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C# How to: Compass Edge Detection

Article Purpose

This article’s objective is to illustrate concepts relating to Compass Edge Detection. The edge detection methods implemented in this article include: Prewitt, Sobel, Scharr, Kirsch and Isotropic.

Wasp: Scharr 3 x 3 x 8

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 sample source code accompanying this article includes a Windows Forms based sample application. When using the sample application users are able to load source/input images from and save result images to the local file system. The user interface provides a combobox which contains the supported methods of Compass Edge Detection. Selecting an item from the combobox results in the related Compass Edge Detection method being applied to the current source/input image. Supported methods are:

Prewitt3x3x4 – 3×3 Prewitt kernels in 4 compass directions
Prewitt3x3x8 – 3×3 Prewitt kernels in 8 compass directions
Prewitt5x5x4 – 5×5 Prewitt kernels in 4 compass directions
Sobel3x3x4 – 3×3 Sobel kernels in 4 compass directions
Sobel3x3x8 – 3×3 Sobel kernels in 8 compass directions
Sobel5x5x4 – 5×5 Sobel kernels in 4 compass directions
Scharr3x3x4 – 3×3 Scharr kernels in 4 compass directions
Scharr3x3x8 – 3×3 Scharr kernels in 8 compass directions
Scharr5x5x4 – 5×5 Scharr kernels in 4 compass directions
Kirsch3x3x4 – 3×3 Kirsch kernels in 4 compass directions
Kirsch3x3x8 – 3×3 Kirsch kernels in 8 compass directions
Isotropic3x3x4 – 3×3 Isotropic kernels in 4 compass directions
Isotropic3x3x8 – 3×3 Isotropic kernels in 8 compass directions

The following image is a screenshot of the Compass Edge Detection Sample Application in action:

Bee: Isotropic 3 x 3 x 8

Compass Edge Detection Overview

Compass Edge Detection as a concept title can be explained through the implementation of compass directions. Compass Edge Detection can be implemented through image convolution, using multiple matrix kernels, each suited to detecting edges in a specific direction. Often the edge directions implemented are:

North
North East
East
South East
South
South West
West
North West

Each of the compass directions listed above differ by 45 degrees. Applying a kernel rotation of 45 degrees to an existing direction specific edge detection kernel results in a new kernel suited to detecting edges in the next compass direction.

Various edge detection kernels can be implemented in Compass Edge Detection. This article and accompanying sample source code implements the following kernel types:

Prewitt
Sobel
Kirsch
Scharr
Isotropic

Prey Mantis: Sobel 3 x 3 x 8

The steps required when implementing Compass Edge Detection can be described as follows:

Determine the compass kernels. When an edge detection kernel suited to a specific direction is known, the edge detection kernels suited to the 7 remaining compass directions can be calculated. Rotating a kernel by 45 degrees around a central axis equates to the kernel suited to the next compass direction. As an example, if the edge detection kernel suited to detect edges in a northerly direction were to be rotated clockwise by 45 degrees around a central axis the result would be an edge detection kernel suited to edges in a North Easterly direction.
Iterate source image pixels. Every pixel forming part of the source/input image should be iterated, implementing convolution using each of the compass kernels.
Determine the most responsive kernel convolution. After having applied each compass kernel to the pixel currently being iterated, the most responsive compass kernel determines the output value. In other words, after having applied convolution eight times on the same pixel using each compass direction the output value should be set to the highest value calculated.
Validate and set output result. Ensure that the highest value returned from convolution does not equate to less than 0 or more than 255. Should a value be less than zero the result should be assigned as zero. In a similar fashion, should a value exceed 255 the result should be assigned as 255.

Prewitt Compass Kernels

LadyBug: Prewitt 3 x 3 x 8

Rotating Convolution Kernels

Kernels can be rotated by implementing a rotate transform. Repeatedly rotating by 45 degrees results in calculating 8 kernels, each suited to a different direction. The algorithm implemented when performing a rotate transform can be expressed as follows:

Rotate Horizontal Algorithm

Rotate Vertical Algorithm

I’ve published an in-depth article on matrix rotation available here: C# How to: Image Transform Rotate

