xGradImg,yGradImg =	gaussianGradient2dImg (inImg,inStdDev)
xGradImg,yGradImg =	gaussianGradient2dImg (inImg,inStdDevX,inStdDevY,inOptGradientGaussianCoverage)
image =	gaussianXGradient2dImg (inImg,inStdDev)
image =	gaussianYGradient2dImg (inImg,inStdDev)

Detailed Description

Compute X and Y gradients of an input image convolving it with 2d Gaussian kernels.

Used Gaussian gradient kernel $GaussKnl^{X}_{XY}$ and $GaussKnl^{Y}_{XY}$ coefficients are defined as follow :

$GaussKnl^{X}_{XY}[o_x, o_y] = -\dfrac{o_x}{2\pi\sigma^4}e^{-\dfrac{o_x^2+o_y^2}{2\sigma^2}}$

$GaussKnl^{Y}_{XY}[o_x, o_y] = -\dfrac{o_y}{2\pi\sigma^4}e^{-\dfrac{o_x^2+o_y^2}{2\sigma^2}}$

where :

$\sigma$ is defined by InStdDev attribute

Size $[n_x, n_y]$ of this finite kernel is controlled by InOptGradientGaussianCoverage attribute.
This parameter defined the minimum distribution spread ratio which should be reach regards to an infinite Gaussian distribution.
We define for example $n_x$ such that :

$n_x = \max(MinHalfKernelSize, \min(\{n\}\in \mathbb{N}^+) / \sum_{o_x=-\dfrac{n_x}{2}}^{\dfrac{n_x}{2}}{GaussKnl_X[o_x]}>= GaussianRatio \times \sum_{o_x=-\infty}^{+\infty}{GaussKnl_X[o_x]})$

where :

$GaussKnl_X[o_x] = \dfrac{1}{\sqrt{2\pi}\sigma}e^{-\dfrac{o_x^2}{2\sigma^2}}$

On output image values are given by:

$OutOptGradXImg[x, y] = \sum_{o_y=-\dfrac{n_y}{2}}^{\dfrac{n_y}{2}}{\sum_{o_x=-\dfrac{n_x}{2}}^{\dfrac{n_x}{2}}{InImg[x+o_x, y+o_y] \times GaussKnl^{X}_{XY}[o_x, o_y]}}$

$OutOptGradYImg[x, y] = \sum_{o_y=-\dfrac{n_y}{2}}^{\dfrac{n_y}{2}}{\sum_{o_x=-\dfrac{n_x}{2}}^{\dfrac{n_x}{2}}{InImg[x+o_x, y+o_y] \times GaussKnl^{Y}_{XY}[o_x, o_y]}}$

A detailled analysis of this filter has been done in J. Canny (1986) "A computational approach to edge detection", IEEE Trans. Pattern Analysis and Machine Intelligence, vol 8, pages 679-714.

Output images OutOptGradXImg and OutOptGradYImg are optional (at least one must be provided). Input and output images must have same size.

Here is an example of a Gaussian gradient operation applied to an 8-bits grey levels input image (with $InStdDev=3$ ):

See also: http://en.wikipedia.org/wiki/Edge_detection#cite_note-8

Example of Python code :

Example imports

import PyIPSDK

import PyIPSDK.IPSDKIPLFiltering as filter

Code Example

    # opening of input images
    inImg = PyIPSDK.loadTiffImageFile(inputImgPath)
    
    # gaussian gradient filter 2d computation
    outGxImg, outGyImg = filter.gaussianGradient2dImg(inImg, 1.5)

Example of C++ code :

Example informations

Header file

#include <IPSDKIPL/IPSDKIPLFiltering/Processor/GaussianGradient2dImg/GaussianGradient2dImg.h>

Code Example

    // opening input image
    ImagePtr pInImg = loadTiffImageFile(inputImgPath);
        
    // compute gaussian gradient on input image
    GradientXYImg gradientXY = gaussianGradient2dImg(pInImg, inStdDev, inStdDev, createGaussianCoverage(inOptGaussianRatio, minHalfKernelSize));