## Posts Tagged 'Convolution filters'

### Article Purpose

The objective of this article is to explore various algorithms. The types of discussed are: , , , and . All instances are implemented by means of .

### 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 towards the bottom middle part of the screen relates the various methods discussed.

If desired a user can save the resulting 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 on :

Edge detection is the name for a set of mathematical methods which aim at identifying points in a at which the 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 and the problem of finding signal discontinuities over time is known as . Edge detection is a fundamental tool in , and , particularly in the areas of and .

### Image Convolution

A good introduction article  to 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 targeting the class. The ConvolutionFilter method is intended to apply a user defined and optionally covert an 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),
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 has been overloaded to accept two matrices, representing a vertical and a horizontal . 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),
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 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 method of counts as one of the commonly used implementations. From 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 and calculated as sum of differences over the nearest neighbours of the central pixel.

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

### Laplacian 3×3

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

```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  produces result with a noticeable difference between colour and grayscale . The detected edges are expressed in a fair amount of fine detail, although the has a tendency to be sensitive to .

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

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

```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 variations can be combined in an attempt to produce results best suited to the input . In this case we first apply a 3×3 followed by a 3×3 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 followed by a 3×3 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 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 filter implements a 3×3 , followed by a 5×5 . The resulting appears significantly brighter when compared to a 3×3 .

```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 results in a higher degree of smoothing, equating to less .

```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 most applicable when implementing a filter depends on expressed by a source . In this scenario the first variations (Type 1) appears to result in less .

```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

is another common implementation of . We gain the following from :

The Sobel operator is used in , particularly within edge detection algorithms. Technically, it is a , computing an approximation of the 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 filters discussed earlier, filter results differ significantly when comparing colour and grayscale . The filter tends to be less sensitive to compared to the filter. The detected edge lines are not as finely detailed/granular as the detected edge lines resulting from 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 discussed in this article the method is also a fairly common implementation. From we gain the following quote:

The Prewitt operator is used in , particularly within algorithms. Technically, it is a , computing an approximation of the 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 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 filter, resulting express a significant difference when comparing colour and grayscale .

```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 method is often implemented in the form of Compass . In the following scenario we only implement two components: Horizontal and Vertical. Resulting 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 ### Related Articles and Feedback

Feedback and questions are always encouraged. If you know of an alternative implementation or have ideas on a more efficient implementation please share in the comments section.

I’ve published a number of articles related to imaging and images of which you can find URL links here:

### Article Purpose

This article is intended to serve as an introduction to the concepts related to creating and processing filters being applied on . The filters discussed are: Blur, Gaussian Blur, Soften, Motion Blur, High Pass, Edge Detect, Sharpen and Emboss.

### Using the Sample Application

A Sample Application has been included with this article’s sample source code. The Sample Application has been developed to target the platform. Using the Sample Application users are able to select a source/input from the local file system and from a drop down select a filter to apply. Filtered can be saved to the local file system when a user clicks the ‘Save’ button.

The following screenshot shows the Image Convolution Filter sample application in action. ### Image Convolution

Before delving into discussions on technical implementation details it is important to have a good understanding of the concepts behind .

In relation to can be considered as algorithms being implemented resulting in translating input/source . Algorithms being applied generally take the form of accepting two input values and producing a third value considered to be a modified version of one of the input values.

can be implemented to produce filters such as: Blurring, Smoothing, Edge Detection, Sharpening and Embossing. The resulting filtered still bares a relation to the input source .

### Convolution Matrix

In this article we will be implementing through means of a or representing the algorithms required to produce resulting filtered . A should be considered as a two dimensional array or grid. It is required that the number or rows and columns be of an equal size, which is furthermore required to not be a factor of two. Examples of valid dimensions could be 3×3 or 5×5. Dimensions such as 2×2 or 4×4 would not be valid. Generally the sum total of all the values expressed in a equates to one, although it is not a strict requirement.

