org.openimaj.image.processing.convolution

## Class BasicDerivativeKernels

• java.lang.Object
• org.openimaj.image.processing.convolution.BasicDerivativeKernels

• ```public class BasicDerivativeKernels
extends Object```
A set of standard derivative kernels. These kernels help estimate the derivative over various orders at a point in a matrix. This is approximated by applying a finite difference derivative operation on a gaussian kernel with a very low sigma. i.e. a gaussian kernel that looks like: [ [0,0,0], [0,1,0], [0,0,0] ] By successive derivative calculations in the x direction and y direction it is possible to estimate derivatives in both directions as well.
Author:
Jonathon Hare (jsh2@ecs.soton.ac.uk)
• ### Field Summary

Fields
Modifier and Type Field and Description
`static FConvolution` `DX_KERNEL`
kernel approximating the first derivative of a low-sigma gaussian in the x-direction [-0.5, 0, 0.5].
`static FConvolution` `DXX_KERNEL`
kernel approximating the second derivative of a low sigma gaussian in the x-direction [1, -2, 1].
`static FConvolution` `DXXXX_KERNEL`
kernel approximating the fourth derivative of a low sigma gaussian in the x-direction [1,-4,6,-4,1]^T Useful for giving an estimate of the fourth derivative in y of any given point
`static FConvolution` `DXXYY_KERNEL`
kernel approximating the second derivative of a low sigma gaussian in the x-direction and y-direction [[1,-2,1],[-2,4,-2],[1,-2,1]] .
`static FConvolution` `DXY_KERNEL`
kernel approximating the first derivative of a low sigma gaussian in the x-direction and y-direction [[-0.25, 0, 0.25], [0, 0, 0], [0.25, 0, -0.25]] .
`static FConvolution` `DY_KERNEL`
kernel approximating the first derivative of a low-sigma gaussian in the y-direction [-0.5, 0, 0.5]'.
`static FConvolution` `DYY_KERNEL`
kernel approximating the second derivative of a low sigma gaussian in the y-direction [1, -2, 1]'.
`static FConvolution` `DYYYY_KERNEL`
kernel approximating the fourth derivative of a low sigma gaussian in the y-direction [1,-4,6,-4,1]^T Useful for giving an estimate of the fourth derivative in y of any given point
• ### Constructor Summary

Constructors
Constructor and Description
`BasicDerivativeKernels()`

• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Field Detail

• #### DX_KERNEL

`public static final FConvolution DX_KERNEL`
kernel approximating the first derivative of a low-sigma gaussian in the x-direction [-0.5, 0, 0.5]. Useful for giving an estimate of the second derivative in x of any given point
• #### DY_KERNEL

`public static final FConvolution DY_KERNEL`
kernel approximating the first derivative of a low-sigma gaussian in the y-direction [-0.5, 0, 0.5]'. Useful for giving an estimate of the second derivative in y of any given point
• #### DXX_KERNEL

`public static final FConvolution DXX_KERNEL`
kernel approximating the second derivative of a low sigma gaussian in the x-direction [1, -2, 1]. Useful for giving an estimate of the second derivative in x of any given point
• #### DXY_KERNEL

`public static final FConvolution DXY_KERNEL`
kernel approximating the first derivative of a low sigma gaussian in the x-direction and y-direction [[-0.25, 0, 0.25], [0, 0, 0], [0.25, 0, -0.25]] . Useful for giving an estimate of the first order derivative in x then y of any given point
• #### DYY_KERNEL

`public static final FConvolution DYY_KERNEL`
kernel approximating the second derivative of a low sigma gaussian in the y-direction [1, -2, 1]'. Useful for giving an estimate of the second derivative in y of any given point
• #### DXXXX_KERNEL

`public static final FConvolution DXXXX_KERNEL`
kernel approximating the fourth derivative of a low sigma gaussian in the x-direction [1,-4,6,-4,1]^T Useful for giving an estimate of the fourth derivative in y of any given point
• #### DXXYY_KERNEL

`public static final FConvolution DXXYY_KERNEL`
kernel approximating the second derivative of a low sigma gaussian in the x-direction and y-direction [[1,-2,1],[-2,4,-2],[1,-2,1]] . Useful for giving an estimate of the second order derivative in x then y of any given point
• #### DYYYY_KERNEL

`public static final FConvolution DYYYY_KERNEL`
kernel approximating the fourth derivative of a low sigma gaussian in the y-direction [1,-4,6,-4,1]^T Useful for giving an estimate of the fourth derivative in y of any given point
• ### Constructor Detail

• #### BasicDerivativeKernels

`public BasicDerivativeKernels()`