Butterfly: Sobel 3 x 3 x 8

Implementing Kernel Rotation

The sample source code defines the RotateMatrix method. This method accepts as parameter a single kernel, defined as a two dimensional array of type double. In addition the method also expects as a parameter the degree to which the specified kernel should be rotated. The definition as follows:

public static double[, ,] RotateMatrix(double[,] baseKernel,  
                                             double degrees) 
{
    double[, ,] kernel = new double[(int )(360 / degrees),  
        baseKernel.GetLength(0), baseKernel.GetLength(1)]; 

 
    int xOffset = baseKernel.GetLength(1) / 2; 
    int yOffset = baseKernel.GetLength(0) / 2; 

 
    for (int y = 0; y < baseKernel.GetLength(0); y++) 
    { 
        for (int x = 0; x < baseKernel.GetLength(1); x++) 
        { 
            for (int compass = 0; compass <  
                kernel.GetLength(0); compass++) 
            { 
                double radians = compass * degrees * 
                                 Math.PI / 180.0; 

 
                int resultX = (int)(Math.Round((x - xOffset) * 
                           Math.Cos(radians) - (y - yOffset) * 
                           Math.Sin(radians)) + xOffset); 

 
                int resultY = (int )(Math.Round((x - xOffset) * 
                            Math.Sin(radians) + (y - yOffset) * 
                            Math.Cos(radians)) + yOffset); 

 
                kernel[compass, resultY, resultX] = 
                                            baseKernel[y, x]; 
            } 
        } 
    }

 
    return kernel; 
}

Butterfly: Prewitt 3 x 3 x 8

Implementing Compass Edge Detection

The sample source code defines several kernels which are implemented in convolution. The following code snippet provides the definition of all kernels defined:

public static double[, ,] Prewitt3x3x4 
{
    get 
    {
        double[,] baseKernel = new double[,]  
         { {  -1,  0,  1,  },  
           {  -1,  0,  1,  },  
           {  -1,  0,  1,  }, }; 

 
        double[, ,] kernel = RotateMatrix(baseKernel, 90); 

 
        return kernel; 
    }  
}  

 
public static double[, ,] Prewitt3x3x8 
{  
    get 
    {  
        double[,] baseKernel = new double[,]  
         { {  -1,  0,  1,  },  
           {  -1,  0,  1,  },  
           {  -1,  0,  1,  }, }; 

 
        double[, ,] kernel = RotateMatrix(baseKernel, 45); 

 
        return kernel; 
    }  
}  

 
public static double[, ,] Prewitt5x5x4 
{  
    get 
    {  
        double[,] baseKernel = new double[,]  
         { {  -2, -1,  0,  1, 2,  },  
           {  -2, -1,  0,  1, 2,  }, 
           {  -2, -1,  0,  1, 2,  }, 
           {  -2, -1,  0,  1, 2,  },  
           {  -2, -1,  0,  1, 2,  }, }; 

 
        double[, ,] kernel = RotateMatrix(baseKernel, 90); 

 
        return kernel; 
    }  
}  

 
public static double[, ,] Kirsch3x3x4 
{  
    get 
    {  
        double[,] baseKernel = new double[,]  
         { {  -3, -3,  5,  },  
           {  -3,  0,  5,  },  
           {  -3, -3,  5,  }, }; 

 
        double[, ,] kernel = RotateMatrix(baseKernel, 90); 

 
        return kernel; 
    }  
}  

 
public static double[, ,] Kirsch3x3x8 
{  
    get 
    {  
        double[,] baseKernel = new double[,]  
         { {  -3, -3,  5,  },  
           {  -3,  0,  5,  },  
           {  -3, -3,  5,  }, }; 

 
        double[, ,] kernel = RotateMatrix(baseKernel, 45); 

 
        return kernel; 
    }  
}  

 
public static double[, ,] Sobel3x3x4 
{  
    get 
    {  
        double[,] baseKernel = new double[,]  
         { {  -1,  0,  1,  },  
           {  -2,  0,  2,  },  
           {  -1,  0,  1,  }, }; 

 
        double[, ,] kernel = RotateMatrix(baseKernel, 90); 

 
        return kernel; 
    }  
}  

 
public static double[, ,] Sobel3x3x8 
{  
    get 
    {  
        double[,] baseKernel = new double[,]  
         { {  -1,  0,  1,  },  
           {  -2,  0,  2,  },  
           {  -1,  0,  1,  }, }; 

 
        double[, ,] kernel = RotateMatrix(baseKernel, 45); 

 
        return kernel; 
    }  
}  

 
public static double[, ,] Sobel5x5x4 
{  
    get 
    {  
        double[,] baseKernel = new double[,]  
         { {   -5,  -4,  0,   4,  5,  },  
           {   -8, -10,  0,  10,  8,  }, 
           {  -10, -20,  0,  20, 10,  }, 
           {   -8, -10,  0,  10,  8,  },  
           {   -5,  -4,  0,   4,  5,  }, }; 

 
        double[, ,] kernel = RotateMatrix(baseKernel, 90); 