The following table represents an example /:

 2 0 0 0 -1 0 0 0 -1

An important aspect to keep in mind: When implementing a the value of a pixel will be determined by the values of the pixel’s neighbouring pixels. The values contained in a represent factor values intended to be multiplied with pixel values. In a the centre pixel represents the pixel currently being modified. Neighbouring matrix values express the factor to be applied to the corresponding neighbouring pixels in regards to the pixel currently being modified.

### The ConvolutionFilterBase class

The sample code defines the class ConvolutionFilterBase. This class is intended to represent the minimum requirements of a . When defining a we will be inheriting from the ConvolutionFilterBase class. Because this class and its members have been defined as , implementing classes are required to implement all defined members.

The following code snippet details the ConvolutionFilterBase definition:

```public abstract class ConvolutionFilterBase
{
public abstract string FilterName
{
get;
}

public abstract double Factor
{
get;
}

public abstract double Bias
{
get;
}

public abstract double[,] FilterMatrix
{
get;
}
}```

As to be expected the member property FilterMatrix is intended to represent a two dimensional array containing a . In some instances when the sum total of values do not equate to 1  a filter might implement a Factor value other than the default of 1. Additionally some filters may also require a Bias value to be added the final result value when calculating the matrix.

### Calculating a Convolution Filter

Calculating filters and creating the resulting can be achieved by invoking the ConvolutionFilter method. This method is defined as an targeting the class. The definition of the ConvolutionFilter as follows:

``` public static Bitmap ConvolutionFilter<T>(this Bitmap sourceBitmap, T filter)
where T : ConvolutionFilterBase
{
BitmapData sourceData = sourceBitmap.LockBits(new Rectangle (0, 0,
sourceBitmap.Width, sourceBitmap.Height),

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;

int filterWidth = filter.FilterMatrix.GetLength(1);
int filterHeight = filter.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]) *
filter.FilterMatrix[filterY + filterOffset,
filterX + filterOffset];

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

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

blue = filter.Factor * blue + filter.Bias;
green = filter.Factor * green + filter.Bias;
red = filter.Factor * red + filter.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 following section provides a detailed discussion of the ConvolutionFilter .

### ConvolutionFilter<T> – Method Signature

```public static Bitmap ConvolutionFilter<T>
(this Bitmap sourceBitmap,
T filter)
where T : ConvolutionFilterBase ```

The ConvolutionFilter method defines a generic type T constrained by the requirement to be of type ConvolutionFilterBase. The filter parameter being of generic type T has to be of type ConvolutionFilterBase or a type which inherits from the ConvolutionFilterBase class.

Notice how the sourceBitmap parameter type definition is preceded by the indicating the method can be implemented as an . Keep in mind are required to be declared as static.

The sourceBitmap parameter represents the source/input upon which the filter is to be applied. Note that the ConvolutionFilter method is implemented as immutable. The input parameter values are not modified, instead a new instance will be created and returned.

### ConvolutionFilter<T> – Creating the Data Buffer

```BitmapData sourceData = sourceBitmap.LockBits
(new Rectangle(0, 0,
sourceBitmap.Width,
sourceBitmap.Height),
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);```

In order to access the underlying ARGB values from a object we first need to lock the into memory by invoking the method. Locking a into memory prevents the from moving a object to a new location in memory.

When invoking the method the source code instantiates a object from the return value. The property represents the number of in a single pixel row. In this scenario the property should be equal to the ’s width in pixels multiplied by four seeing as every pixel consists of four : Alpha, Red, Green and Blue.

The ConvolutionFilter method defines two buffers, of which the size is set to equal the size of the ’s underlying data. The property of type represents the memory address of the first value of a ’s underlying buffer. Using the method we specify the starting point memory address from where to start copying the ’s buffer.

Important to remember is the next operation being performed: invoking the method. If a has been locked into memory ensure releasing the lock by invoking the method.

