Field of Science

That about says it

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Truly, time to get out

2 comments:

  1. Not too much erudite, but very effective, indeed. ;)

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  2. colin@barrass-brough.org4:09 PM, February 05, 2009

    Character Recognition
    This might interest you, from my weblog www.barrass-brough.org

    06/07/06 02:10 [Thursday]

    I have been preparing - in my mind and in a diagram (Fig. 1) - an explanation of my ideas about the way neural structures recognise patterns.

    Fig. 1(a) shows a computer model of a structure of neurons, and Fig. 1(b) more the way it would be embodied in a living organism. The red spots are to be thought of as terminations in a pre-processing part of the brain of dendritic links from sense organs. You could think of the array of red spots as cells in the retina. The green spots represent the same thing stored up from a past occasion. You could think of the array of green spots as a memory trace (from one particular sense organ, eg a recording of the state of the retina on some past occasion).

    What I allege happens is the signal at a red spot - the excitement of a cell in the retina - is transmitted outwards to surrounding green spots, with decay as the signal travels further. (In Fig. 1(b) I have shown an indication of three linking dendrites between present excitement and past excitement.) The green spots receiving the signal respond according to

    (1) the signal received (which depends on the excitement of the sense organ at that particular spot and inversely on the dissimilarity in position between red spot and green spot)

    (2) the strength of the memory trace - how excited the green spot was at the time the memory trace was recorded.

    In the computer model - Fig. 1(a) - the ‘dissimilarity in position’ can be taken to be the distance apart of the red cell and the green cell in question. In the program I have been writing recently the ‘excitement’ of the cells is taken to be either black or white (for purposes of character recognition), and the response of a green cell with a memory of past black excitement to a present black signal in a red cell is taken to be

    distancemeasure = Exp(-distanceparam * ((a1 - b1) * (a1 - b1) + (a2 - b2) * (a2 - b2)))

    where the red cell is at (a1,a2) and the green cell is at (b1,b2).

    distanceparam is a parameter controlling the decay of the signal as it gets further from the site of present excitement. In fact I have found it useful to have two different distancemeasures, corresponding to a low distanceparam giving more significance to the general overall shape of the characters being compared and to a high distanceparam giving more significance to local dissimilarities (but I am still looking into the matter).

    The overall response of the green array corresponding to each memory trace is calculated (simply by adding up the distancemeasure for all pairings of red cells and green cells, although I am finding it [as I say] necessary further to look into subtracting a factor for local dissimilarities) and the memory trace corresponding to the highest responding green array (the ‘best match’) is selected. This works a lot of the time in recognising characters.

    The reason I am using the above formula for distancemeasure is that the obvious measure of dissimilarity in position is the Cartesian distance, and to convert to the exponential form without (say) taking the square root is easy and has the advantages of the ‘bell curve’ shape of the graph. That is the response is reasonable up to a certain dissimilarity in position and then rapidly falls off. However there are considerations involving the relationship between the number of distancemeasures being added up (which varies as the square of the number of red and green cells) and the sort of value each distancemeasure takes in relation to the dissimilarity in position (the number of cells in a given area varying as the square of the Cartesian radius from the central cell).

    Increasing the resolution - by increasing the number of red and green cells so that each one corresponds more closely to a signal from the sense organ at a particular position - would increase the response as the square of the cell density. On the other hand there must be a discounting effect - eg from inhibitory neurons or from habituation - as those of us with higher resolution do not necessarily respond more.

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