Step detection | Software by Default

Posts Tagged 'Step detection'

C# How to: Difference Of Gaussians

Article purpose

In this article we explore the concept of Difference of Gaussians edge detection. This article implements image convolution as a means of achieving Gaussian blurring. All of the concepts explored are implemented by accessing and manipulating the raw pixel data exposed by an image, no GDI+ or conventional drawing code is required.

Sample source code

This article is accompanied by a sample source code Visual Studio project which is available for download here.

Using the Sample Application

The concepts explored in this article can be easily replicated by making use of the Sample Application, which forms part of the associated sample source code accompanying this article.

When using the Difference Of Gaussians sample application you can specify a input/source image by clicking the Load Image button. The dropdown combobox towards the bottom middle part of the screen relates the various edge detection methods discussed.

If desired a user can save the resulting edge detection image to the local file system by clicking the Save Image button.

The following image is screenshot of the Difference Of Gaussians sample application in action:

What is Difference of Gaussians?

Difference of Gaussians, commonly abbreviated as DoG, is a method of implementing image edge detection. Central to the Difference of Gaussians method of edge detection is the application of Gaussian image blur.

From Wikipedia we gain the following explanation:

In imaging science, Difference of Gaussians is a feature enhancement algorithm that involves the subtraction of one blurred version of an original image from another, less blurred version of the original. In the simple case of grayscale images, the blurred images are obtained by convolving the original grayscale images with Gaussian kernels having differing standard deviations. Blurring an image using a Gaussian kernel suppresses only high-frequency spatial information. Subtracting one image from the other preserves spatial information that lies between the range of frequencies that are preserved in the two blurred images. Thus, the difference of Gaussians is a band-pass filter that discards all but a handful of spatial frequencies that are present in the original grayscale image.

In simple terms Difference of Gaussians can be implemented by applying two Gaussian blurs of different intensity levels to the same source image. The resulting image is then created by subtracting the two images of different Gaussian blurring.

Applying a Convolution Matrix filter

In the sample source code accompanying this article Gaussian image blurring is applied by invoking the ConvolutionFilter method. This method accepts a two dimensional array of type double representing the convolution matrix/kernel. This method is also capable of first converting source images to grayscale, which can be specified as a method parameter. Resulting images sometimes tend to be very dark, which can be corrected by specifying a suitable bias value.

The following code snippet provides the implementation of the ConvolutionFilter method:

 private static Bitmap ConvolutionFilter(Bitmap sourceBitmap,  
                                     double[,] filterMatrix,  
                                          double factor = 1,  
                                               int bias = 0,  
                                     bool grayscale = false )  
{ 
     BitmapData sourceData = sourceBitmap.LockBits(new Rectangle (0, 0, 
                              sourceBitmap.Width, sourceBitmap.Height), 
                                                ImageLockMode.ReadOnly,  
                                          PixelFormat.Format32bppArgb); 

  
     byte[] pixelBuffer = new byte[sourceData.Stride * sourceData.Height]; 
     byte[] resultBuffer = new byte[sourceData.Stride * sourceData.Height]; 

  
     Marshal.Copy(sourceData.Scan0, pixelBuffer, 0, pixelBuffer.Length); 
     sourceBitmap.UnlockBits(sourceData); 

  
     if (grayscale == true) 
     {
         float rgb = 0; 

  
         for (int k = 0; k < pixelBuffer.Length; k += 4) 
         { 
             rgb = pixelBuffer[k] * 0.11f; 
             rgb += pixelBuffer[k + 1] * 0.59f; 
             rgb += pixelBuffer[k + 2] * 0.3f; 

  
             pixelBuffer[k] = (byte )rgb; 
             pixelBuffer[k + 1] = pixelBuffer[k]; 
             pixelBuffer[k + 2] = pixelBuffer[k]; 
             pixelBuffer[k + 3] = 255; 
         } 
     } 

  
     double blue = 0.0; 
     double green = 0.0; 
     double red = 0.0; 

  
     int filterWidth = filterMatrix.GetLength(1); 
     int filterHeight = filterMatrix.GetLength(0); 

  
     int filterOffset = (filterWidth-1) / 2; 
     int calcOffset = 0; 

  
     int byteOffset = 0; 

  
     for (int offsetY = filterOffset; offsetY <  
         sourceBitmap.Height - filterOffset; offsetY++) 
     { 
         for (int  offsetX = filterOffset; offsetX <  
             sourceBitmap.Width - filterOffset; offsetX++) 
         { 
             blue = 0; 
             green = 0; 
             red = 0; 

  
             byteOffset = offsetY *  
                          sourceData.Stride +  
                          offsetX * 4; 

   
             for (int  filterY = -filterOffset;  
                 filterY <= filterOffset; filterY++) 
             {
                 for (int  filterX = -filterOffset; 
                     filterX <= filterOffset; filterX++) 
                 { 

   
                     calcOffset = byteOffset +  
                                  (filterX * 4) +  
                                  (filterY * sourceData.Stride); 

  
                     blue += (double)(pixelBuffer[calcOffset]) * 
                             filterMatrix[filterY + filterOffset,  
                                          filterX + filterOffset]; 

  
                     green += (double)(pixelBuffer[calcOffset + 1]) * 
                              filterMatrix[filterY + filterOffset,  
                                           filterX + filterOffset]; 

