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Course CVCis: Computer Vision with C#
Chapter C6: The Complete Code of the Fourier Transform Project
Copyright © by V. Miszalok, last update: 2011-09-13
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Main Menu after start of VC# 2010 Express: File -> New Project... -> Visual Studio installed templates: Windows Forms Application
Name: fourier_transform1 -> Location: C:\temp -> Create directory for solution: switch off -> OK
Delete two superfluous files: Form1.Designer.cs and Program.cs.
Replace the preprogrammed code of Form1.cs by:
using System;
using System.Drawing;
using System.Windows.Forms;
using System.Collections;
using System.Text;
using System.IO;
public class Form1 : Form
{ [STAThread] static void Main() { Application.Run( new Form1() ); }
const Int32 xSize = 16;
const Int32 ySize = 16;
Byte[,] i0 = new Byte[ySize, xSize];// raster matrix
Byte threshold = 1;
Brush[] brush = new Brush[10];//for 10 different gray values
Brush redbrush = new SolidBrush( Color.Red );
Brush bluebrush = new SolidBrush( Color.Blue );
Brush graybrush = new SolidBrush( Color.Gray );
Brush greenbrush = new SolidBrush( Color.Green );
Pen redpen1 = new Pen( Color.Red, 1 );
Pen redpen5 = new Pen( Color.Red, 5 );
Pen greenpen = new Pen( Color.Green, 5 );
Pen bluepen = new Pen( Color.Blue, 5 );
Pen yellowpen = new Pen( Color.Yellow,5 );
Pen whitepen;
Font arial10 = new Font( "Arial", 10 );
Font arial20 = new Font( "Arial", 20 );
Button[] button = new Button[ySize];
Int32 i, x, y, dx, dy, backtransform;
Point p0, p1;
struct crackcode { public Point start; public String cracks; }
struct FPoint { public float x; public float y; }
crackcode cc;
Graphics g;
ArrayList pointArray = new ArrayList();
ArrayList phi1;
float[] phi2, phi3, fr, fi;
public Form1()
{ BackColor = Color.White;
Text = "Fourier Transform";
SetStyle( ControlStyles.ResizeRedraw, true );
Width = 800;
Height = 600;
for ( i=0; i < 10; i++ )// 10 brushes with 10 different gray values
brush[i] = new SolidBrush( Color.FromArgb( i*25, i*25, i*25 ) );
for ( y=0; y < ySize; y++ )//a column of buttons
{ button[y] = new Button();
Controls.Add( button[y] );
button[y].BackColor = Color.Gray;
button[y].Text = "nothing";
button[y].Name = y.ToString();
button[y].Click += new EventHandler( do_it );
}
button[0].Name = button[0].Text = "FourierTransf";
button[1].Name = "Back";
button[2].Name = button[2].Text = "Clear";
button[3].Name = "Threshold";
button[4].Name = button[4].Text = "Noise";
button[1].Text = "Back=0";
button[3].Text = "Threshold=1";
cc.cracks = "";
} // end of constructor
protected override void OnPaint( PaintEventArgs e )
{ g = e.Graphics;
String s;
Rectangle r = ClientRectangle;
dx = r.Width / (xSize+2);
dy = (r.Height - 2 * FontHeight ) / ySize;
for ( y=0; y < ySize; y++ )
{ button[y].Top = y*dy+1;
button[y].Left = xSize*dx+1;
button[y].Width = r.Width - button[y].Left - 2;
button[y].Height = dy-2;
}
button[1].Text = "Back=" + backtransform.ToString();
button[3].Text = "Threshold=" + threshold.ToString();
//draw the raster matrix
for ( y=0; y < ySize; y++ )
for ( x=0; x < xSize; x++ )
g.FillRectangle( brush[i0[y,x]], x*dx, y*dy, dx, dy );
//draw the initial invitation
if ( cc.cracks.Length == 0 )
{ s = "Draw something -> FourierTransf -> BackTransf";
