants/accounting-and-reporting-policy/true-and-fair-concept. For an expensive, lawyerly view of what accountants mean by the phrase ‘true and fair’, used above.