   
                     red += (double)(pixelBuffer[calcOffset + 2]) * 
                            filterMatrix[filterY + filterOffset,  
                                         filterX + filterOffset]; 
                 }
             }

   
             blue = factor * blue + bias; 
             green = factor * green + bias; 
             red = factor * red + bias; 

  
             if (blue > 255) 
             { blue = 255; } 
             else if (blue < 0) 
             { blue = 0; } 

  
             if (green > 255) 
             { green = 255; } 
             else if (green < 0) 
             { green = 0; } 

  
             if (red > 255) 
             { red = 255; } 
             else if (red < 0) 
             { red = 0; } 

  
             resultBuffer[byteOffset] = (byte )(blue); 
             resultBuffer[byteOffset + 1] = (byte )(green); 
             resultBuffer[byteOffset + 2] = (byte )(red); 
             resultBuffer[byteOffset + 3] = 255; 
        }
    } 

  
     Bitmap resultBitmap = new Bitmap(sourceBitmap.Width,
                                      sourceBitmap.Height); 
  
     BitmapData resultData = resultBitmap.LockBits(new Rectangle (0, 0, 
                              resultBitmap.Width, resultBitmap.Height), 
                                               ImageLockMode .WriteOnly, 
                                          PixelFormat.Format32bppArgb); 

  
     Marshal.Copy(resultBuffer, 0, resultData.Scan0, resultBuffer.Length); 
     resultBitmap.UnlockBits(resultData); 

   
     return resultBitmap; 
}

The Gaussian Matrix

The sample source code defines three Gaussian matrix/kernel values, a 3×3 matrix and two slightly different 5×5 matrices. The Gaussian3x3 matrix requires a factor of 1 / 16, the Gaussian5x5Type1 matrix a factor of 1 / 159 and the factor required by the Gaussian5x5Type2 equates to 1 / 256.

public static class Matrix
{
    public static double[,] Gaussian3x3
    {
        get
        {
            return new double[,]  
            { { 1, 2, 1, }, 
              { 2, 4, 2, },
              { 1, 2, 1, }, };
        }
    }

  
    public static double[,] Gaussian5x5Type1
    {
        get  
        {
            return new double[,]  
             { { 2, 04, 05, 04, 2  }, 
               { 4, 09, 12, 09, 4  }, 
               { 5, 12, 15, 12, 5  },
               { 4, 09, 12, 09, 4  },
               { 2, 04, 05, 04, 2  }, };
        }
    }

  
    public static double[,] Gaussian5x5Type2
    {
        get 
        {
            return new   double[,] 
             { {  1,   4,  6,  4,  1  }, 
               {  4,  16, 24, 16,  4  }, 
               {  6,  24, 36, 24,  6  },
               {  4,  16, 24, 16,  4  },
               {  1,   4,  6,  4,  1  }, };
        }
    }
}

Subtracting Images

When implementing the Difference of Gaussians method of edge detection after having applied two varying levels of Gaussian blurring the resulting images need to be subtracted. The sample source code associated with this article implements the SubtractImage extension method when subtracting images.

The following code snippet details the implementation of the SubtractImage extension method:

private static void SubtractImage(this Bitmap subtractFrom,  
                                  Bitmap subtractValue,  
                                  bool invert = false,
                                  int bias = 0) 
{ 
    BitmapData sourceData = 
               subtractFrom.LockBits(new Rectangle(0, 0, 
               subtractFrom.Width, subtractFrom.Height), 
               ImageLockMode.ReadWrite, 
               PixelFormat.Format32bppArgb); 

   
    byte[] resultBuffer = new byte[sourceData.Stride *
                                  sourceData.Height]; 

  
    Marshal.Copy(sourceData.Scan0, resultBuffer, 0,
                               resultBuffer.Length); 

   
    BitmapData subtractData =
               subtractValue.LockBits(new Rectangle(0, 0, 
               subtractValue.Width, subtractValue.Height), 
               ImageLockMode.ReadOnly, 
               PixelFormat.Format32bppArgb); 

   
    byte[] subtractBuffer = new byte[subtractData.Stride *  
                                     subtractData.Height]; 

   
    Marshal.Copy(subtractData.Scan0, subtractBuffer, 0,  
                                 subtractBuffer.Length); 

   
    subtractValue.UnlockBits(subtractData); 

   
    int blue = 0; 
    int green = 0; 
    int red = 0; 

   
    for (int k = 0; k < resultBuffer.Length &&  
                    k < subtractBuffer.Length; k += 4) 
    { 
        if (invert == true ) 
        { 
            blue = 255 - resultBuffer[k] -  
                   subtractBuffer[k] + bias; 

   
            green = 255 - resultBuffer[k + 1] -  
                    subtractBuffer[k + 1] + bias; 

   
            red = 255 - resultBuffer[k + 2] -  
                  subtractBuffer[k + 2] + bias; 
        } 
        else  
        { 
            blue = resultBuffer[k] -  
                   subtractBuffer[k] + bias; 

   
            green = resultBuffer[k + 1] -  
                    subtractBuffer[k + 1] + bias; 

   
            red = resultBuffer[k + 2] -  
                  subtractBuffer[k + 2] + bias; 
        } 

   
        blue = (blue < 0 ? 0 : (blue > 255 ? 255 : blue)); 
        green = (green < 0 ? 0 : (green > 255 ? 255 : green)); 
        red = (red < 0 ? 0 : (red > 255 ? 255 : red)); 

   
        resultBuffer[k] = (byte )blue; 
        resultBuffer[k + 1] = (byte )green; 
        resultBuffer[k + 2] = (byte )red; 
        resultBuffer[k + 3] = 255; 
    } 

   
    Marshal.Copy(resultBuffer, 0, sourceData.Scan0,  
                               resultBuffer.Length); 

   
    subtractFrom.UnlockBits(sourceData); 
}

Difference of Gaussians Extension methods

The sample source code implements Difference of Gaussians edge detection by means of two extension methods: DifferenceOfGaussians3x5Type1 and DifferenceOfGaussians3x5Type2. Both methods are virtually identical, the only difference being the 5×5 Gaussian matrix being implemented.

