Example Image Derivative

• 

  Input image

• 

  X derivative

• 

  XYX derivative

Example of how to compute different image derivatives. The gradient (1st order derivative) is probably the important image derivative and is used as a first step when extracting many types of image features. The code below shows how gradient, Hessian (2nd order), and arbitrary image derivatives can be computed.

Example Code:

• ExampleImageDerivative.java

Concepts:

• Image Derivative
• Gradient
• Hessian

Relevant Applets:

• Gradient

Example Code

/**
 * Example showing how to compute different image derivatives using built in functions.
 *
 * @author Peter Abeles
 */
public class ExampleImageDerivative {
	public static void main(String[] args) {
		BufferedImage input = UtilImageIO.loadImage(UtilIO.pathExample("simple_objects.jpg"));

		// We will use floating point images here, but ImageUInt8 with ImageSInt16 for derivatives also works
		ImageFloat32 grey = new ImageFloat32(input.getWidth(),input.getHeight());
		ConvertBufferedImage.convertFrom(input, grey);

		// First order derivative, also known as the gradient
		ImageFloat32 derivX = new ImageFloat32(grey.width,grey.height);
		ImageFloat32 derivY = new ImageFloat32(grey.width,grey.height);

		GImageDerivativeOps.gradient(DerivativeType.SOBEL, grey, derivX, derivY, BorderType.EXTENDED);

		// Second order derivative, also known as the Hessian
		ImageFloat32 derivXX = new ImageFloat32(grey.width,grey.height);
		ImageFloat32 derivXY = new ImageFloat32(grey.width,grey.height);
		ImageFloat32 derivYY = new ImageFloat32(grey.width,grey.height);

		GImageDerivativeOps.hessian(DerivativeType.SOBEL, derivX, derivY, derivXX, derivXY, derivYY, BorderType.EXTENDED);

		// There's also a built in function for computing arbitrary derivatives
		AnyImageDerivative<ImageFloat32,ImageFloat32> derivative =
				GImageDerivativeOps.createAnyDerivatives(DerivativeType.SOBEL, ImageFloat32.class, ImageFloat32.class);

		// the boolean sequence indicates if its an X or Y derivative
		derivative.setInput(grey);
		ImageFloat32 derivXYX = derivative.getDerivative(true, false, true);

		// Visualize the results
		ListDisplayPanel gui = new ListDisplayPanel();
		gui.addImage(ConvertBufferedImage.convertTo(grey,null),"Input Grey");
		gui.addImage(VisualizeImageData.colorizeSign(derivX, null, -1),"Sobel X");
		gui.addImage(VisualizeImageData.colorizeSign(derivY, null, -1),"Sobel Y");
		// Use colors to show X and Y derivatives in one image.  Looks pretty.
		gui.addImage(VisualizeImageData.colorizeGradient(derivX, derivY, -1),"Sobel X and Y");
		gui.addImage(VisualizeImageData.colorizeSign(derivXX, null,-1),"Sobel XX");
		gui.addImage(VisualizeImageData.colorizeSign(derivXY, null,-1),"Sobel XY");
		gui.addImage(VisualizeImageData.colorizeSign(derivYY, null,-1),"Sobel YY");
		gui.addImage(VisualizeImageData.colorizeSign(derivXYX, null,-1),"Sobel XYX");

		ShowImages.showWindow(gui,"Image Derivatives",true);
	}
}