神经网络[OCR]

Question

I come looking for general tips about the program I'm writing now.

The goal is: Use neural network program to recognize 3 letters [D,O,M] (or display "nothing is recognized" if i input anything other than those 3).

Here's what I have so far:

A class for my single neuron

public class neuron
{
    double[] weights;
    public neuron()
    {
        weights = null;
    }
    public neuron(int size)
    {
        weights = new double[size + 1];
        Random r = new Random();
        for (int i = 0; i <= size; i++)
        {
            weights[i] = r.NextDouble() / 5 - 0.1;
        }
    }
    public double output(double[] wej)
    {
        double s = 0.0;
        for (int i = 0; i < weights.Length; i++) s += weights[i] * wej[i];
        s = 1 / (1 + Math.Exp(s));
        return s;
    }
}

A class for a layer:

public class layer 
{
    neuron[] tab;
    public layer()
    {
        tab = null;
    }
    public layer(int numNeurons, int numInputs)
    {
        tab = new neuron[numNeurons];
        for (int i = 0; i < numNeurons; i++)
        {
            tab[i] = new neuron(numInputs);
        }
    }
    public double[] compute(double[] wejscia)
    {
        double[] output = new double[tab.Length + 1];
        output[0] = 1;
        for (int i = 1; i <= tab.Length; i++)
        {
            output[i] = tab[i - 1].output(wejscia);
        }
        return output;
    }
}

And finally a class for a network

public class network
{
    layer[] layers = null;
    public network(int numLayers, int numInputs, int[] npl)
    {
        layers = new layer[numLayers];
        for (int i = 0; i < numLayers; i++)
        {
            layers[i] = new layer(npl[i], (i == 0) ? numInputs : (npl[i - 1]));
        }

    }
    double[] compute(double[] inputs)
    {
        double[] output = layers[0].compute(inputs);
        for (int i = 1; i < layers.Length; i++)
        {
            output = layers[i].compute(output);

        }
        return output;
    }
}

Now for the algorythm I chose:

I have a picture box, size 200x200, where you can draw a letter (or read one from jpg file).

I then convert it to my first array(get the whole picture) and 2nd one(cut the non relevant background around it) like so:

Bitmap bmp2 = new Bitmap(this.pictureBox1.Image);
        int[,] binaryfrom = new int[bmp2.Width, bmp2.Height];

        int minrow=0, maxrow=0, mincol=0, maxcol=0;
        for (int i = 0; i < bmp2.Height; i++)
        {
            for (int j = 0; j < bmp2.Width; j++)
            {
                if (bmp2.GetPixel(j, i).R == 0)
                {
                    binaryfrom[i, j] = 1;
                    if (minrow == 0) minrow = i;
                    if (maxrow < i) maxrow = i;
                    if (mincol == 0) mincol = j;
                    else if (mincol > j) mincol = j;
                    if (maxcol < j) maxcol = j;
                }
                else
                {
                    binaryfrom[i, j] = 0;
                }
            }
        }


        int[,] boundaries = new int[binaryfrom.GetLength(0)-minrow-(binaryfrom.GetLength(0)-(maxrow+1)),binaryfrom.GetLength(1)-mincol-(binaryfrom.GetLength(1)-(maxcol+1))];

        for(int i = 0; i < boundaries.GetLength(0); i++)
        {
            for(int j = 0; j < boundaries.GetLength(1); j++)
            {
                boundaries[i, j] = binaryfrom[i + minrow, j + mincol];

            }
        }

And convert it to my final array of 12x8 like so (i know I could shorten this a fair bit, but wanted to have every step in different loop so I can see what went wrong easier[if anything did]):

int[,] finalnet = new int[12, 8];

        int k = 1;
        int l = 1;

        for (int i = 0; i < finalnet.GetLength(0); i++)
        {
            for (int j = 0; j < finalnet.GetLength(1); j++)
            {
                finalnet[i, j] = 0;
            }
        }