Both methods create two new images, each having a Gaussian blur of different levels of intensity applied. The two new images are subtracted in order to create a single resulting image.

The following source code snippet provides the implementation of the DifferenceOfGaussians3x5Type1 and DifferenceOfGaussians3x5Type2 extension methods:

public static Bitmap DifferenceOfGaussians3x5Type1(
                                  this Bitmap sourceBitmap,  
                                  bool grayscale = false, 
                                  bool invert = false, 
                                  int bias = 0) 
{
    Bitmap bitmap3x3 = ExtBitmap.ConvolutionFilter(sourceBitmap, 
                       Matrix.Gaussian3x3, 1.0 / 16.0, 
                       0, grayscale); 

  
    Bitmap bitmap5x5 = ExtBitmap.ConvolutionFilter(sourceBitmap, 
                       Matrix.Gaussian5x5Type1, 1.0 / 159.0,
                       0, grayscale); 

  
    bitmap3x3.SubtractImage(bitmap5x5, invert, bias); 

  
    return bitmap3x3; 
} 

  
public static Bitmap DifferenceOfGaussians3x5Type2(
                                  this Bitmap sourceBitmap,  
                                  bool grayscale = false, 
                                  bool invert = false, 
                                  int bias = 0) 
{ 
    Bitmap bitmap3x3 = ExtBitmap.ConvolutionFilter(sourceBitmap, 
                       Matrix.Gaussian3x3, 1.0 / 16.0, 
                       0, true ); 

  
    Bitmap bitmap5x5 = ExtBitmap.ConvolutionFilter(sourceBitmap, 
                       Matrix.Gaussian5x5Type2, 1.0 / 256.0,
                       0, true ); 

 
    bitmap3x3.SubtractImage(bitmap5x5, invert, bias); 

  
    return bitmap3x3; 
}

Sample Images

The original sample image used in this article is licensed under the Creative Commons Attribution-Share Alike 2.0 Generic license. The original author is attributed as Andrew Dunn – http://www.andrewdunnphoto.com/

The Original Image

Difference Of Gaussians 3×5 Type1

Difference Of Gaussians 3×5 Type2

Difference Of Gaussians 3×5 Type1 Bias 128

Difference Of Gaussians 3×5 Type 2 Bias 96

C# How to: Image Edge Detection

Published May 11, 2013 Augmented Reality , C# , Code Samples , Edge Detection , Extension Methods , Graphic Filters , Graphics , How to , Image Convolution , Image Filters , Microsoft , Opensource , Wikipedia 32 Comments
Tags: Augmented Reality, Bitmap ARGB, Bitmap Filters, Bitmap.LockBits, BitmapData, Blob detection, C#, Change detection, Code Sample, Computer vision, Convolution filters, Convolution Kernel, Convolution matrix, Edge Detect, Edge enhance, Feature extraction, Gaussian, Gaussian Blur, Graphic Filters, Image Noise, Image processing, Image Transform, Kirsch, Laplacian, Laplacian matrix, Laplacian of Gaussian, Machine vision, Matrix, Pixel Filters, Pixel Manipulation, Prewitt, Sobel, Step detection

Article Purpose

The objective of this article is to explore various edge detection algorithms. The types of edge detection discussed are: Laplacian, Laplacian of Gaussian, Sobel, Prewitt and Kirsch. All instances are implemented by means of Image Convolution.

Sample source code

This article is accompanied by a sample source code Visual Studio project which is available for download here.

Using the Sample Application

The concepts explored in this article can be easily replicated by making use of the Sample Application, which forms part of the associated sample source code accompanying this article.

When using the Image Edge Detection sample application you can specify a input/source image by clicking the Load Image button. The dropdown combobox towards the bottom middle part of the screen relates the various edge detection methods discussed.

If desired a user can save the resulting edge detection image to the local file system by clicking the Save Image button.

The following image is screenshot of the Image Edge Detection sample application in action:

Edge Detection

A good description of edge detection forms part of the main Edge Detection article on Wikipedia:

Edge detection is the name for a set of mathematical methods which aim at identifying points in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. The points at which image brightness changes sharply are typically organized into a set of curved line segments termed edges. The same problem of finding discontinuities in 1D signals is known as step detection and the problem of finding signal discontinuities over time is known as change detection. Edge detection is a fundamental tool in image processing, machine vision and computer vision, particularly in the areas of feature detection and feature extraction.

Image Convolution

A good introduction article to Image Convolution can be found at: http://homepages.inf.ed.ac.uk/rbf/HIPR2/convolve.htm. From the article we learn the following:

Convolution is a simple mathematical operation which is fundamental to many common image processing operators. Convolution provides a way of `multiplying together’ two arrays of numbers, generally of different sizes, but of the same dimensionality, to produce a third array of numbers of the same dimensionality. This can be used in image processing to implement operators whose output pixel values are simple linear combinations of certain input pixel values.

In an image processing context, one of the input arrays is normally just a graylevel image. The second array is usually much smaller, and is also two-dimensional (although it may be just a single pixel thick), and is known as the kernel.

