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# Neural Network OCR

, 11 Aug 2005 GPL3
Some ideas about optical character recognition using neural networks.
 AForge.Imaging.dll AForge.Math.dll AForge.NeuralNet.dll NeuroOCR.exe SourceGrid2.dll SourceLibrary.dll AForge Math Math.csproj.user NeuralNet Learning NeuralNet.csproj.user NeuroOCR App.ico NeuroOCR.csproj.user References AForge.Imaging.dll SourceGrid2.dll SourceLibrary.dll ```// AForge Math Library // // Copyright � Andrew Kirillov, 2005 // andrew.kirillov@gmail.com // namespace AForge.Math { using System; /// /// Fourier transformation direction /// public enum FourierDirection { Forward = 1, Backward = -1 }; /// /// Fourier Transformation /// public class FourierTransform { // One dimensional Discrete Fourier Transform public static void DFT(Complex[] data, FourierDirection direction) { int n = data.Length; double arg, cos, sin; Complex[] dst = new Complex[n]; // for each destination element for (int i = 0; i < n; i++) { dst[i] = Complex.Zero; arg = - (int) direction * 2.0 * System.Math.PI * (double) i / (double) n; // sum source elements for (int j = 0; j < n; j++) { cos = System.Math.Cos(j * arg); sin = System.Math.Sin(j * arg); dst[i].Re += (float) (data[j].Re * cos - data[j].Im * sin); dst[i].Im += (float) (data[j].Re * sin + data[j].Im * cos); } } // copy elements if (direction == FourierDirection.Forward) { // devide also for forward transform for (int i = 0; i < n; i++) { data[i].Re = dst[i].Re / n; data[i].Im = dst[i].Im / n; } } else { for (int i = 0; i < n; i++) { data[i].Re = dst[i].Re; data[i].Im = dst[i].Im; } } } // Two dimensional Discrete Fourier Transform public static void DFT2(Complex[,] data, FourierDirection direction) { int n = data.GetLength(0); // rows int m = data.GetLength(1); // columns double arg, cos, sin; Complex[] dst = new Complex[System.Math.Max(n, m)]; // process rows for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { dst[j] = Complex.Zero; arg = - (int) direction * 2.0 * System.Math.PI * (double) j / (double) m; // sum source elements for (int k = 0; k < m; k++) { cos = System.Math.Cos(k * arg); sin = System.Math.Sin(k * arg); dst[j].Re += (float) (data[i, k].Re * cos - data[i, k].Im * sin); dst[j].Im += (float) (data[i, k].Re * sin + data[i, k].Im * cos); } } // copy elements if (direction == FourierDirection.Forward) { // devide also for forward transform for (int j = 0; j < m; j++) { data[i, j].Re = dst[j].Re / m; data[i, j].Im = dst[j].Im / m; } } else { for (int j = 0; j < m; j++) { data[i, j].Re = dst[j].Re; data[i, j].Im = dst[j].Im; } } } // process columns for (int j = 0; j < m; j++) { for (int i = 0; i < n; i++) { dst[i] = Complex.Zero; arg = - (int) direction * 2.0 * System.Math.PI * (double) i / (double) n; // sum source elements for (int k = 0; k < n; k++) { cos = System.Math.Cos(k * arg); sin = System.Math.Sin(k * arg); dst[i].Re += (float) (data[k, j].Re * cos - data[k, j].Im * sin); dst[i].Im += (float) (data[k, j].Re * sin + data[k, j].Im * cos); } } // copy elements if (direction == FourierDirection.Forward) { // devide also for forward transform for (int i = 0; i < n; i++) { data[i, j].Re = dst[i].Re / n; data[i, j].Im = dst[i].Im / n; } } else { for (int i = 0; i < n; i++) { data[i, j].Re = dst[i].Re; data[i, j].Im = dst[i].Im; } } } } // One dimensional Fast Fourier Transform public static void FFT(Complex[] data, FourierDirection direction) { int n = data.Length; int m = Tools.Log2(n); // reorder data first ReorderData(data); // compute FFT int tn = 1, tm; for (int k = 1; k <= m; k++) { Complex[] rotation = FourierTransform.GetComplexRotation(k, direction); tm = tn; tn <<= 1; for (int i = 0; i < tm; i++) { Complex t = rotation[i]; for (int even = i; even < n; even += tn) { int odd = even + tm; Complex ce = data[even]; Complex co = data[odd]; float tr = co.Re * t.Re - co.Im * t.Im; float ti = co.Re * t.Im + co.Im * t.Re; data[even].Re += tr; data[even].Im += ti; data[odd].Re = ce.Re - tr; data[odd].Im = ce.Im - ti; } } } if (direction == FourierDirection.Forward) { for (int i = 0; i < n; i++) { data[i].Re /= (float) n; data[i].Im /= (float) n; } } } // Two dimensional Fast Fourier Transform public static void FFT2(Complex[,] data, FourierDirection direction) { int k = data.GetLength(0); int n = data.GetLength(1); // check data size if ((!Tools.IsPowerOf2(k)) || (!Tools.IsPowerOf2(n)) || (k < minLength) || (k > maxLength) || (n < minLength) || (n > maxLength)) { throw new ArgumentException(); } // process rows Complex[] row = new Complex[n]; for (int i = 0; i < k; i++) { // copy row for (int j = 0; j < n; j++) row[j] = data[i, j]; // transform it FourierTransform.FFT(row, direction); // copy back for (int j = 0; j < n; j++) data[i, j] = row[j]; } // process columns Complex[] col = new Complex[k]; for (int j = 0; j < n; j++) { // copy column for (int i = 0; i < k; i++) col[i] = data[i, j]; // transform it FourierTransform.FFT(col, direction); // copy back for (int i = 0; i < k; i++) data[i, j] = col[i]; } } #region Private Region private const int minLength = 2; private const int maxLength = 16384; private const int minBits = 1; private const int maxBits = 14; private static int[][] reversedBits = new int[maxBits][]; private static Complex[,][] complexRotation = new Complex[maxBits, 2][]; // Get array, indicating which data members should be swapped before FFT private static int[] GetReversedBits(int numberOfBits) { if ((numberOfBits < minBits) || (numberOfBits > maxBits)) throw new ArgumentOutOfRangeException(); // check if the array is already calculated if (reversedBits[numberOfBits - 1] == null) { int n = Tools.Pow2(numberOfBits); int[] rBits = new int[n]; // calculate the array for (int i = 0; i < n; i++) { int oldBits = i; int newBits = 0; for (int j = 0; j < numberOfBits; j++) { newBits = (newBits << 1) | (oldBits & 1); oldBits = (oldBits >> 1); } rBits[i] = newBits; } reversedBits[numberOfBits - 1] = rBits; } return reversedBits[numberOfBits - 1]; } // Get rotation of complex number private static Complex[] GetComplexRotation(int numberOfBits, FourierDirection direction) { int directionIndex = (direction == FourierDirection.Forward) ? 0 : 1; // check if the array is already calculated if (complexRotation[numberOfBits - 1, directionIndex] == null) { int n = 1 << (numberOfBits - 1); float uR = 1.0f; float uI = 0.0f; double angle = System.Math.PI / n * (int) direction; float wR = (float) System.Math.Cos(angle); float wI = (float) System.Math.Sin(angle); float t; Complex[] rotation = new Complex[n]; for (int i = 0; i < n; i++ ) { rotation[i] = new Complex(uR, uI); t = uR * wI + uI * wR; uR = uR * wR - uI * wI; uI = t; } complexRotation[numberOfBits - 1, directionIndex] = rotation; } return complexRotation[numberOfBits - 1, directionIndex]; } // Reorder data for FFT using private static void ReorderData(Complex[] data) { int len = data.Length; // check data length if ((len < minLength) || (len > maxLength) || (!Tools.IsPowerOf2(len))) throw new ArgumentException(); int[] rBits = GetReversedBits(Tools.Log2(len)); for (int i = 0; i < len; i++) { int s = rBits[i]; if (s > i) { Complex t = data[i]; data[i] = data[s]; data[s] = t; } } } #endregion } } ```

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