Measure allowing to compute the zeroth to the third moment ponderated by the gray level of each pixel for shape.

The GreyMoments measurement computes the $0^{th}$ , $1^{st}$ , $2^{nd}$ and $3^{rd}$ order scale-invariant central moment for each shape, ponderated by the voxels intensities.

The central moment $m_{ij}$ for a given 2d shape $Shape$ are computed by :

$m_{ij} = \sum_{\lbrace x, y \rbrace \in Shape}{ \left(x - \bar{x} \right)^i \left(y - \bar{y} \right)^j I(x, y)}$

Where $\left(\bar{x}, \bar{y}\right)$ are the coordinates of the shape grey barycenter (see GreyBarycenter).

The corresponding scale-invariant central moment $\mu_{ij}$ is calculated by normalizing $m_{ij}$ as follows : The central moment $m_{ij}$ for a given 2d shape $Shape$ are computed by :

$\mu_{ij} = \frac{m_{ij}}{m^{1 + \left(i+j \right)/2}_{00}}$

The central grey moments for a 3d shape are computed using the same formula, using the z-axis in addition to the x and y axises [1] :

$m_{ijk} = \sum_{\lbrace x, y, z \rbrace \in Shape}{ \left(x - \bar{x} \right)^i \left(y - \bar{y} \right)^j \left(z - \bar{z} \right)^k I(x, y)}$

Where the grey 3d shape barycenter has coordinates $\left(\bar{x}, \bar{y}, \bar{z}\right)$ .

The scale-invariant 3d moments can be obtained with the following equation :

$\mu_{ijk} = \frac{m_{ijk}}{m^{1 + \left(i+j+k \right)/3}_{000}}$

Here is an example of 2d grey moment measurement :

References

[1] "Moments and Moment Invariants in Pattern Recognition, Chap. 2 Moment Invariants to Translation, Rotation and Scaling",Flusser, J.; Suk, T. & Zitova, B., John Wiley & Sons, Ltd, 2009, 13-47

Measure allowing to compute the zeroth to the third moment ponderated by the gray level of each pixel for shape

Measure synthesis :

Measure Type	Measure Unit Type	Parameter Type	Result Type	Shape Requirements
Intensity	None	None	Custom	Row Intersections

See Shape measurement for additional information on these pictograms

Example of Python code :

Generic example in 2d case :

import PyIPSDK

import PyIPSDK.IPSDKIPLShapeAnalysis as shapeanalysis

    # Create the infoset
    inMeasureInfoSet2d = PyIPSDK.createMeasureInfoSet2d()
    PyIPSDK.createMeasureInfo(inMeasureInfoSet2d, "GreyMomentsMsr")
    
    #Perform the analysis
    outMeasureSet = shapeanalysis.labelAnalysis2d(inGreyImg, inLabelImg2d, inMeasureInfoSet2d)
    
    # save results to csv format
    PyIPSDK.saveCsvMeasureFile(os.path.join(tmpPath,  "shape_analysis_results.csv"), outMeasureSet)
    
    # retrieve measure results
    outMsr = outMeasureSet.getMeasure("GreyMomentsMsr")
    
    # retrieve measure values
    outMsrValues = outMsr.getMeasureResult().getColl(0)
    print("First label first grey moment measurement equal " + str(outMsrValues[1].getMoment(shapeanalysis.GreyMomentsData.eGreyMoment3Id.eGM3I_X0Y0Z0)))

Generic example in 3d case :

import PyIPSDK

import PyIPSDK.IPSDKIPLShapeAnalysis as shapeanalysis

    # Create the infoset
    inMeasureInfoSet3d = PyIPSDK.createMeasureInfoSet3d()
    PyIPSDK.createMeasureInfo(inMeasureInfoSet3d, "GreyMomentsMsr")
    
    #Perform the analysis
    outMeasureSet = shapeanalysis.labelAnalysis3d(inGreyImg, inLabelImg, inMeasureInfoSet3d)
    
    # save results to csv format
    PyIPSDK.saveCsvMeasureFile(os.path.join(tmpPath,  "shape_analysis_results.csv"), outMeasureSet)
    # retrieve measure results
    outMsr = outMeasureSet.getMeasure("GreyMomentsMsr")
    
    # retrieve measure values
    outMsrValues = outMsr.getMeasureResult().getColl(0)
    print("First label (X0, Y0, Z0) moment measurement equal " + str(outMsrValues[1].getMoment(shapeanalysis.GreyMomentsData.eGreyMoment3Id.eGM3I_X0Y0Z0)))

Example of C++ code :

Example informations

Associated library

IPSDKIPLShapeAnalysis

Code Example

    // opening grey level input image
    ImagePtr pInGreyImg2d = loadTiffImageFile(inputGreyImgPath);
    // read entity shape 2d collection used for processing
    Shape2dCollPtr pShape2dColl = boost::make_shared<Shape2dColl>();
    IPSDK_REQUIRE(readFromXmlFile(inputShape2dCollPath, *pShape2dColl) == true);
    // define a measure info set
    MeasureInfoSetPtr pMeasureInfoSet = MeasureInfoSet::create2dInstance();
    createMeasureInfo(pMeasureInfoSet, "GreyMomentsMsr");
    
    // compute measure on shape 2d collection
    MeasureSetPtr pOutMeasureSet = shapeAnalysis2d(pInGreyImg2d, pShape2dColl, pMeasureInfoSet);
    // retrieve associated results
    const MeasureConstPtr& pGreyMomentsOutMsr = pOutMeasureSet->getMeasure("GreyMomentsMsr");
    const GreyMomentsMsrResults& outResults = static_cast<const GreyMomentsMsrResults&>(pGreyMomentsOutMsr->getMeasureResult());