ImageDev

ImageCurvature3d

Computes local gray level curvature in a two-dimensional image.

Access to parameter description

This algorithm computes, for each voxel of an input image, two local texture curvature attributes. The curvature estimation takes the voxel size into account.

The curvature is extracted from the gradient structure tensor of the input image.
Each voxel is then associated with two principle curvatures : $\kappa_{Max}$ and $\kappa_{Min}$.
The $\kappa_{Max}$ stands for maximum local curvature, whereas $\kappa_{Min}$ stands for minimum curvature.
Two important indicators can be extracted from these values: Gaussian curvature can be used to characterize local surface comportment:
<b> Figure 1.</b> Saddle-shaped 3D curvature (image: Eric Gaba)
Figure 1. Saddle-shaped 3D curvature (image: Eric Gaba)


References:
See also

Function Syntax

This function returns a ImageCurvature3dOutput structure containing outputMaximumImage and outputMinimumImage.
// Output structure of the imageCurvature3d function.
struct ImageCurvature3dOutput
{
    /// The maximum curvature output image. Each pixel value represents the maximum curvature in the world coordinates system. Its dimensions are forced to the same values as the input. Its data type is forced to floating point.
    std::shared_ptr< iolink::ImageView > outputMaximumImage;
    /// The minimum curvature output image. Each pixel value represents the minimum curvature in the world coordinates system. Its dimensions are forced to the same values as the input. Its data type is forced to floating point.
    std::shared_ptr< iolink::ImageView > outputMinimumImage;
};

// Function prototype
ImageCurvature3dOutput imageCurvature3d( std::shared_ptr< iolink::ImageView > inputImage, std::shared_ptr< iolink::ImageView > inputMaskImage, double standardDeviation, std::shared_ptr< iolink::ImageView > outputMaximumImage = NULL, std::shared_ptr< iolink::ImageView > outputMinimumImage = NULL );
This function returns a tuple containing output_maximum_image and output_minimum_image.
// Function prototype.
image_curvature_3d( input_image,
                    input_mask_image,
                    standard_deviation = 4,
                    output_maximum_image = None,
                    output_minimum_image = None )
This function returns a ImageCurvature3dOutput structure containing outputMaximumImage and outputMinimumImage.
/// Output structure of the ImageCurvature3d function.
public struct ImageCurvature3dOutput
{
    /// 
    /// The maximum curvature output image. Each pixel value represents the maximum curvature in the world coordinates system. Its dimensions are forced to the same values as the input. Its data type is forced to floating point.
    /// 
    public IOLink.ImageView outputMaximumImage;
    /// 
    /// The minimum curvature output image. Each pixel value represents the minimum curvature in the world coordinates system. Its dimensions are forced to the same values as the input. Its data type is forced to floating point.
    /// 
    public IOLink.ImageView outputMinimumImage;
};

// Function prototype.
public static ImageCurvature3dOutput
ImageCurvature3d( IOLink.ImageView inputImage,
                  IOLink.ImageView inputMaskImage,
                  double standardDeviation = 4,
                  IOLink.ImageView outputMaximumImage = null,
                  IOLink.ImageView outputMinimumImage = null );

Class Syntax

Parameters

Class Name ImageCurvature3d

Parameter Name Description Type Supported Values Default Value
input
inputImage
The input image. Image Binary, Label, Grayscale or Multispectral nullptr
input
inputMaskImage
The binary image designating the area to process. If it equals null, the algorithm is applied on the whole image. This image must have same dimensions as the input image. Image Binary nullptr
input
standardDeviation
The standard deviation for Gaussian filter, expressed in world coordinates of the input image. Float64 >0 4
output
outputMaximumImage
The maximum curvature output image. Each pixel value represents the maximum curvature in the world coordinates system. Its dimensions are forced to the same values as the input. Its data type is forced to floating point. Image nullptr
output
outputMinimumImage
The minimum curvature output image. Each pixel value represents the minimum curvature in the world coordinates system. Its dimensions are forced to the same values as the input. Its data type is forced to floating point. Image nullptr

Object Examples

auto foam = readVipImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "foam.vip" );
auto foam_sep = readVipImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "foam_sep.vip" );

ImageCurvature3d imageCurvature3dAlgo;
imageCurvature3dAlgo.setInputImage( foam );
imageCurvature3dAlgo.setInputMaskImage( foam_sep );
imageCurvature3dAlgo.setStandardDeviation( 4.0 );
imageCurvature3dAlgo.execute();

std::cout << "outputMaximumImage:" << imageCurvature3dAlgo.outputMaximumImage()->toString();
std::cout << "outputMinimumImage:" << imageCurvature3dAlgo.outputMinimumImage()->toString();
foam = imagedev.read_vip_image(imagedev_data.get_image_path("foam.vip"))
foam_sep = imagedev.read_vip_image(imagedev_data.get_image_path("foam_sep.vip"))

image_curvature_3d_algo = imagedev.ImageCurvature3d()
image_curvature_3d_algo.input_image = foam
image_curvature_3d_algo.input_mask_image = foam_sep
image_curvature_3d_algo.standard_deviation = 4.0
image_curvature_3d_algo.execute()

print( "output_maximum_image:", str( image_curvature_3d_algo.output_maximum_image ) )
print( "output_minimum_image:", str( image_curvature_3d_algo.output_minimum_image ) )
ImageView foam = Data.ReadVipImage( @"Data/images/foam.vip" );
ImageView foam_sep = Data.ReadVipImage( @"Data/images/foam_sep.vip" );

ImageCurvature3d imageCurvature3dAlgo = new ImageCurvature3d
{
    inputImage = foam,
    inputMaskImage = foam_sep,
    standardDeviation = 4.0
};
imageCurvature3dAlgo.Execute();

Console.WriteLine( "outputMaximumImage:" + imageCurvature3dAlgo.outputMaximumImage.ToString() );
Console.WriteLine( "outputMinimumImage:" + imageCurvature3dAlgo.outputMinimumImage.ToString() );

Function Examples

auto foam = readVipImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "foam.vip" );
auto foam_sep = readVipImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "foam_sep.vip" );

auto result = imageCurvature3d( foam, foam_sep, 4.0 );

std::cout << "outputMaximumImage:" << result.outputMaximumImage->toString();
std::cout << "outputMinimumImage:" << result.outputMinimumImage->toString();
foam = imagedev.read_vip_image(imagedev_data.get_image_path("foam.vip"))
foam_sep = imagedev.read_vip_image(imagedev_data.get_image_path("foam_sep.vip"))

result_output_maximum_image, result_output_minimum_image = imagedev.image_curvature_3d( foam, foam_sep, 4.0 )

print( "output_maximum_image:", str( result_output_maximum_image ) )
print( "output_minimum_image:", str( result_output_minimum_image ) )
ImageView foam = Data.ReadVipImage( @"Data/images/foam.vip" );
ImageView foam_sep = Data.ReadVipImage( @"Data/images/foam_sep.vip" );

Processing.ImageCurvature3dOutput result = Processing.ImageCurvature3d( foam, foam_sep, 4.0 );

Console.WriteLine( "outputMaximumImage:" + result.outputMaximumImage.ToString() );
Console.WriteLine( "outputMinimumImage:" + result.outputMinimumImage.ToString() );