### ConvolutionFilter<T> – Iterating Rows and Columns

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

int filterWidth = filter.FilterMatrix.GetLength(1);
int filterHeight = filter.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; ```

The ConvolutionFilter method employs two for loops in order to iterate each pixel represented in the ARGB data buffer. Defining two for loops to iterate a one dimensional array simplifies the concept of accessing the array in terms of rows and columns.

Note that the inner loop is limited to the width of the source/input parameter, in other words the number of horizontal pixels. Remember that the data buffer represents four , Alpha, Red, Green and Blue, for each pixel. The inner loop therefore iterates entire pixels.

As discussed earlier the filter has to be declared as a two dimensional array with the same odd number of rows and columns. If the current pixel being processed relates to the element at the centre of the matrix, the width of the matrix less one divided by two equates to the neighbouring pixel index values.

The index of the current pixel can be calculated by multiplying the current row index (offsetY) and the number of ARGB byte values per row of pixels (sourceData.Stride), to which is added the current column/pixel index (offsetX) multiplied by four.

### ConvolutionFilter<T> – Iterating the Matrix

```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]) *
filter.FilterMatrix[filterY + filterOffset,
filterX + filterOffset];

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

red += (double)(pixelBuffer[calcOffset + 2]) *
filter.FilterMatrix[filterY + filterOffset,
filterX + filterOffset];
}
}```

The ConvolutionFilter method iterates the two dimensional by implementing two for loops, iterating rows and for each row iterating columns. Both loops have been declared to have a starting point equal to the negative value of half the length (filterOffset). Initiating the loops with negative values simplifies implementing the concept of neighbouring pixels.

The first statement performed within the inner loop calculates the index of the neighbouring pixel in relation to the current pixel. Next the value is applied as a factor to the corresponding neighbouring pixel’s individual colour components. The results are added to the totals variables blue, green and red.

In regards to each iteration iterating in terms of an entire pixel, to access individual colour components the source code adds the required colour component offset. Note: ARGB colour components are in fact expressed in reversed order: Blue, Green, Red and Alpha. In other words, a pixel’s first (offset 0) represents Blue, the second (offset 1) represents Green, the third (offset 2) represents Red and the last (offset 3) representing the Alpha component.

### ConvolutionFilter<T> – Applying the Factor and Bias

```blue = filter.Factor * blue + filter.Bias;
green = filter.Factor * green + filter.Bias;
red = filter.Factor * red + filter.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; ```

After iterating the matrix and calculating the matrix values of the current pixel’s Red, Green and Blue colour components we apply the Factor and add the Bias defined by the filter parameter.

Colour components may only contain a value ranging from 0 to 255 inclusive. Before we assign the newly calculated colour component value we ensure that the value falls within the required range. Values which exceed 255 are set to 255 and values less than 0 are set to 0. Note that assignment is implemented in terms of the result buffer, the original source buffer remains unchanged.

