image =	laplacianDoG3dImg (inImg3d,inStdDev)
image =	laplacianDoG3dImg (inImg3d,inStdDev,inOptStdDevFactor,inOptSmoothingGaussianCoverage)

Detailed Description

laplacian algorithm of input 3d image using a difference of gaussian approximation

This image filter computes a blurred approximation of laplacian of an image. This is a band-pass filter which can be used to enhance edges present in an image while reducing noise. A major drawback of this filter is the resulting overall image contrast reduction. It can be combined with a zero crossing detection algorithm to automatically detect edges.

Given a gaussian smoothing operation on an input image $InImg$ using standard deviation $\sigma$ :

$G_{\sigma}(InImg[x, y, z]) = \sum_{o_z=-\dfrac{n_z}{2}}^{\dfrac{n_z}{2}}{\sum_{o_y=-\dfrac{n_y}{2}}^{\dfrac{n_y}{2}}{\sum_{o_x=-\dfrac{n_x}{2}}^{\dfrac{n_x}{2}}{InImg3d[x+o_x, y+o_y, z+o_z] \times GaussKnl^{\sigma}_{XYZ}[o_x, o_y, o_z]}}}$

(see Gaussian Smoothing 3d for more informations)

Laplacian with difference of gaussian approximation algorithm defines an excitatory ( $\sigma_E=InStdDev$ ) and an inhibitory ( $\sigma_I=InStdDev \times InOptStdDevFactor$ ) standard deviation to compute its output :

$OutImg = G_{\sigma_E}(InImg) - G_{\sigma_I}(InImg)$

Here is an example of a laplacian DoG operation applied to an 8-bits grey levels input image (with $InStdDev=1$ ) :

Please refer to Laplacian DoG 2d for an analysis of $InStdDev$ action on output of this filter.

See also: D. Marr, E. Hildreth, 29 Feb 1980, "Theory of Edge Detection", Proceedings of the Royal Society of London. Series B, Biological Sciences, Vol. 207, No. 1167, pp. 187-217.; http://en.wikipedia.org/wiki/Difference_of_Gaussians

Example of Python code :

Example imports

import PyIPSDK

import PyIPSDK.IPSDKIPLFiltering as filter

Code Example

    # opening of input images
    inImg = PyIPSDK.loadTiffImageFile(inputImgPath)
    
    # laplacian difference of gaussian filter 3d computation
    outImg = filter.laplacianDoG3dImg(inImg, 1.5)

Example of C++ code :

Example informations

Header file

#include <IPSDKIPL/IPSDKIPLFiltering/Processor/LaplacianDoG3dImg/LaplacianDoG3dImg.h>

Code Example

    // opening input image
    ImagePtr pInImg = loadTiffImageFile(inputImgPath, eTiffDirectoryMode::eTDM_Volume);
        
    // compute laplacian on input image
    ImagePtr pOutImg = laplacianDoG3dImg(pInImg, 3);