edu.mines.jtk.dsp
Class LocalLaplacianFilter

java.lang.Object
  edu.mines.jtk.dsp.LocalLaplacianFilter

public class LocalLaplacianFilter
extends java.lang.Object

Local Laplacian filter defined by non-constant diffusion tensors. The Laplacian operator appears in diffusion equations, and this filter is useful in the context of anisotropic diffusion filtering.

This filter computes y = y+G'DGx where G is an approximation to the gradient operator, G' is its adjoint, and D is a local diffusion tensor that determines for each image sample the direction of the Laplacian filter.

Local Laplacian filters are rarely used alone. While zeroing some features in images, they tend to attenuate many other features as well. Therefore, these filters are typically used in combinations with others.

For example, the filter implied by (I+G'DG)y = G'DGx acts as a notch filter. It attenuates features for which G'DGx is zero while preserving other features. Diffusivities d (inside D) control the width of the notch. Note that application of this filter requires solving a sparse symmetric positive-definite system of equations.

An even simpler example is the filter implied by (I+G'DG)y = x. This filter smooths features in the directions implied by the tensors D. Again, application of this filter requires solving a sparse symmetric positive-definite system of equations.

The accumulation of the filter output in y = y+G'DGx is useful when constructing such combination filters. For y = 0, this filter computes y = G'DGx. For y = x, this filter computes y = (I+G'DG)x.

Version:

2008.08.27

Author:

Dave Hale, Colorado School of Mines

Constructor Summary

LocalLaplacianFilter()
Constructs a local Laplacian filter.

LocalLaplacianFilter(double scale)
Constructs a local Laplacian filter.

Method Summary

void	apply(Tensors2 d, float[][] x, float[][] y) Computes y = y+G'DGx for 2D arrays x and y.
void	apply(Tensors3 d, float[][][] x, float[][][] y) Computes y = y+G'DGx for 3D arrays x and y.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LocalLaplacianFilter

public LocalLaplacianFilter()

Constructs a local Laplacian filter.

LocalLaplacianFilter

public LocalLaplacianFilter(double scale)

Constructs a local Laplacian filter.

Parameters:

scale - scale factor for all diffusion coefficients.

Method Detail

apply

public void apply(Tensors2 d,
                  float[][] x,
                  float[][] y)

Computes y = y+G'DGx for 2D arrays x and y.

Parameters:

x - input array. Must be distinct from the array y.

y - input/output array. Must be distinct from the array x.

apply

public void apply(Tensors3 d,
                  float[][][] x,
                  float[][][] y)

Computes y = y+G'DGx for 3D arrays x and y.

Parameters:

x - input array. Must be distinct from the array y.

y - input/output array. Must be distinct from the array x.