### ConvolutionFilter<T> – Returning the Result

```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 final steps performed by the ConvolutionFilter method involves creating a new object instance and copying the calculated result buffer. In a similar fashion to reading underlying pixel data we copy the result buffer to the object.

### Creating Filters

The main requirement when creating a filter is to inherit from the ConvolutionBaseFilter class. The following sections of this article will discuss various filter types and variations where applicable.

To illustrate the different effects resulting from applying filters all of the filters discussed make use of the same source . The original file is licensed under the Creative Commons Attribution 2.0 Generic license and can be downloaded from: ### Blur Filters

is typically used to reduce and detail. The filter’s matrix size affects the level of . A larger results in higher level of , whereas a smaller results in a lesser level of .

### Blur3x3Filter

The Blur3x3Filter results in a slight to medium level of . The consists of 9 elements in a 3×3 configuration. ```public class Blur3x3Filter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "Blur3x3Filter"; }
}

private double factor = 1.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { 0.0, 0.2, 0.0, },
{ 0.2, 0.2, 0.2, },
{ 0.0, 0.2, 0.2, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### Blur5x5Filter

The Blur5x5Filter results in a medium level of . The consists of 25 elements in a 5×5 configuration. Notice the factor of 1.0 / 13.0. ```public class Blur5x5Filter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "Blur5x5Filter"; }
}

private double factor = 1.0 / 13.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { 0, 0, 1, 0, 0, },
{ 0, 1, 1, 1, 0, },
{ 1, 1, 1, 1, 1, },
{ 0, 1, 1, 1, 0, },
{ 0, 0, 1, 0, 0, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### Gaussian3x3BlurFilter

The Gaussian3x3BlurFilter implements a through a matrix of 9 elements in a 3×3 configuration. The sum total of all elements equal 16, therefore the Factor is defined as 1.0 / 16.0. Applying this filter results in a slight to medium level of . ```public class Gaussian3x3BlurFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "Gaussian3x3BlurFilter"; }
}

private double factor = 1.0 / 16.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { 1, 2, 1, },
{ 2, 4, 2, },
{ 1, 2, 1, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### Gaussian5x5BlurFilter

The Gaussian5x5BlurFilter implements a through a matrix of 25 elements in a 5×5 configuration. The sum total of all elements equal 159, therefore the Factor is defined as 1.0 / 159.0. Applying this filter results in a medium level of . ```public class Gaussian5x5BlurFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "Gaussian5x5BlurFilter"; }
}

private double factor = 1.0 / 159.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
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 override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### MotionBlurFilter

By implementing the MotionBlurFilter resulting indicate the appearance of a high level of associated with motion/movement. This filter is a combination of left to right and right to left . The matrix consists of 81 elements in a 9×9 configuration. ```public class MotionBlurFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "MotionBlurFilter"; }
}

private double factor = 1.0 / 18.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { 1, 0, 0, 0, 0, 0, 0, 0, 1, },
{ 0, 1, 0, 0, 0, 0, 0, 1, 0, },
{ 0, 0, 1, 0, 0, 0, 1, 0, 0, },
{ 0, 0, 0, 1, 0, 1, 0, 0, 0, },
{ 0, 0, 0, 0, 1, 0, 0, 0, 0, },
{ 0, 0, 0, 1, 0, 1, 0, 0, 0, },
{ 0, 0, 1, 0, 0, 0, 1, 0, 0, },
{ 0, 1, 0, 0, 0, 0, 0, 1, 0, },
{ 1, 0, 0, 0, 0, 0, 0, 0, 1, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### MotionBlurLeftToRightFilter

The MotionBlurLeftToRightFilter creates the effect of as a result of left to right movement. The matrix consists of 81 elements in a 9×9 configuration. ```public class MotionBlurLeftToRightFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "MotionBlurLeftToRightFilter"; }
}

private double factor = 1.0 / 9.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { 1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 1, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 1, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 1, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 1, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 1, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 1, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 1, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### MotionBlurRightToLeftFilter

The MotionBlurRightToLeftFilter creates the effect of as a result of right to left movement. The consists of 81 elements in a 9×9 configuration. ```public class MotionBlurRightToLeftFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "MotionBlurRightToLeftFilter"; }