 
        return kernel; 
    }  
}  

 
public static double[, ,] Scharr3x3x4 
{  
    get 
    {  
        double[,] baseKernel = new double[,]  
         { {  -1,  0,  1,  },  
           {  -3,  0,  3,  },  
           {  -1,  0,  1,  }, }; 

 
        double[, ,] kernel = RotateMatrix(baseKernel, 90); 

 
        return kernel; 
    }  
}  

 
public static double[, ,] Scharr3x3x8 
{  
    get 
    {  
        double[,] baseKernel = new double[,]  
         { {  -1,  0,  1,  },  
           {  -3,  0,  3,  },  
           {  -1,  0,  1,  }, }; 

 
        double[, ,] kernel = RotateMatrix(baseKernel, 45); 

 
        return kernel; 
    }  
}  

 
public static double[, ,] Scharr5x5x4 
{  
    get 
    {  
        double[,] baseKernel = new double[,]  
         { {   -1,  -1,  0,   1,  1,  },  
           {   -2,  -2,  0,   2,  2,  }, 
           {   -3,  -6,  0,   6,  3,  }, 
           {   -2,  -2,  0,   2,  2,  },  
           {   -1,  -1,  0,   1,  1,  }, }; 

 
        double[, ,] kernel = RotateMatrix(baseKernel, 90); 

 
        return kernel; 
    }  
}  

 
public static double[, ,] Isotropic3x3x4 
{  
    get 
    {  
        double[,] baseKernel = new double[,]  
         { {             -1,  0,             1,  },  
           {  -Math.Sqrt(2),  0,  Math.Sqrt(2),  },  
           {             -1,  0,             1,  },  }; 

 
        double[, ,] kernel = RotateMatrix(baseKernel, 90); 

 
        return kernel; 
    }  
}  

 
public static double[, ,] Isotropic3x3x8 
{  
    get 
     {  
        double[,] baseKernel = new double[,]  
         { {             -1,  0,             1,  },  
           {  -Math.Sqrt(2),  0,  Math.Sqrt(2),  },  
           {             -1,  0,             1,  }, }; 

 
        double[, ,] kernel = RotateMatrix(baseKernel, 45); 

  
        return kernel; 
    }  
}

Notice how each property invokes the RotateMatrix method discussed in the previous section.

Butterfly: Scharr 3 x 3 x 8

The CompassEdgeDetectionFilter method is defined as an extension method targeting the Bitmap class. The purpose of this method is to act as a wrapper method encapsulating the technical implementation. The definition as follows:

public static Bitmap CompassEdgeDetectionFilter(this Bitmap sourceBitmap,  
                                    CompassEdgeDetectionType compassType) 
{ 
    Bitmap resultBitmap = null; 

 
    switch (compassType) 
    {
        case CompassEdgeDetectionType.Sobel3x3x4: 
             { 
                resultBitmap =  
                sourceBitmap.ConvolutionFilter(Matrix.Sobel3x3x4, 1.0 / 4.0); 
             } break; 
        case CompassEdgeDetectionType.Sobel3x3x8: 
             { 
                resultBitmap =  
                sourceBitmap.ConvolutionFilter(Matrix.Sobel3x3x8, 1.0/ 4.0); 
             } break; 
        case CompassEdgeDetectionType.Sobel5x5x4: 
             { 
                resultBitmap = 
                sourceBitmap.ConvolutionFilter(Matrix.Sobel5x5x4, 1.0/ 84.0); 
             } break; 
        case CompassEdgeDetectionType.Prewitt3x3x4: 
             { 
                resultBitmap = 
                sourceBitmap.ConvolutionFilter(Matrix.Prewitt3x3x4, 1.0 / 3.0); 
             } break; 
        case CompassEdgeDetectionType.Prewitt3x3x8: 
             { 
                resultBitmap = 
                sourceBitmap.ConvolutionFilter(Matrix.Prewitt3x3x8, 1.0/ 3.0); 
             } break; 
        case CompassEdgeDetectionType.Prewitt5x5x4: 
             { 
                resultBitmap = 
                sourceBitmap.ConvolutionFilter(Matrix.Prewitt5x5x4, 1.0 / 15.0); 
             } break; 
        case CompassEdgeDetectionType.Scharr3x3x4: 
             { 
                resultBitmap = 
                sourceBitmap.ConvolutionFilter(Matrix.Scharr3x3x4, 1.0 / 4.0); 
             } break; 
        case CompassEdgeDetectionType.Scharr3x3x8: 
             { 
                resultBitmap = 
                sourceBitmap.ConvolutionFilter(Matrix.Scharr3x3x8, 1.0 / 4.0); 
             } break; 
        case CompassEdgeDetectionType .Scharr5x5x4: 
             { 
                resultBitmap = 
                sourceBitmap.ConvolutionFilter(Matrix.Scharr5x5x4, 1.0 / 21.0); 
             } break; 
        case CompassEdgeDetectionType.Kirsch3x3x4: 
             { 
                resultBitmap = 
                sourceBitmap.ConvolutionFilter(Matrix.Kirsch3x3x4, 1.0 / 15.0); 
             } break; 
        case CompassEdgeDetectionType.Kirsch3x3x8: 
             { 
                resultBitmap = 
                sourceBitmap.ConvolutionFilter(Matrix.Kirsch3x3x8, 1.0 / 15.0); 
             } break; 
        case CompassEdgeDetectionType.Isotropic3x3x4: 
             { 
                resultBitmap = 
                sourceBitmap.ConvolutionFilter(Matrix.Isotropic3x3x4, 1.0 / 3.4); 
             } break; 
        case CompassEdgeDetectionType.Isotropic3x3x8: 
             { 
                resultBitmap = 
                sourceBitmap.ConvolutionFilter(Matrix.Isotropic3x3x8, 1.0 / 3.4); 
             } break; 
     } 

