CorrelationByDifference2d
Performs a correlation by the difference between a two-dimensional grayscale image and a grayscale kernel.
Access to parameter description
For an introduction: section Image Correlation.
This algorithm performs a correlation with a difference metric between a gray level image $I$ and a gray level kernel $K$, returning the correlation image $O$.
The different possibilities for selecting a correlation peak are presented below using a 1-D correlation between an image and kernel. In the image, the kernel appears 6 times with different contrast and luminosity.
Figure 1. 1D image and kernel
The 6 examples show the kernel appearing with different contrast and luminosity.
Figure 2. Examples of possible 1D correlation
The correlation by difference metric is computed in accordance with the CorrelationMode parameter.
Figure 3. Example of Difference 1D direct correlation
Figure 4. Example of Difference 1D mean correlation
Figure 5. Example of Difference 1D variance correlation
Figure 6. Example of Difference 1D mean and variance correlation
where: $$ \mu(K)=\frac{\sum\limits_{i=1}^{kx} \sum\limits_{j=1}^{ky} K(i,j)}{kx\times ky} $$ $$ \mu(I)(n,m)=\frac{\sum\limits_{i=1}^{kx} \sum\limits_{j=1}^{ky} I(n+i,m+j)}{kx\times ky} $$ $$ \sigma^2(K)=\sum_{i=1}^{kx} \sum_{j=1}^{ky} \left(K(i,j)-\mu(K)\right)^{2} $$ $$ \sigma^2(I)(n,m)=\sum_{i=1}^{kx} \sum_{j=1}^{ky} \left( I(n+i-\frac{kx}{2},m+j-\frac{ky}{2} ) - \mu(I)(n,m)\right)^{2} $$
Note: This algorithm returns the main correlation peak in the outputMeasurement object. More correlation peaks can be extracted from the outputImage correlation image with the LocalMaxima2d algorithm.
See also
Access to parameter description
For an introduction: section Image Correlation.
This algorithm performs a correlation with a difference metric between a gray level image $I$ and a gray level kernel $K$, returning the correlation image $O$.
The different possibilities for selecting a correlation peak are presented below using a 1-D correlation between an image and kernel. In the image, the kernel appears 6 times with different contrast and luminosity.
Figure 1. 1D image and kernel
The 6 examples show the kernel appearing with different contrast and luminosity.
Figure 2. Examples of possible 1D correlation
The correlation by difference metric is computed in accordance with the CorrelationMode parameter.
DIRECT Correlation Mode
$$ O(n,m)=\sum_{i=1}^{kx} \sum_{j=1}^{ky} \left|K(i,j)-I(n+i-\frac{kx}{2},m+j-\frac{ky}{2})\right| $$ In this mode, 3 of the 6 patterns matching the kernel are detected. These are only patterns having similar luminosity. The best matching is obtained with the similar contrast and luminosity pattern.Figure 3. Example of Difference 1D direct correlation
MEAN Correlation Mode
$$ O(n,m)=\sum_{i=1}^{kx} \sum_{j=1}^{ky} \left|\left(K(i,j)-\mu(K)\right)-\left(I(n+i-\frac{kx}{2}, m+j-\frac{ky}{2})-\mu(I)(n,m)\right)\right| $$ In this mode, 2 of the 6 patterns matching the kernel are detected. These are only patterns having similar contrast. The confidence rate is the same for the 2 patterns.Figure 4. Example of Difference 1D mean correlation
VARIANCE Correlation Mode
$$ O(n,m)=\frac{\sum\limits_{i=1}^{kx} \sum\limits_{j=1}^{ky} \left|K(i,j)-I(n+i-\frac{kx}{2}, m+j-\frac{ky}{2})\right|}{\sqrt{\sigma^2(K)\times \sigma^2(I)(n,m)}} $$ In this mode, 3 of the 6 patterns matching the kernel are detected. These are only patterns having similar luminosity. The confidence rate is the same for the 3 patterns.Figure 5. Example of Difference 1D variance correlation