g.DrawString( s, arial10, redbrush, (xSize*dx)/4, 0 );
return;
}
//draw the crack code
x = cc.start.X;
y = cc.start.Y;
for ( i = 0; i < cc.cracks.Length; i++ )
switch ( cc.cracks[i] )
{ case 'e': g.DrawLine( redpen5, x*dx, y*dy, (x+1)*dx, y*dy ); x++; break;
case 's': g.DrawLine( redpen5, x*dx, y*dy, x*dx, (y+1)*dy ); y++; break;
case 'w': g.DrawLine( redpen5, x*dx, y*dy, (x-1)*dx, y*dy ); x--; break;
case 'n': g.DrawLine( redpen5, x*dx, y*dy, x*dx, (y-1)*dy ); y--; break;
}
g.FillRectangle( bluebrush, x*dx-5, y*dy-5, 11, 11 );
//draw some info into the white space below the image
try
{ s = " No. of cracks = " + cc.cracks.Length.ToString() + " ";
s += " No. of Fourier steps = " + fr.Length.ToString();
g.DrawString( s, arial10, redbrush, 0, ySize*dy );
} catch { return; }
//draw both Fourier coefficient curves
g.DrawString( "fr", arial20, greenbrush, 10, 10 );
g.DrawString( "fi", arial20, bluebrush , 10, 40 );
float x0, y0, x1, y1, y0fr, y1fr, y0fi, y1fi, y_zoom = 3;
for ( i=0; i < fr.Length; i++ )
{ x0 = i * xSize*dx / fr.Length;
x1 = (i+1) * xSize*dx / fr.Length;
y0fr = y_zoom * fr[i ] + r.Height/2;
y0fi = y_zoom * fi[i ] + r.Height/2;
//fr[i+1], fi[i+1] can be beyond the arrays. If so, set them to 0.
try { y1fr = y_zoom * fr[i+1] + r.Height/2;
y1fi = y_zoom * fi[i+1] + r.Height/2; }
catch { y1fr = y1fi = r.Height/2; }
g.DrawLine( greenpen, x0, y0fr, x1, y1fr );
g.DrawLine( bluepen , x0, y0fi, x1, y1fi );
}
//draw the no.s of coefficents on the x-axis
Int32 step = fr.Length < (ySize*dy / 10) ? 1 : 2;
for ( i=0; i <= fr.Length; i+=step )
{ x0 = i * xSize*dx / fr.Length;
if ( i <= backtransform ) g.FillRectangle( graybrush, x0-4, r.Height/2-5, 17, 17 );
g.DrawString( i.ToString(), arial10, redbrush, x0-4, r.Height/2-5 );
}
//create a polygon (with float x, y) from the back-transformed phi3
const double angle_to_arcus = 2 * Math.PI / 360;
double circular_angle_per_crack = 360.0f / cc.cracks.Length;
double angle = 0;
FPoint[] polygon_f = new FPoint[phi3.Length];
float xmin, ymin, xmax, ymax;
xmin = xmax = polygon_f[0].x = cc.start.X;
ymin = ymax = polygon_f[0].y = cc.start.Y;
for ( i=0; i < phi3.Length-1; i++ )
{ angle = angle + angle_to_arcus * (phi3[i] - circular_angle_per_crack);
x1 = polygon_f[i+1].x = polygon_f[i].x - (float)Math.Cos( angle );
y1 = polygon_f[i+1].y = polygon_f[i].y - (float)Math.Sin( angle );
if ( x1 > xmax ) xmax = x1;
if ( y1 > ymax ) ymax = y1;
if ( x1 < xmin ) xmin = x1;
if ( y1 < ymin ) ymin = y1;
}
//The following 6 lines keep the complete polygon inside the window
float w = xmax - xmin + cc.start.X;
float h = ymax - ymin + cc.start.Y;
if (xmin < 0 ) for ( i=0; i < phi3.Length; i++ ) polygon_f[i].x -= xmin;
if (ymin < 0 ) for ( i=0; i < phi3.Length; i++ ) polygon_f[i].y -= ymin;
if (w > xSize) for ( i=0; i < phi3.Length; i++ ) polygon_f[i].x *= xSize/w;
if (h > ySize) for ( i=0; i < phi3.Length; i++ ) polygon_f[i].y *= ySize/h;
//draw the polygon
for ( i=0; i < phi3.Length-1; i++ )
{ x0 = polygon_f[i].x; x1 = polygon_f[i+1].x;
y0 = polygon_f[i].y; y1 = polygon_f[i+1].y;
g.DrawLine( yellowpen, x0*dx, y0*dy, x1*dx, y1*dy );
}
//close the polygon
x0 = polygon_f[phi3.Length-1].x; x1 = polygon_f[0].x;
y0 = polygon_f[phi3.Length-1].y; y1 = polygon_f[0].y;
g.DrawLine( yellowpen, x0*dx, y0*dy, x1*dx, y1*dy );
} // end of OnPaint(...)