        while (k <= finalnet.GetLength(0))
            {
                while (l <= finalnet.GetLength(1))
                {
                    for (int i = (int)(boundaries.GetLength(0) / finalnet.GetLength(0)) * (k - 1); i < (int)(boundaries.GetLength(0) / finalnet.GetLength(0)) * k; i++)
                    {
                        for (int j = (int)(boundaries.GetLength(1) / finalnet.GetLength(1)) * (l - 1); j < (int)(boundaries.GetLength(1) / finalnet.GetLength(1)) * l; j++)
                        {
                            if (boundaries[i, j] == 1) finalnet[k-1, l-1] = 1;
                        }
                    }
                    l++;
                }
                l = 1;
                k++;
            }
        int a = boundaries.GetLength(0);
        int b = finalnet.GetLength(1);
       if((a%b) != 0){

            k = 1;

            while (k <= finalnet.GetLength(1))
            {
                for (int i = (int)(boundaries.GetLength(0) / finalnet.GetLength(0)) * finalnet.GetLength(0); i < boundaries.GetLength(0); i++)
                {
                    for (int j = (int)(boundaries.GetLength(1) / finalnet.GetLength(1)) * (k - 1); j < (int)(boundaries.GetLength(1) / finalnet.GetLength(1)) * k; j++)
                    {
                        if (boundaries[i, j] == 1) finalnet[finalnet.GetLength(0) - 1, k - 1] = 1;
                    }

                }
                k++;
            }
        }

        if (boundaries.GetLength(1) % finalnet.GetLength(1) != 0)
        {
            k = 1;

            while (k <= finalnet.GetLength(0))
            {
                for (int i = (int)(boundaries.GetLength(0) / finalnet.GetLength(0)) * (k - 1); i < (int)(boundaries.GetLength(0) / finalnet.GetLength(0)) * k; i++)
                {
                    for (int j = (int)(boundaries.GetLength(1) / finalnet.GetLength(1)) * finalnet.GetLength(1); j < boundaries.GetLength(1); j++)
                    {
                        if (boundaries[i, j] == 1) finalnet[k - 1, finalnet.GetLength(1) - 1] = 1;
                    } 
                }
                k++;
            }

            for (int i = (int)(boundaries.GetLength(0) / finalnet.GetLength(0)) * finalnet.GetLength(0); i < boundaries.GetLength(0); i++)
            {
                for (int j = (int)(boundaries.GetLength(1) / finalnet.GetLength(1)) * finalnet.GetLength(1); j < boundaries.GetLength(1); j++)
                {
                    if (boundaries[i, j] == 1) finalnet[finalnet.GetLength(0) - 1, finalnet.GetLength(1) - 1] = 1;
                }
            }
        }

The result is a 12x8 (I can change it in the code to get it from some form controls) array of 0 and 1, where 1 form the rough shape of a letter you drawn.

Now my questions are: Is this a correct algorythm? Is my function

1/(1+Math.Exp(x))

good one to use here? What should be the topology? 2 or 3 layers, and if 3, how many neurons in hidden layer? I have 96 inputs (every field of the finalnet array), so should I also take 96 neurons in the first layer? Should I have 3 neurons in the final layer or 4(to take into account the "not recognized" case), or is it not necessary?

Thank you for your help.

EDIT: Oh, and I forgot to add, I'm gonna train my network using Backpropagation algorythm.

Answer 1

1. You may need 4 layers at least to get accurate results using back propagation method. 1 input, 2 middle layers, and an output layer.

2. 12 * 8 matrix is too small(and you may end up in data loss which will result in total failure) - try some thing 16 * 16. If you want to reduce the size then you have to peel out the outer layers of black pixels further.

3. Think about training the network with your reference characters.

4. Remember that you have to feed back the output back to the input layer again and iterate it multiple times.

Answer 2

A while back I created a neural net to recognize digits 0-9 (python, sorry), so based on my (short) experience, 3 layers are ok and 96/50/3 topology will probably do a good job. As for the output layer, it's your choice; you can either backpropagate all 0s when the input image is not a D, O or M or use the fourth output neuron to indicate that the letter was not recognized. I think that the first option would be the best one because it's simpler (shorter training time, less problems debugging the net...), you just need to apply a threshold under which you classify the image as 'not recognized'.
I also used the sigmoid as activation function, I didn't try others but it worked :)