 
    return resultBitmap; 
}

Rose: Scharr 3 x 3 x 8

Notice from the code snippet listed above, each case statement invokes the ConvolutionFilter method. This method has been defined as an extension method targeting the Bitmap class. The ConvolutionFilter extension method performs the actual task of image convolution. This method implements each kernel passed as a parameter, the highest result value will be determined as the output value. The definition as follows:

private static Bitmap ConvolutionFilter(this Bitmap sourceBitmap,  
                                     double[,,] filterMatrix,  
                                           double factor = 1,  
                                                int bias = 0)  
{
    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); 


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


    double blueCompass = 0.0; 
    double greenCompass = 0.0; 
    double redCompass = 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 compass = 0; compass <  
                 filterMatrix.GetLength(0); compass++) 
             {


                blueCompass = 0.0; 
                greenCompass = 0.0; 
                redCompass = 0.0; 


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


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


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


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


                blue = (blueCompass > blue ? blueCompass : blue); 
                green = (greenCompass > green ? greenCompass : green); 
                red = (redCompass > red ? redCompass : red); 
             }


            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; 
}

Rose: Isotropic 3 x 3 x 8

Sample Images

This article features a number of sample images. All featured images have been licensed allowing for reproduction. The following image files feature a sample images:

Wasp – Licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Download from Wikimedia
Ladybug – Licensed under the Creative Commons Attribution-Share Alike 2.0 Generic license. Download from Wikipedia
Ant – Released into the public domain by its author, Sean.hoyland. This applies worldwide. In some countries this may not be legally possible; if so: Sean.hoyland grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. Download from Wikipedia
Prey Mantis – Licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Download from Wikipedia
Bee – Licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Download from Wikipedia
Red Pierrot Butterfly 1– Licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Download from WikiMedia
Siproeta Epaphus Butterfly – Licensed under the Creative Commons Attribution 3.0 Unported license. Download from WikiMedia
Red Pierrot Butterfly 2 – Licensed under the Creative Commons Attribution 2.0 Generic license. Download from Wikipedia
Iceberg Rose – Licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Attribution: Stan Shebs. Download from Wikipedia
Heidi Klum Rose – Licensed under the Creative Commons Attribution-Share Alike 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic license. Download from Wikipedia
Viceroy Butterfly – Licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Attributed to D. Gordon E. Robertson. Download from Wikipedia

The Original Image

Butterfly: Isotropic 3 x 3 x 4

Butterfly: Isotropic 3 x 3 x 8

Butterfly: Kirsch 3 x 3 x 4

Butterfly: Kirsch 3 x 3 x 8

Butterfly: Prewitt 3 x 3 x 4

Butterfly: Prewitt 3 x 3 x 8

Butterfly: Prewitt 5 x 5 x 4

Butterfly: Scharr 3 x 3 x 4

Butterfly: Scharr 3 x 3 x 8

Butterfly: Scharr 5 x 5 x 4

Butterfly: Sobel 3 x 3 x 4

Butterfly: Sobel 3 x 3 x 8

Butterfly: Sobel 5 x 5 x 4

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 'Sobel'

C# How to: Compass Edge Detection

Article Purpose

Sample Source Code

Using the Sample Application

Compass Edge Detection Overview

Rotating Convolution Kernels

Implementing Kernel Rotation

Implementing Compass Edge Detection

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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

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Dewald Esterhuizen

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