protected override void OnMouseDown( MouseEventArgs e )
{ p0.X = e.X;
p0.Y = e.Y;
pointArray.Add( p0 );
whitepen = new Pen( Color.White, dx < dy ? dx : dy );
whitepen.StartCap = whitepen.EndCap = System.Drawing.Drawing2D.LineCap.Round;
}
protected override void OnMouseMove( MouseEventArgs e )
{ if ( e.Button == MouseButtons.None ) return;
p1.X = e.X;
p1.Y = e.Y;
//Insert an additional point if the distance is too far
if ( Math.Abs( p1.X - p0.X ) >= dx || Math.Abs( p1.Y - p0.Y ) >= dy )
pointArray.Add( new Point( (p1.X + p0.X)/2, (p1.Y + p0.Y)/2 ) );
pointArray.Add( p1 );
g = this.CreateGraphics();
g.DrawLine( whitepen, p0, p1 );
p0 = p1;
}
private void do_it( object sender, System.EventArgs e )
{ switch( ((Button)sender).Name)
{ case "Threshold"://*************************************
if ( ++threshold > 9 ) threshold = 1;
button[3].Text = "Threshold=" + threshold.ToString();
cc.cracks =""; break;
case "Noise"://****************************************
Random random = new Random();
for ( y=0; y < ySize; y++ )
for ( x=0; x < xSize; x++ )
{ Int32 noise = random.Next() % 3 - 1;//gives -1 or 0 or +1
noise += i0[y,x];//add former gray value
if (noise < 0) i0[y,x] = 0;
else if (noise > 9) i0[y,x] = 9;
else i0[y,x] = (Byte)noise;
}
cc.cracks =""; break;
case "Clear"://*******************************************
for ( y=0; y < ySize; y++ )
for ( x=0; x < xSize; x++ ) i0[y,x] = 0;
backtransform = threshold = 1;
cc.cracks =""; pointArray.Clear(); break;
case "FourierTransf"://***********************************
//Digitize*****************************************
for ( i = 0; i < pointArray.Count; i++ )
{ Point vertex = (Point)pointArray[i];
x = vertex.X / dx;
y = vertex.Y / dy;
try { if ( i0[y,x] < 9 ) i0[y,x]++; } catch{};
}
//Crack Code 8*****************************************
//Search for a vertical start crack
Byte leftpix;
for ( y=0; y < ySize; y++ )
for ( x=0; x < xSize; x++ )
{ if ( x > 0 ) leftpix = i0[y,x-1]; else leftpix = 0;
if ( leftpix < threshold && i0[y,x] >= threshold )
{ cc.start.X = x; cc.start.Y = y; goto start_crack_found; }
}
return; //nothing to start with
start_crack_found:
Int32 xmin = x, xmax = x, ymin = y, ymax = ++y;
phi1 = new ArrayList(); phi1.Add(-90);
System.Text.StringBuilder cracks = new System.Text.StringBuilder();
cracks.Append('s');
Char last_crack = 's';
do
{ switch ( last_crack )
{ case 'e': if ( x == xSize ) { phi1.Add(-90); goto n; }
if ( y < ySize && i0[y ,x ] >= threshold) { phi1.Add(+90); goto s; }
if ( i0[y-1,x ] >= threshold) { phi1.Add( 0); goto e; }
{ phi1.Add(-90); goto n; }
case 's': if ( y == ySize ) { phi1.Add(-90); goto e; }
if ( x > 0 && i0[y ,x-1] >= threshold) { phi1.Add(+90); goto w; }
if ( i0[y ,x ] >= threshold) { phi1.Add( 0); goto s; }
{ phi1.Add(-90); goto e; }
case 'w': if ( x == 0 ) { phi1.Add(-90); goto s; }
if ( y > 0 && i0[y-1,x-1] >= threshold) { phi1.Add(+90); goto n; }
if ( i0[y ,x-1] >= threshold) { phi1.Add( 0); goto w; }