Single Matrix Convolution

The sample source code implements the ConvolutionFilter method, an extension method targeting the Bitmap class. The ConvolutionFilter method is intended to apply a user defined matrix and optionally covert an image to grayscale. The implementation as follows:

private static Bitmap ConvolutionFilter(Bitmap sourceBitmap, 
                                     double[,] filterMatrix, 
                                          double factor = 1, 
                                               int bias = 0, 
                                     bool grayscale = false) 
{
    BitmapData sourceData = 
                   sourceBitmap.LockBits(new Rectangle(0, 0,
                   sourceBitmap.Width, sourceBitmap.Height),
                                     ImageLockMode.ReadOnly, 
                                PixelFormat.Format32bppArgb);

  
    byte[] pixelBuffer = new byte[sourceData.Stride *
                                  sourceData.Height];

 
    byte[] resultBuffer = new byte[sourceData.Stride *
                                   sourceData.Height];

  
    Marshal.Copy(sourceData.Scan0, pixelBuffer, 0,
                               pixelBuffer.Length);

 
    sourceBitmap.UnlockBits(sourceData);

  
    if(grayscale == true)
    {
        float rgb = 0;

  
        for(int k = 0; k < pixelBuffer.Length; k += 4)
        {
            rgb = pixelBuffer[k] * 0.11f;
            rgb += pixelBuffer[k + 1] * 0.59f;
            rgb += pixelBuffer[k + 2] * 0.3f;

  
            pixelBuffer[k] = (byte)rgb;
            pixelBuffer[k + 1] = pixelBuffer[k];
            pixelBuffer[k + 2] = pixelBuffer[k];
            pixelBuffer[k + 3] = 255;
        }
    }

  
    double blue = 0.0;
    double green = 0.0;
    double red = 0.0;

  
    int filterWidth = filterMatrix.GetLength(1);
    int filterHeight = filterMatrix.GetLength(0);

  
    int filterOffset = (filterWidth-1) / 2;
    int calcOffset = 0;

  
    int byteOffset = 0;

  
    for(int offsetY = filterOffset; offsetY < 
        sourceBitmap.Height - filterOffset; offsetY++)
    {
        for(int offsetX = filterOffset; offsetX < 
            sourceBitmap.Width - filterOffset; offsetX++)
        {
            blue = 0;
            green = 0;
            red = 0;

  
            byteOffset = offsetY * 
                         sourceData.Stride + 
                         offsetX * 4;

  
            for(int filterY = -filterOffset; 
                filterY <= filterOffset; filterY++)
            {
                for(int filterX = -filterOffset;
                    filterX <= filterOffset; filterX++)
               {

  
                   calcOffset = byteOffset + 
                                (filterX * 4) + 
                                (filterY * sourceData.Stride);

  
                   blue += (double)(pixelBuffer[calcOffset]) *
                           filterMatrix[filterY + filterOffset, 
                                        filterX + filterOffset];

  
                   green += (double)(pixelBuffer[calcOffset+1]) *
                            filterMatrix[filterY + filterOffset, 
                                         filterX + filterOffset];

  
                   red += (double)(pixelBuffer[calcOffset+2]) *
                          filterMatrix[filterY + filterOffset, 
                                       filterX + filterOffset];
                }
            }

  
            blue = factor * blue + bias;
            green = factor * green + bias;
            red = factor * red + bias;

  
            if(blue > 255)
            { blue = 255;}
            else if(blue < 0)
            { blue = 0;}

  
            if(green > 255)
            { green = 255;}
            else if(green < 0)
            { green = 0;}

  
            if(red > 255)
            { red = 255;}
            else if(red < 0)
            { red = 0;}

  
            resultBuffer[byteOffset] = (byte)(blue);
            resultBuffer[byteOffset + 1] = (byte)(green);
            resultBuffer[byteOffset + 2] = (byte)(red);
            resultBuffer[byteOffset + 3] = 255;
        }
    }

  
    Bitmap resultBitmap = new Bitmap(sourceBitmap.Width, 
                                    sourceBitmap.Height);

  
    BitmapData resultData =
               resultBitmap.LockBits(new Rectangle(0, 0,
               resultBitmap.Width, resultBitmap.Height),
                                ImageLockMode.WriteOnly,
                            PixelFormat.Format32bppArgb);

  
    Marshal.Copy(resultBuffer, 0, resultData.Scan0,
                               resultBuffer.Length);
    resultBitmap.UnlockBits(resultData);

  
    return resultBitmap;
}

Horizontal and Vertical Matrix Convolution

The ConvolutionFilter extension method has been overloaded to accept two matrices, representing a vertical matrix and a horizontal matrix. The implementation as follows:

public static Bitmap ConvolutionFilter(this Bitmap sourceBitmap,
                                        double[,] xFilterMatrix,
                                        double[,] yFilterMatrix,
                                              double factor = 1,
                                                   int bias = 0,
                                         bool grayscale = false)
{
    BitmapData sourceData = 
                   sourceBitmap.LockBits(new Rectangle(0, 0,
                   sourceBitmap.Width, sourceBitmap.Height),
                                     ImageLockMode.ReadOnly,
                                PixelFormat.Format32bppArgb);

  
    byte[] pixelBuffer = new byte[sourceData.Stride * 
                                  sourceData.Height];

  
    byte[] resultBuffer = new byte[sourceData.Stride *
                                   sourceData.Height];

