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()

Method Summary

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()