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ImageDev

Rotate2d

Applies a rotation of a given angle on a two-dimensional image around a given point or the center of the image.

Access to parameter description

For an introduction: section 2D Rotations.

This algorithm performs a rotation of an image by a user-defined angle θ and a center C.
The new coordinates (x′,y′) can be expressed as a function of the old coordinates (x,y): {x′=(x−x0)⋅cosθ−(y−y0)⋅sinθ+x0y′=(x−x0)⋅sinθ+(y−y0)⋅cosθ+y0} where (x0,y0) are the coordinates of the center of the rotation. Or in matrix notation: [x′y′]=[cosθ−sinθsinθcosθ]⋅[x−x0y−y0]+[x0y0] If the dimensions of the output image are the same as those of the input, the destination pixels may be outside the image, and these pixels are then ignored. An output resizing option automatically modifies the dimensions of the image to make all the input data visible in the output image. This option is enabled by default.
On the other hand, some pixels in the output image may not have a corresponding pixel in the input image. In this case, a user-defined padding value is assigned to these pixels.

Furthermore, the (x,y) coordinates obtained are not always integers, even though an image is a discrete space. The following figure illustrates the grid of the resultant image, the point M′ being a pixel in this image. The points are generated from the rotation of the original image and do not fit on the grid.
<b> Figure 1.</b> Image grid rotation
Figure 1. Image grid rotation

To calculate the intensity of each pixel M′, two methods are possible:
If dj denotes the distance M′jM′, fi is defined as: fi=j=4∏j=1j≠idj e.g., f1=d2d3d4.

The choice of the fi's ensures that the interpolated value is equal to g′j if M′ matches M′j. This method gives better results but requires more computation time.

<b> (a) </b>
(a)
<b> (b) </b>
(b)
<b> (c) </b>
(c)
Figure 1. Centered 30 degrees rotation of a 1024x1024 image: (a) the input image,
(b) rotation without output resizing (1024x1024 image), (c) rotation with output resizing (1398x1398 image).

See also

Function Syntax

This function returns outputImage. 
// Function prototype
std::shared_ptr< iolink::ImageView >
rotate2d( std::shared_ptr< iolink::ImageView > inputImage,
          double rotationAngle,
          Rotate2d::CenterMode centerMode,
          iolink::Vector2d rotationCenter,
          Rotate2d::InterpolationType interpolationType,
          bool outputResizing,
          double paddingValue,
          std::shared_ptr< iolink::ImageView > outputImage = nullptr );

Class Syntax

Parameters

Parameter Name Description Type Supported Values Default Value
input
inputImage
The input image. Image Binary, Label, Grayscale or Multispectral nullptr
input
rotationAngle
The angle of the rotation in degrees. Float64 Any value 90
input
centerMode
The way to define the rotation center
IMAGE_CENTER The rotation center is the center of the input image.
OTHER The rotation center is user-defined. It can be set with the rotationCenter parameter.
Enumeration IMAGE_CENTER
input
rotationCenter
The rotation center coordinates. This parameter is ignored in IMAGE_CENTER mode. Vector2d Any value {0.f, 0.f}
input
interpolationType
The interpolation mode. Method used to calculate the intensity of each pixel in the result image.
NEAREST_NEIGHBOR Assign the gray level of the nearest pixel.
LINEAR Assign the bilinear interpolation from the four nearest pixels.
Enumeration NEAREST_NEIGHBOR
input
outputResizing
Resize the output image to make all input data visible in the output image if set to True. Preserve the input dimension if set to False. Bool true
input
paddingValue
The background value for pixels with no correpondant point in the input image. Float64 Any value 0
output
outputImage
The output image. Its type is forced to the same values as the input. Its dimensions are identical to or greater than the input image, according to the outputResizing parameter. Image nullptr

Object Examples

auto polystyrene = ioformat::readImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene.tif" );

Rotate2d rotate2dAlgo;
rotate2dAlgo.setInputImage( polystyrene );
rotate2dAlgo.setRotationAngle( 40.5 );
rotate2dAlgo.setCenterMode( Rotate2d::CenterMode::IMAGE_CENTER );
rotate2dAlgo.setRotationCenter( {15.5, 32} );
rotate2dAlgo.setInterpolationType( Rotate2d::InterpolationType::NEAREST_NEIGHBOR );
rotate2dAlgo.setOutputResizing( true );
rotate2dAlgo.setPaddingValue( 0 );
rotate2dAlgo.execute();

std::cout << "outputImage:" << rotate2dAlgo.outputImage()->toString();

Function Examples

auto polystyrene = ioformat::readImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene.tif" );

auto result = rotate2d( polystyrene, 40.5, Rotate2d::CenterMode::IMAGE_CENTER, {15.5, 32}, Rotate2d::InterpolationType::NEAREST_NEIGHBOR, true, 0 );

std::cout << "outputImage:" << result->toString();