  
    Marshal.Copy(sourceData.Scan0, pixelBuffer, 0,
                               pixelBuffer.Length);

  
    sourceBitmap.UnlockBits(sourceData);

  
    if (grayscale == true)
    {
        float rgb = 0;

  
        for (int k = 0; k < pixelBuffer.Length; k += 4)
        {
            rgb = pixelBuffer[k] * 0.11f;
            rgb += pixelBuffer[k + 1] * 0.59f;
            rgb += pixelBuffer[k + 2] * 0.3f;

  
            pixelBuffer[k] = (byte)rgb;
            pixelBuffer[k + 1] = pixelBuffer[k];
            pixelBuffer[k + 2] = pixelBuffer[k];
            pixelBuffer[k + 3] = 255;
        }
    }

  
    double blueX = 0.0;
    double greenX = 0.0;
    double redX = 0.0;

  
    double blueY = 0.0;
    double greenY = 0.0;
    double redY = 0.0;

  
    double blueTotal = 0.0;
    double greenTotal = 0.0;
    double redTotal = 0.0;

  
    int filterOffset = 1;
    int calcOffset = 0;

  
    int byteOffset = 0;

  
    for (int offsetY = filterOffset; offsetY <
        sourceBitmap.Height - filterOffset; offsetY++)
    {
        for (int offsetX = filterOffset; offsetX <
            sourceBitmap.Width - filterOffset; offsetX++)
        {
            blueX = greenX = redX = 0;
            blueY = greenY = redY = 0;

  
            blueTotal = greenTotal = redTotal = 0.0;

  
            byteOffset = offsetY *
                         sourceData.Stride +
                         offsetX * 4;

  
            for (int filterY = -filterOffset;
                filterY <= filterOffset; filterY++)
            {
                for (int filterX = -filterOffset;
                    filterX <= filterOffset; filterX++)
                {
                    calcOffset = byteOffset +
                                 (filterX * 4) +
                                 (filterY * sourceData.Stride);

  
                    blueX += (double)
                              (pixelBuffer[calcOffset]) *
                              xFilterMatrix[filterY + 
                                            filterOffset,
                                            filterX + 
                                            filterOffset];

  
                    greenX += (double)
                          (pixelBuffer[calcOffset + 1]) *
                              xFilterMatrix[filterY +
                                            filterOffset,
                                            filterX +
                                            filterOffset];

  
                    redX += (double)
                          (pixelBuffer[calcOffset + 2]) *
                              xFilterMatrix[filterY +
                                            filterOffset,
                                            filterX +
                                            filterOffset];

  
                    blueY += (double)
                              (pixelBuffer[calcOffset]) *
                              yFilterMatrix[filterY +
                                            filterOffset,
                                            filterX +
                                            filterOffset];

  
                    greenY += (double)
                          (pixelBuffer[calcOffset + 1]) *
                              yFilterMatrix[filterY +
                                            filterOffset,
                                            filterX +
                                            filterOffset];

  
                    redY += (double)
                          (pixelBuffer[calcOffset + 2]) *
                              yFilterMatrix[filterY +
                                            filterOffset,
                                            filterX +
                                            filterOffset];
                }
            }

  
            blueTotal = Math.Sqrt((blueX * blueX) +
                                  (blueY * blueY));

  
            greenTotal = Math.Sqrt((greenX * greenX) +
                                   (greenY * greenY));

  
            redTotal = Math.Sqrt((redX * redX) +
                                 (redY * redY));

  
            if (blueTotal > 255)
            { blueTotal = 255; }
            else if (blueTotal < 0)
            { blueTotal = 0; }

  
            if (greenTotal > 255)
            { greenTotal = 255; }
            else if (greenTotal < 0)
            { greenTotal = 0; }

  
            if (redTotal > 255)
            { redTotal = 255; }
            else if (redTotal < 0)
            { redTotal = 0; }

  
            resultBuffer[byteOffset] = (byte)(blueTotal);
            resultBuffer[byteOffset + 1] = (byte)(greenTotal);
            resultBuffer[byteOffset + 2] = (byte)(redTotal);
            resultBuffer[byteOffset + 3] = 255;
        }
    }

  
    Bitmap resultBitmap = new Bitmap(sourceBitmap.Width,
                                     sourceBitmap.Height);

  
    BitmapData resultData =
               resultBitmap.LockBits(new Rectangle(0, 0,
               resultBitmap.Width, resultBitmap.Height),
                                ImageLockMode.WriteOnly,
                            PixelFormat.Format32bppArgb);

  
    Marshal.Copy(resultBuffer, 0, resultData.Scan0,
                               resultBuffer.Length);
    resultBitmap.UnlockBits(resultData);

  
    return resultBitmap;
}

Original Sample Image

The original source image used to create all of the edge detection sample images in this article has been licensed under the Creative Commons Attribution-Share Alike 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic license. The original image is attributed to Kenneth Dwain Harrelson and can be downloaded from Wikipedia.

Laplacian Edge Detection

The Laplacian method of edge detection counts as one of the commonly used edge detection implementations. From Wikipedia we gain the following definition:

Discrete Laplace operator is often used in image processing e.g. in edge detection and motion estimation applications. The discrete Laplacian is defined as the sum of the second derivatives Laplace operator Coordinate expressions and calculated as sum of differences over the nearest neighbours of the central pixel.

A number of matrix/kernel variations may be applied with results ranging from slight to fairly pronounced. In the following sections of this article we explore two common matrix implementations, 3×3 and 5×5.

Laplacian 3×3

When implementing a 3×3 Laplacian matrix you will notice little difference between colour and grayscale result images.

public static Bitmap 
Laplacian3x3Filter(this Bitmap sourceBitmap, 
                      bool grayscale = true)
{
    Bitmap resultBitmap = 
           ExtBitmap.ConvolutionFilter(sourceBitmap, 
                                Matrix.Laplacian3x3,
                                  1.0, 0, grayscale);

 
    return resultBitmap;
}

public static double[,] Laplacian3x3
{ 
   get   
   { 
       return new double[,]
       { { -1, -1, -1, },  
         { -1,  8, -1, },  
         { -1, -1, -1, }, }; 
   } 
}

Laplacian 3×3

Laplacian 3×3 Grayscale

Laplacian 5×5

The 5×5 Laplacian matrix produces result images with a noticeable difference between colour and grayscale images. The detected edges are expressed in a fair amount of fine detail, although the Laplacian matrix has a tendency to be sensitive to image noise.