{ phi1.Add(-90); goto s; }
case 'n': if ( y == 0 ) { phi1.Add(-90); goto w; }
if ( x < xSize && i0[y-1,x ] >= threshold) { phi1.Add(+90); goto e; }
if ( i0[y-1,x-1] >= threshold) { phi1.Add( 0); goto n; }
{ phi1.Add(-90); goto w; }
}
e: last_crack = 'e'; cracks.Append( 'e' ); x++; continue;
s: last_crack = 's'; cracks.Append( 's' ); y++; continue;
w: last_crack = 'w'; cracks.Append( 'w' ); x--; continue;
n: last_crack = 'n'; cracks.Append( 'n' ); y--; continue;
} while ( x != cc.start.X || y != cc.start.Y ); //end of do
cc.cracks = cracks.ToString();
Int32 N = cc.cracks.Length;
//Bad property of function phi1: All phi1[i] sum up to -360 degrees
phi2 = new float[N]; //Fourier transform needs float values
phi3 = new float[N]; //Back transform creates float values
float circular_angle_per_crack = 360.0f / N;
for ( i=0; i < N; i++ )//Construction of a phi2 with a sum of 0
phi2[i] = (Int32)phi1[i] + circular_angle_per_crack;
//Fourier Transform*****************************************************************
fr = new float[N/2+1];
fi = new float[N/2+1];
FourierTransform( phi2, fr, fi ); //output = fr, fi
//just for fun: immediate back transform
backtransform = fr.Length;
FourierBackTransform( fr, fi, phi3, backtransform ); //output = phi3
break;
case "Back"://*************************************
if ( cc.cracks.Length == 0 ) return;
if ( ++backtransform > fr.Length ) backtransform = 0;
FourierBackTransform( fr, fi, phi3, backtransform ); //output = phi3
break;
} // end of switch, end of all cases
Invalidate();
} // end of protected void do_it( object sender, System.EventArgs e )
private void FourierTransform( float[] a, float[] fr, float[] fi )
{ int Na = a.Length, Nf = fr.Length;
float sum_r, sum_i; fr[0] = fi[0] = 0;
for ( i=0; i < Na; i++ ) fr[0] += a[i]; fr[0] /= Na;//fr[0] is the average = 0.
double dpi_div_N, x1_dpi_div_N, x2_x1_dpi_div_N;
dpi_div_N = 2 * Math.PI / Na;
for ( int x1 = 1; x1 < Nf; x1++ )
{ sum_r = sum_i = 0;
x1_dpi_div_N = (double)x1 * dpi_div_N;
for ( int x2 = 0; x2 < Na; x2++ )
{ x2_x1_dpi_div_N = (double)x2 * x1_dpi_div_N;
sum_r += a[x2] * (float)Math.Cos( -x2_x1_dpi_div_N );
sum_i += a[x2] * (float)Math.Sin( -x2_x1_dpi_div_N );
}
fr[x1] = 2 * sum_r / (float)Na;
fi[x1] = 2 * sum_i / (float)Na;
}
fr[Nf-1] /= 2; fi[Nf-1] /= 2;
} // end of private void FourierTransform(...)
private void FourierBackTransform( float[] fr, float[] fi, float[] a, int Nf )
{ if ( Nf > fr.Length ) return;
int Na = a.Length;
Array.Clear( a, 0, a.Length );
double dpi_div_N, x1_dpi_div_N, x2_x1_dpi_div_N;
dpi_div_N = 2 * Math.PI / Na;
for ( int x1 = 0; x1 < Na; x1++ )
{ x1_dpi_div_N = (double)x1 * dpi_div_N;
for ( int x2 = 0; x2 < Nf; x2++ )
{ x2_x1_dpi_div_N = (double)x2 * x1_dpi_div_N;
a[x1] += fr[x2] * (float)Math.Cos( x2_x1_dpi_div_N ) -
fi[x2] * (float)Math.Sin( x2_x1_dpi_div_N );
}
}
} // end of private void FourierBackTransform(...)
}
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