MEAN_VARIANCE Correlation Mode
$$ O(n,m)=\frac{\sum\limits_{i=1}^{kx} \sum\limits_{j=1}^{ky} \left|\left(K(i,j)-\mu(K)\right) -\left(I(n+i-\frac{kx}{2},m+j-\frac{ky}{2})-\mu(I)(n,m)\right)\right|}{\sqrt{\sigma^2(K)\times \sigma^2(I)(n,m)}} $$ In this mode, the 6 patterns matching the kernel are detected, with the same confidence rate.Figure 6. Example of Difference 1D mean and variance correlation
where: $$ \mu(K)=\frac{\sum\limits_{i=1}^{kx} \sum\limits_{j=1}^{ky} K(i,j)}{kx\times ky} $$ $$ \mu(I)(n,m)=\frac{\sum\limits_{i=1}^{kx} \sum\limits_{j=1}^{ky} I(n+i,m+j)}{kx\times ky} $$ $$ \sigma^2(K)=\sum_{i=1}^{kx} \sum_{j=1}^{ky} \left(K(i,j)-\mu(K)\right)^{2} $$ $$ \sigma^2(I)(n,m)=\sum_{i=1}^{kx} \sum_{j=1}^{ky} \left( I(n+i-\frac{kx}{2},m+j-\frac{ky}{2} ) - \mu(I)(n,m)\right)^{2} $$
Note: This algorithm returns the main correlation peak in the outputMeasurement object. More correlation peaks can be extracted from the outputImage correlation image with the LocalMaxima2d algorithm.
See also
Function Syntax
This function returns a CorrelationByDifference2dOutput structure containing the outputImage and outputMeasurement output parameters.
// Output structure.
struct CorrelationByDifference2dOutput
{
std::shared_ptr< iolink::ImageView > outputImage;
CorrelationMsr::Ptr outputMeasurement;
};
// Function prototype.
CorrelationByDifference2dOutput
correlationByDifference2d( std::shared_ptr< iolink::ImageView > inputImage,
std::shared_ptr< iolink::ImageView > inputKernelImage,
CorrelationByDifference2d::OffsetMode offsetMode,
CorrelationByDifference2d::CorrelationMode correlationMode,
std::shared_ptr< iolink::ImageView > outputImage = NULL,
CorrelationMsr::Ptr outputMeasurement = NULL );
This function returns a tuple containing the output_image and output_measurement output parameters.
// Function prototype.
correlation_by_difference_2d( input_image,
input_kernel_image,
offset_mode = CorrelationByDifference2d.OffsetMode.OFFSET_1,
correlation_mode = CorrelationByDifference2d.CorrelationMode.DIRECT,
output_image = None,
output_measurement = None )
This function returns a CorrelationByDifference2dOutput structure containing the outputImage and outputMeasurement output parameters.
/// Output structure of the CorrelationByDifference2d function.
public struct CorrelationByDifference2dOutput
{
public IOLink.ImageView outputImage;
public CorrelationMsr outputMeasurement;
};
// Function prototype.
public static CorrelationByDifference2dOutput
CorrelationByDifference2d( IOLink.ImageView inputImage,
IOLink.ImageView inputKernelImage,
CorrelationByDifference2d.OffsetMode offsetMode = ImageDev.CorrelationByDifference2d.OffsetMode.OFFSET_1,
CorrelationByDifference2d.CorrelationMode correlationMode = ImageDev.CorrelationByDifference2d.CorrelationMode.DIRECT,
IOLink.ImageView outputImage = null,
CorrelationMsr outputMeasurement = null );
Class Syntax
Parameters
| Class Name | CorrelationByDifference2d |
|---|
| Parameter Name | Description | Type | Supported Values | Default Value | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
 |
inputImage |
The input grayscale image. | Image | Binary, Label or Grayscale | nullptr | ||||||||
|
inputKernelImage |
The correlation kernel. | Image | Binary, Label or Grayscale | nullptr | ||||||||
|
offsetMode |
The calculation offset, in pixels. The greater this value, computation is faster but detection is less precise.
|
Enumeration | OFFSET_1 | |||||||||
|
correlationMode |
The normalization mode for correlation.