}

private double factor = 1.0 / 9.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { 0, 0, 0, 0, 0, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 1, 0, },
{ 0, 0, 0, 0, 0, 0, 1, 0, 0, },
{ 0, 0, 0, 0, 0, 1, 0, 0, 0, },
{ 0, 0, 0, 0, 1, 0, 0, 0, 0, },
{ 0, 0, 0, 1, 0, 0, 0, 0, 0, },
{ 0, 0, 1, 0, 0, 0, 0, 0, 0, },
{ 0, 1, 0, 0, 0, 0, 0, 0, 0, },
{ 1, 0, 0, 0, 0, 0, 0, 0, 0, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### Soften Filter

The SoftenFilter can be used to smooth or soften an . The consists of 9 elements in a 3×3 configuration. ```public class SoftenFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "SoftenFilter"; }
}

private double factor = 1.0 / 8.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { 1, 1, 1, },
{ 1, 1, 1, },
{ 1, 1, 1, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### Sharpen Filters

Sharpening an does not add additional detail to an image but rather adds emphasis to existing image details. is sometimes referred to as image crispness.

### SharpenFilter

This filter is intended as a general usage . In a variety of scenarios this filter should provide a reasonable level of depending on source quality. ```public class SharpenFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "SharpenFilter"; }
}

private double factor = 1.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { -1, -1, -1, },
{ -1,  9, -1, },
{ -1, -1, -1, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### Sharpen3x3Filter

The Sharpen3x3Filter results in a medium level of , less intense when compared to the SharpenFilter discussed previously. ```public class Sharpen3x3Filter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "Sharpen3x3Filter"; }
}

private double factor = 1.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { {  0, -1,  0, },
{ -1,  5, -1, },
{  0, -1,  0, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### Sharpen3x3FactorFilter

The Sharpen3x3FactorFilter provides a level of similar to the Sharpen3x3Filter explored previously. Both filters define a 9 element 3×3 . The filters differ in regards to Factor values. The Sharpen3x3Filter matrix values equate to a sum total of 1, the Sharpen3x3FactorFilter in contrast equate to a sum total of 3. The Sharpen3x3FactorFilter defines a Factor of 1 / 3, resulting in sum total being negated to 1. ```public class Sharpen3x3FactorFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "Sharpen3x3FactorFilter"; }
}

private double factor = 1.0 / 3.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { {  0, -2,  0, },
{ -2, 11, -2, },
{  0, -2,  0, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### Sharpen5x5Filter

The Sharpen5x5Filter matrix defines 25 elements in a 5×5 configuration. The level of resulting from implementing this filter to a greater extent is depended on the source . In some scenarios result images may appear slightly softened. ```public class Sharpen5x5Filter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "Sharpen5x5Filter"; }
}

private double factor = 1.0 / 8.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { -1, -1, -1, -1, -1, },
{ -1,  2,  2,  2, -1, },
{ -1,  2,  8,  2,  1, },
{ -1,  2,  2,  2, -1, },
{ -1, -1, -1, -1, -1, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### IntenseSharpenFilter

The IntenseSharpenFilter produces result with overly emphasized edge lines. ```public class IntenseSharpenFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "IntenseSharpenFilter"; }
}

private double factor = 1.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { 1,  1, 1, },
{ 1, -7, 1, },
{ 1,  1, 1, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### Edge Detection Filters

is the first step towards feature detection and feature extraction in . Edges are generally perceived in in areas exhibiting sudden differences in brightness.

### EdgeDetectionFilter

The EdgeDetectionFilter is intended to be used as a general purpose filter, considered appropriate in the majority of scenarios applied. ```public class EdgeDetectionFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "EdgeDetectionFilter"; }
}

private double factor = 1.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { -1, -1, -1, },
{ -1,  8, -1, },
{ -1, -1, -1, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### EdgeDetection45DegreeFilter

The EdgeDetection45DegreeFilter has the ability to detect edges at 45 degree angles more effectively than other filters. ```public class EdgeDetection45DegreeFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "EdgeDetection45DegreeFilter"; }
}

private double factor = 1.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { -1,  0,  0,  0,  0, },
{  0, -2,  0,  0,  0, },
{  0,  0,  6,  0,  0, },
{  0,  0,  0, -2,  0, },
{  0,  0,  0,  0, -1, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### HorizontalEdgeDetectionFilter