public static Bitmap 
Laplacian5x5Filter(this Bitmap sourceBitmap, 
                      bool grayscale = true)
{
    Bitmap resultBitmap =
           ExtBitmap.ConvolutionFilter(sourceBitmap, 
                                Matrix.Laplacian5x5,
                                  1.0, 0, grayscale);

 
    return resultBitmap;
}

public static double[,] Laplacian5x5 
{ 
    get   
    { 
       return new double[,]
       { { -1, -1, -1, -1, -1, },  
         { -1, -1, -1, -1, -1, },  
         { -1, -1, 24, -1, -1, },  
         { -1, -1, -1, -1, -1, },  
         { -1, -1, -1, -1, -1  } }; 
    } 
}

Laplacian 5×5

Laplacian 5×5 Grayscale

Laplacian of Gaussian

The Laplacian of Gaussian (LoG) is a common variation of the Laplacian filter. Laplacian of Gaussian is intended to counter the noise sensitivity of the regular Laplacian filter.

Laplacian of Gaussian attempts to remove image noise by implementing image smoothing by means of a Gaussian blur. In order to optimize performance we can calculate a single matrix representing a Gaussian blur and Laplacian matrix.

public static Bitmap 
LaplacianOfGaussian(this Bitmap sourceBitmap)
{
    Bitmap resultBitmap =
           ExtBitmap.ConvolutionFilter(sourceBitmap, 
                         Matrix.LaplacianOfGaussian, 
                                       1.0, 0, true);

 
    return resultBitmap;
}

public static double[,] LaplacianOfGaussian
{ 
    get   
    { 
        return new double[,]
        { {  0,  0, -1,  0,  0 },  
          {  0, -1, -2, -1,  0 },  
          { -1, -2, 16, -2, -1 }, 
          {  0, -1, -2, -1,  0 }, 
          {  0,  0, -1,  0,  0 } };
    } 
}

Laplacian of Gaussian

Laplacian (3×3) of Gaussian (3×3)

Different matrix variations can be combined in an attempt to produce results best suited to the input image. In this case we first apply a 3×3 Gaussian blur followed by a 3×3 Laplacian filter.

public static Bitmap 
Laplacian3x3OfGaussian3x3Filter(this Bitmap sourceBitmap)
{
    Bitmap resultBitmap =
           ExtBitmap.ConvolutionFilter(sourceBitmap, 
                                 Matrix.Gaussian3x3,
                                1.0 / 16.0, 0, true);

 
    resultBitmap = ExtBitmap.ConvolutionFilter(resultBitmap, 
                         Matrix.Laplacian3x3, 1.0, 0, false);

 
    return resultBitmap;
}

public static double[,] Laplacian3x3
{ 
   get   
   { 
       return new double[,]
       { { -1, -1, -1, },  
         { -1,  8, -1, },  
         { -1, -1, -1, }, }; 
   } 
}

public static double[,] Gaussian3x3
{ 
   get   
   { 
       return new double[,]
       { { 1, 2, 1, },  
         { 2, 4, 2, },  
         { 1, 2, 1, } }; 
   } 
}

Laplacian 3×3 Of Gaussian 3×3

Laplacian (3×3) of Gaussian (5×5 – Type 1)

In this scenario we apply a variation of a 5×5 Gaussian blur followed by a 3×3 Laplacian filter.

public static Bitmap 
Laplacian3x3OfGaussian5x5Filter1(this Bitmap sourceBitmap)
{
    Bitmap resultBitmap = 
           ExtBitmap.ConvolutionFilter(sourceBitmap, 
                            Matrix.Gaussian5x5Type1,
                               1.0 / 159.0, 0, true);

 
    resultBitmap = ExtBitmap.ConvolutionFilter(resultBitmap, 
                         Matrix.Laplacian3x3, 1.0, 0, false);

 
    return resultBitmap;
}

public static double[,] Laplacian3x3
{ 
   get   
   { 
       return new double[,]
       { { -1, -1, -1, },  
         { -1,  8, -1, },  
         { -1, -1, -1, }, }; 
   } 
}

public static double[,] Gaussian5x5Type1 
{ 
   get   
   { 
       return new double[,]   
       { { 2, 04, 05, 04, 2 },  
         { 4, 09, 12, 09, 4 },  
         { 5, 12, 15, 12, 5 }, 
         { 4, 09, 12, 09, 4 }, 
         { 2, 04, 05, 04, 2 }, }; 
   } 
}

Laplacian 3×3 Of Gaussian 5×5 – Type 1

Laplacian (3×3) of Gaussian (5×5 – Type 2)

The following implementation is very similar to the previous implementation. Applying a variation of a 5×5 Gaussian blur results in slight differences.

public static Bitmap 
Laplacian3x3OfGaussian5x5Filter2(this Bitmap sourceBitmap)
{
    Bitmap resultBitmap = 
           ExtBitmap.ConvolutionFilter(sourceBitmap, 
                            Matrix.Gaussian5x5Type2,
                               1.0 / 256.0, 0, true);

 
    resultBitmap = ExtBitmap.ConvolutionFilter(resultBitmap, 
                         Matrix.Laplacian3x3, 1.0, 0, false);

 
    return resultBitmap;
}

public static double[,] Laplacian3x3
{ 
   get   
   { 
       return new double[,]
       { { -1, -1, -1, },  
         { -1,  8, -1, },  
         { -1, -1, -1, }, }; 
   } 
}

public static double[,] Gaussian5x5Type2 
{ 
   get   
   {
       return new double[,]  
       { {  1,   4,  6,  4,  1 },  
         {  4,  16, 24, 16,  4 },  
         {  6,  24, 36, 24,  6 }, 
         {  4,  16, 24, 16,  4 }, 
         {  1,   4,  6,  4,  1 }, }; 
   }
}