|
Enumeration | DIRECT | |||||||||
 |
outputImage |
The output correlation image. Its dimensions are forced to the same values as the input. Its data type is forced to floating point. | Image | nullptr | |||||||||
|
outputMeasurement |
The correlation matching results. | CorrelationMsr | nullptr | |||||||||
Object Examples
std::shared_ptr< iolink::ImageView > polystyrene = ioformat::readImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene.tif" ); CorrelationByDifference2d correlationByDifference2dAlgo; correlationByDifference2dAlgo.setInputImage( polystyrene ); correlationByDifference2dAlgo.setInputKernelImage( polystyrene ); correlationByDifference2dAlgo.setOffsetMode( CorrelationByDifference2d::OffsetMode::OFFSET_1 ); correlationByDifference2dAlgo.setCorrelationMode( CorrelationByDifference2d::CorrelationMode::DIRECT ); correlationByDifference2dAlgo.execute(); std::cout << "outputImage:" << correlationByDifference2dAlgo.outputImage()->toString(); std::cout << "minComputed: " << correlationByDifference2dAlgo.outputMeasurement()->minComputed( 0 ) ;
polystyrene = ioformat.read_image(imagedev_data.get_image_path("polystyrene.tif"))
correlation_by_difference_2d_algo = imagedev.CorrelationByDifference2d()
correlation_by_difference_2d_algo.input_image = polystyrene
correlation_by_difference_2d_algo.input_kernel_image = polystyrene
correlation_by_difference_2d_algo.offset_mode = imagedev.CorrelationByDifference2d.OFFSET_1
correlation_by_difference_2d_algo.correlation_mode = imagedev.CorrelationByDifference2d.DIRECT
correlation_by_difference_2d_algo.execute()
print( "output_image:", str( correlation_by_difference_2d_algo.output_image ) )
print( "minComputed: ", str( correlation_by_difference_2d_algo.output_measurement.min_computed( 0 ) ) )
ImageView polystyrene = ViewIO.ReadImage( @"Data/images/polystyrene.tif" );
CorrelationByDifference2d correlationByDifference2dAlgo = new CorrelationByDifference2d
{
inputImage = polystyrene,
inputKernelImage = polystyrene,
offsetMode = CorrelationByDifference2d.OffsetMode.OFFSET_1,
correlationMode = CorrelationByDifference2d.CorrelationMode.DIRECT
};
correlationByDifference2dAlgo.Execute();
Console.WriteLine( "outputImage:" + correlationByDifference2dAlgo.outputImage.ToString() );
Console.WriteLine( "minComputed: " + correlationByDifference2dAlgo.outputMeasurement.minComputed( 0 ) );
Function Examples
std::shared_ptr< iolink::ImageView > polystyrene = ioformat::readImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene.tif" ); auto result = correlationByDifference2d( polystyrene, polystyrene, CorrelationByDifference2d::OffsetMode::OFFSET_1, CorrelationByDifference2d::CorrelationMode::DIRECT ); std::cout << "outputImage:" << result.outputImage->toString(); std::cout << "minComputed: " << result.outputMeasurement->minComputed( 0 ) ;
polystyrene = ioformat.read_image(imagedev_data.get_image_path("polystyrene.tif"))
result_output_image, result_output_measurement = imagedev.correlation_by_difference_2d( polystyrene, polystyrene, imagedev.CorrelationByDifference2d.OFFSET_1, imagedev.CorrelationByDifference2d.DIRECT )
print( "output_image:", str( result_output_image ) )
print( "minComputed: ", str( result_output_measurement.min_computed( 0 ) ) )
ImageView polystyrene = ViewIO.ReadImage( @"Data/images/polystyrene.tif" ); Processing.CorrelationByDifference2dOutput result = Processing.CorrelationByDifference2d( polystyrene, polystyrene, CorrelationByDifference2d.OffsetMode.OFFSET_1, CorrelationByDifference2d.CorrelationMode.DIRECT ); Console.WriteLine( "outputImage:" + result.outputImage.ToString() ); Console.WriteLine( "minComputed: " + result.outputMeasurement.minComputed( 0 ) );