The HorizontalEdgeDetectionFilter has the ability to detect horizontal edges more effectively than other filters. ```public class HorizontalEdgeDetectionFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "HorizontalEdgeDetectionFilter"; }
}

private double factor = 1.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { {  0,  0,  0,  0,  0, },
{  0,  0,  0,  0,  0, },
{ -1, -1,  2,  0,  0, },
{  0,  0,  0,  0,  0, },
{  0,  0,  0,  0,  0, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### VerticalEdgeDetectionFilter

The VerticalEdgeDetectionFilter has the ability to detect vertical edges more effectively than other filters. ```public class VerticalEdgeDetectionFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "VerticalEdgeDetectionFilter"; }
}

private double factor = 1.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { 0,  0, -1,  0,  0, },
{ 0,  0, -1,  0,  0, },
{ 0,  0,  4,  0,  0, },
{ 0,  0, -1,  0,  0, },
{ 0,  0, -1,  0,  0, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### EdgeDetectionTopLeftBottomRightFilter

This filter closely resembles an indicating object depth whilst still providing a reasonable level of detail. ```public class EdgeDetectionTopLeftBottomRightFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "EdgeDetectionTopLeftBottomRightFilter"; }
}

private double factor = 1.0;
public override double Factor
{
get { return factor; }
}

private double bias = 0.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { -5,  0,  0, },
{  0,  0,  0, },
{  0,  0,  5, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### Emboss Filters

filters produce result with an emphasis on depth, based on lines/edges expressed in an input/source . Result give the impression of being three dimensional to a varying extent, depended on details defined by input .

### EmbossFilter

The EmbossFilter is intended as a general application filter. Take note of the Bias value of 128. Without a bias value, result would be very dark or mostly black. ```public class EmbossFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "EmbossFilter"; }
}

private double factor = 1.0;
public override double Factor
{
get { return factor; }
}

private double bias = 128.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { 2,  0,  0, },
{ 0, -1,  0, },
{ 0,  0, -1, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### Emboss45DegreeFilter

The Emboss45DegreeFilter has the ability to produce result with good emphasis on 45 degree edges/lines. ```public class Emboss45DegreeFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "Emboss45DegreeFilter"; }
}

private double factor = 1.0;
public override double Factor
{
get { return factor; }
}

private double bias = 128.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { -1, -1,  0, },
{ -1,  0,  1, },
{  0,  1,  1, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### EmbossTopLeftBottomRightFilter

The EmbossTopLeftBottomRightFilter provides a more subtle level of result . ```public class EmbossTopLeftBottomRightFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "EmbossTopLeftBottomRightFilter"; }
}

private double factor = 1.0;
public override double Factor
{
get { return factor; }
}

private double bias = 128.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { -1, 0, 0, },
{  0, 0, 0, },
{  0, 0, 1, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### IntenseEmbossFilter

When implementing the IntenseEmbossFilter result provide a good three dimensional/depth level. A drawback of this filter can sometimes be noticed in a reduction detail. ```public class IntenseEmbossFilter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "IntenseEmbossFilter"; }
}

private double factor = 1.0;
public override double Factor
{
get { return factor; }
}

private double bias = 128.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { -1, -1, -1, -1,  0, },
{ -1, -1, -1,  0,  1, },
{ -1, -1,  0,  1,  1, },
{ -1,  0,  1,  1,  1, },
{  0,  1,  1,  1,  1, }, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### High Pass

produce result where only high frequency components are retained. ```public class HighPass3x3Filter : ConvolutionFilterBase
{
public override string FilterName
{
get { return "HighPass3x3Filter"; }
}

private double factor = 1.0 / 16.0;
public override double Factor
{
get { return factor; }
}

private double bias = 128.0;
public override double Bias
{
get { return bias; }
}

private double[,] filterMatrix =
new double[,] { { -1, -2, -1, },
{ -2, 12, -2, },
{ -1, -2, -1,, };

public override double[,] FilterMatrix
{
get { return filterMatrix; }
}
} ```

### Related Articles and Feedback

Feedback and questions are always encouraged. If you know of an alternative implementation or have ideas on a more efficient implementation please share in the comments section.

I’ve published a number of articles related to imaging and images of which you can find URL links here:

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