Laplacian 3×3 Of Gaussian 5×5 – Type 2

Laplacian (5×5) of Gaussian (3×3)

This variation of the Laplacian of Gaussian filter implements a 3×3 Gaussian blur, followed by a 5×5 Laplacian matrix. The resulting image appears significantly brighter when compared to a 3×3 Laplacian matrix.

public static Bitmap 
Laplacian5x5OfGaussian3x3Filter(this Bitmap sourceBitmap)
{
    Bitmap resultBitmap = 
           ExtBitmap.ConvolutionFilter(sourceBitmap, 
                                 Matrix.Gaussian3x3,
                                1.0 / 16.0, 0, true);

 
    resultBitmap = ExtBitmap.ConvolutionFilter(resultBitmap,
                         Matrix.Laplacian5x5, 1.0, 0, false);

 
    return resultBitmap;
}

public static double[,] Laplacian5x5 
{ 
    get   
    { 
       return new double[,]
       { { -1, -1, -1, -1, -1, },  
         { -1, -1, -1, -1, -1, },  
         { -1, -1, 24, -1, -1, },  
         { -1, -1, -1, -1, -1, },  
         { -1, -1, -1, -1, -1  } }; 
    } 
}

public static double[,] Gaussian3x3
{ 
   get   
   { 
       return new double[,]
       { { 1, 2, 1, },  
         { 2, 4, 2, },  
         { 1, 2, 1, } }; 
   } 
}

Laplacian 5×5 Of Gaussian 3×3

Laplacian (5×5) of Gaussian (5×5 – Type 1)

Implementing a larger Gaussian blur matrix results in a higher degree of image smoothing, equating to less image noise.

public static Bitmap 
Laplacian5x5OfGaussian5x5Filter1(this Bitmap sourceBitmap)
{
    Bitmap resultBitmap = 
           ExtBitmap.ConvolutionFilter(sourceBitmap, 
                            Matrix.Gaussian5x5Type1,
                               1.0 / 159.0, 0, true);

 
    resultBitmap = ExtBitmap.ConvolutionFilter(resultBitmap,
                         Matrix.Laplacian5x5, 1.0, 0, false);

 
    return resultBitmap;
}

public static double[,] Laplacian5x5 
{ 
    get   
    { 
       return new double[,]
       { { -1, -1, -1, -1, -1, },  
         { -1, -1, -1, -1, -1, },  
         { -1, -1, 24, -1, -1, },  
         { -1, -1, -1, -1, -1, },  
         { -1, -1, -1, -1, -1  } }; 
    } 
}

public static double[,] Gaussian5x5Type1 
{ 
   get   
   { 
       return new double[,]   
       { { 2, 04, 05, 04, 2 },  
         { 4, 09, 12, 09, 4 },  
         { 5, 12, 15, 12, 5 }, 
         { 4, 09, 12, 09, 4 }, 
         { 2, 04, 05, 04, 2 }, }; 
   } 
}

Laplacian 5×5 Of Gaussian 5×5 – Type 1

Laplacian (5×5) of Gaussian (5×5 – Type 2)

The variation of Gaussian blur most applicable when implementing a Laplacian of Gaussian filter depends on image noise expressed by a source image. In this scenario the first variations (Type 1) appears to result in less image noise.

public static Bitmap 
Laplacian5x5OfGaussian5x5Filter2(this Bitmap sourceBitmap)
{
    Bitmap resultBitmap = 
           ExtBitmap.ConvolutionFilter(sourceBitmap, 
                            Matrix.Gaussian5x5Type2, 
                               1.0 / 256.0, 0, true);

 
    resultBitmap = 
           ExtBitmap.ConvolutionFilter(resultBitmap, 
                                Matrix.Laplacian5x5, 
                                      1.0, 0, false);

 
    return resultBitmap;
}

public static double[,] Laplacian5x5 
{ 
    get   
    { 
       return new double[,]
       { { -1, -1, -1, -1, -1, },  
         { -1, -1, -1, -1, -1, },  
         { -1, -1, 24, -1, -1, },  
         { -1, -1, -1, -1, -1, },  
         { -1, -1, -1, -1, -1  } }; 
    } 
}

public static double[,] Gaussian5x5Type2 
{ 
   get   
   {
       return new double[,]  
       { {  1,   4,  6,  4,  1 },  
         {  4,  16, 24, 16,  4 },  
         {  6,  24, 36, 24,  6 }, 
         {  4,  16, 24, 16,  4 }, 
         {  1,   4,  6,  4,  1 }, }; 
   }
}

Laplacian 5×5 Of Gaussian 5×5 – Type 2

Sobel Edge Detection

Sobel edge detection is another common implementation of edge detection. We gain the following quote from Wikipedia:

The Sobel operator is used in image processing, particularly within edge detection algorithms. Technically, it is a discrete differentiation operator, computing an approximation of the gradient of the image intensity function. At each point in the image, the result of the Sobel operator is either the corresponding gradient vector or the norm of this vector. The Sobel operator is based on convolving the image with a small, separable, and integer valued filter in horizontal and vertical direction and is therefore relatively inexpensive in terms of computations. On the other hand, the gradient approximation that it produces is relatively crude, in particular for high frequency variations in the image.

