# Example Image Derivative

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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:

Concepts:

• Image Derivative
• Gradient
• Hessian

# 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 GrayU8 with GrayS16 for derivatives also works
GrayF32 grey = new GrayF32(input.getWidth(), input.getHeight());
ConvertBufferedImage.convertFrom(input, grey);

// First order derivative, also known as the gradient
GrayF32 derivX = new GrayF32(grey.width, grey.height);
GrayF32 derivY = new GrayF32(grey.width, grey.height);

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

// Second order derivative, also known as the Hessian
GrayF32 derivXX = new GrayF32(grey.width, grey.height);
GrayF32 derivXY = new GrayF32(grey.width, grey.height);
GrayF32 derivYY = new GrayF32(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<GrayF32, GrayF32> derivative =
GImageDerivativeOps.createAnyDerivatives(DerivativeType.SOBEL, GrayF32.class, GrayF32.class);

// the boolean sequence indicates if its an X or Y derivative
derivative.setInput(grey);
GrayF32 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, null), "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);
}
}
```