Measure allowing to compute the z-coordinate of the barycenter ponderated by the gray level of each pixel for shape.

The coordinates $\left[ x_b, y_b \right]^T$ of the grey barycenter for a given 2d or 3d shape are computed as follows :

$\left\lbrace \begin{array}{ccc} x_b & = & \frac{1}{nbElt} \left( \sum_{\left\{x, y, z\right\} \in Shape}{Shape(x, y, z) \times x} \right)\\ y_b & = & \frac{1}{nbElt} \left( \sum_{\left\{x, y, z\right\} \in Shape}{Shape(x, y, z) \times y} \right)\\ z_b & = & \frac{1}{nbElt} \left( \sum_{\left\{x, y, z\right\} \in Shape}{Shape(x, y, z) \times z} \right) \end{array} \right.$

Where $ Shape $ is the set of pixels in the shape and $ nbElt $ is the number of elements (i.e. pixels in 2d case or voxels in 3d case) of the shape.

Here is an example of 3d grey z-barycenter measurement; in that example, the intensity used to compute the measures are 1 if the pixel is inside a shape and 0 otherwise. Consequently, we get the same results than BarycenterZ :

Measure allowing to compute the z-coordinate of the barycenter ponderated by the gray level of each pixel for shape

Measure synthesis :

Measure Type	Measure Unit Type	Parameter Type	Result Type	Shape Requirements
Generic	Length	None	Value (ipsdk::ipReal64)	Row Intersections

See Shape measurement for additional information on these pictograms

Example of Python code :

Generic example in 3d case :

import PyIPSDK

import PyIPSDK.IPSDKIPLShapeAnalysis as shapeanalysis

    # Create the infoset
    inMeasureInfoSet3d = PyIPSDK.createMeasureInfoSet3d()
    PyIPSDK.createMeasureInfo(inMeasureInfoSet3d, "GreyBarycenterZMsr")
    
    #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("GreyBarycenterZMsr")
    
    # retrieve measure values
    outMsrValues = outMsr.getMeasureResult().getColl(0)
    print("First label measurement equal " + str(outMsrValues[1]))

Example of C++ code :

Example informations

Associated library

IPSDKIPLShapeAnalysis

Code Example

    // opening grey level input image
    ImagePtr pInGreyImg3d = loadTiffImageFile(inputGreyImgPath, eTiffDirectoryMode::eTDM_Volume);
    // read entity shape 3d collection used for processing
    Shape3dCollPtr pShape3dColl = boost::make_shared<Shape3dColl>();
    IPSDK_REQUIRE(readFromBinaryFile(inputShape3dCollPath, *pShape3dColl) == true);
    // define a measure info set
    MeasureInfoSetPtr pMeasureInfoSet = MeasureInfoSet::create3dInstance();
    createMeasureInfo(pMeasureInfoSet, "GreyBarycenterZMsr");
    
    // compute measure on shape 3d collection
    MeasureSetPtr pOutMeasureSet = shapeAnalysis3d(pInGreyImg3d, pShape3dColl, pMeasureInfoSet);
    // retrieve associated results
    const MeasureConstPtr& pGreyBarycenterZOutMsr = pOutMeasureSet->getMeasure("GreyBarycenterZMsr");
    const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>& outResults = static_cast<const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>&>(pGreyBarycenterZOutMsr->getMeasureResult());