Unlike the Laplacian filters discussed earlier, Sobel filter results differ significantly when comparing colour and grayscale images. The Sobel filter tends to be less sensitive to image noise compared to the Laplacian filter. The detected edge lines are not as finely detailed/granular as the detected edge lines resulting from Laplacian filters.

public static Bitmap 
Sobel3x3Filter(this Bitmap sourceBitmap, 
                  bool grayscale = true)
{
    Bitmap resultBitmap =
           ExtBitmap.ConvolutionFilter(sourceBitmap, 
                          Matrix.Sobel3x3Horizontal, 
                            Matrix.Sobel3x3Vertical, 
                                  1.0, 0, grayscale);

 
    return resultBitmap;
}

 
public static double[,] Sobel3x3Horizontal
{ 
   get   
   {
       return new double[,]  
       { { -1,  0,  1, },  
         { -2,  0,  2, },  
         { -1,  0,  1, }, }; 
   } 
}

public static double[,] Sobel3x3Vertical 
{ 
   get   
   { 
       return new double[,]  
       { {  1,  2,  1, },  
         {  0,  0,  0, },  
         { -1, -2, -1, }, }; 
   } 
}

Sobel 3×3

Sobel 3×3 Grayscale

Prewitt Edge Detection

As with the other methods of edge detection discussed in this article the Prewitt edge detection method is also a fairly common implementation. From Wikipedia we gain the following quote:

The Prewitt operator is used in image processing, particularly within edge detection algorithms. Technically, it is a discrete differentiation operator, computing an approximation of the gradient of the image intensity function. At each point in the image, the result of the Prewitt operator is either the corresponding gradient vector or the norm of this vector. The Prewitt operator is based on convolving the image with a small, separable, and integer valued filter in horizontal and vertical direction and is therefore relatively inexpensive in terms of computations. On the other hand, the gradient approximation which it produces is relatively crude, in particular for high frequency variations in the image. The Prewitt operator was developed by Judith M. S. Prewitt.

In simple terms, the operator calculates the gradient of the image intensity at each point, giving the direction of the largest possible increase from light to dark and the rate of change in that direction. The result therefore shows how "abruptly" or "smoothly" the image changes at that point, and therefore how likely it is that that part of the image represents an edge, as well as how that edge is likely to be oriented. In practice, the magnitude (likelihood of an edge) calculation is more reliable and easier to interpret than the direction calculation.

Similar to the Sobel filter, resulting images express a significant difference when comparing colour and grayscale images.

public static Bitmap 
PrewittFilter(this Bitmap sourceBitmap, 
                 bool grayscale = true)
{
    Bitmap resultBitmap =
           ExtBitmap.ConvolutionFilter(sourceBitmap, 
                        Matrix.Prewitt3x3Horizontal, 
                          Matrix.Prewitt3x3Vertical, 
                                  1.0, 0, grayscale);

 
    return resultBitmap;
}

public static double[,] Prewitt3x3Horizontal 
{ 
   get   
   { 
       return new double[,]  
       { { -1,  0,  1, },  
         { -1,  0,  1, },  
         { -1,  0,  1, }, }; 
   } 
}

  
public static double[,] Prewitt3x3Vertical 
{ 
   get   
   { 
       return new double[,]  
       { {  1,  1,  1, },  
         {  0,  0,  0, },  
         { -1, -1, -1, }, }; 
   }
}

Prewitt

Prewitt Grayscale

Kirsch Edge Detection

The Kirsch edge detection method is often implemented in the form of Compass edge detection. In the following scenario we only implement two components: Horizontal and Vertical. Resulting images tend to have a high level of brightness.

public static Bitmap 
KirschFilter(this Bitmap sourceBitmap, 
                bool grayscale = true)
{
    Bitmap resultBitmap =
           ExtBitmap.ConvolutionFilter(sourceBitmap, 
                         Matrix.Kirsch3x3Horizontal, 
                           Matrix.Kirsch3x3Vertical, 
                                  1.0, 0, grayscale);

 
    return resultBitmap;
}

public static double[,] Kirsch3x3Horizontal 
{ 
   get   
   {
       return new double[,]  
       { {  5,  5,  5, },  
         { -3,  0, -3, },  
         { -3, -3, -3, }, }; 
   } 
}

public static double[,] Kirsch3x3Vertical
{ 
   get   
   { 
       return new double[,]  
       { {  5, -3, -3, },  
         {  5,  0, -3, },  
         {  5, -3, -3, }, }; 
   } 
}

Kirsch

Kirsch Grayscale

Software by Default

Posts Tagged 'Step detection'

C# How to: Difference Of Gaussians

Article purpose

Sample source code

Using the Sample Application

What is Difference of Gaussians?

Applying a Convolution Matrix filter

The Gaussian Matrix

Subtracting Images

Difference of Gaussians Extension methods

Sample Images

Related Articles and Feedback

Rate this:

Share this:

C# How to: Image Edge Detection

Article Purpose

Sample source code

Using the Sample Application

Edge Detection

Image Convolution

Single Matrix Convolution

Horizontal and Vertical Matrix Convolution

Original Sample Image

Laplacian Edge Detection

Laplacian 3×3

Laplacian 5×5

Laplacian of Gaussian

Laplacian (3×3) of Gaussian (3×3)

Laplacian (3×3) of Gaussian (5×5 – Type 1)

Laplacian (3×3) of Gaussian (5×5 – Type 2)

Laplacian (5×5) of Gaussian (3×3)

Laplacian (5×5) of Gaussian (5×5 – Type 1)

Laplacian (5×5) of Gaussian (5×5 – Type 2)

Sobel Edge Detection

Prewitt Edge Detection

Kirsch Edge Detection

Related Articles and Feedback

Rate this:

Share this:

Dewald Esterhuizen

RSS Feed

Recent Posts

Blog Stats

Follow SoftwareByDefault via Email

Categories

Top Posts & Pages

Archives

C# How to Articles

SoftwareByDefault Online References

Twitter feed

SoftwareByDefault on MSDN

MSDN Articles

Categories

Tags