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# Introduction and Acknowledgements

 Extension: OpenCAD This work is supported by NA-MIC, NCIGT, and the Slicer Community. Author: Vivek Narayan, Jayender Jagadeesan Contact: Jayender Jagadeesan jayender@bwh.harvard.edu This project is supported by P41 RR019703/RR/NCRR NIH HHS/United States, P01 CA067165/CA/NCI NIH HHS/United States and P41 EB015898/EB/NIBIB NIH HHS/United States

# Module Description

The HeterogeneityCAD module is an image feature extraction toolbox primarily to quantify the heterogeneity of tumor images and their label maps.

# Navigating the Module HeterogeneityCAD GUI - Figure 1 HeterogeneityCAD GUI - Figure 2 HeterogeneityCAD GUI - Figure 3

# Quick Instructions for Use

• Add an image or parameter map (.nrrd file) to the Nodes List
• Select a corresponding segmentation label map to use as ROI

# Image Features and Metrics

 First-Order and Distribution Statistics Data Node: The name of the input node - either an image volume or parameter map. Voxel Count: The total number of voxels within the ROI of the grayscale image or parameter map. Energy: A measure of the magnitude of values in an image. A greater amount larger values implies a greater sum of the squares of these values. Entropy: Specifies the uncertainty in the image values. It measures the average amount of information required to encode the image values Minimum Intensity: The value of the voxel(s) in the image ROI with the least value. Maximum Intensity: The value of the voxel(s) in the image ROI with the greatest value. Mean Intensity: The mean of the intensity or parameter values within the image ROI. Median Intensity: The median of the intensity or parameter values within the image ROI. Range: The difference between the highest and lowest voxel values within the image ROI. Mean Deviation: The mean of the distances of each image value from the mean of all the values in the image ROI. Root Mean Square: The square-root of the mean of the squares of the values in the image ROI. It is another measure of the magnitude of the image values. Standard Deviation: Measures the amount of variation or dispersion from the mean of the values in the image ROI. Skewness: Measures the asymmetry of the distribution of values in the image ROI about the mean of the values. Depending on where the tail is elongated and the mass of the distribution is concentrated, this value can be positive or negative. Kurtosis: A measure of the 'peakedness' of the distribution of values in the image ROI. A higher kurtosis implies that the mass of the distribution is concentrated towards the tail(s) rather than towards the mean. A lower kurtosis implies the reverse, that the mass of the distribution is concentrated towards a spike the mean. Variance: The mean of the squared distances of each value in the image ROI from the mean of the values. This is a measure of the spread of the distribution about the mean. Uniformity: A measure of the sum of the squares of each discrete value in the image ROI. This is a measure of the heterogeneity of an image, where a greater uniformity implies a greater heterogeneity or a greater range of discrete image values.
 Shape and Morphology Metrics Volume mm^3: The volume of the specified ROI of the image in cubic millimeters. Volume cc: The volume of the specified ROI of the image in cubic centimeters. Surface Area mm^2: The surface area of the specified ROI of the image in square millimeters. Surface:Volume Ratio: The ratio of the surface area (square millimeters) to the volume (cubic millimeters) of the specified ROI of the image. Compactness 1: A dimensionless measure, independent of scale and orientation. Compactness 1 is defined as the ratio of volume to the (surface area)^(1.5). This is a measure of the compactness of the shape of the image ROI Compactness 2: a dimensionless measure, independent of scale and orientation. This is a measure of the compactness of the shape of the image ROI. Maximum 3D Diameter: The maximum, pairwise euclidean distance between surface voxels of the image ROI. Spherical Disproportion: The ratio of the surface area of the image ROI to the surface area of a sphere with the same volume as the image ROI. Sphericity: A measure of the roundness or spherical nature of the image ROI, where the sphericity of a sphere is the maximum value of 1.
 Renyi Dimensions Box-Counting Dimension: Part of the family of Renyi Dimensions, where q=0 for Renyi Entropy calculations. This represents the fractal dimension or the slope of the curve on a plot of log(N) vs. log(1/s) where 'N' is the number of boxes occupied by the image ROI at each scale, 's', of an overlaid grid. Information Dimension: Part of the family of Renyi Dimensions, where q=1 for Renyi Entropy calculations. Correlation Dimension: Part of the family of Renyi Dimensions, where q=2 for Renyi Entropy calculations.
 Geometrical Measures Extruded Surface Area: The surface area of the binary object when the image ROI is "extruded" into 4D, where the parameter or intensity value defines the shape of the Fourth dimension. Extruded Volume: The volume of the binary object when the image ROI is 'extruded' into 4D, where the parameter or intensity value defines the shape of the Fourth dimension Extruded Surface:Volume Ratio: The ratio of the surface area to the volume of the binary object when the image ROI is 'extruded' into 4D, where the parameter or intensity value defines the shape of the Fourth dimension. Extruded Box-Dimension:
 Texture: Gray-Level Co-occurrence Matrix (GLCM) Autocorrelation: A measure of the magnitude of the fineness and coarseness of texture. \sum_{i=1}^{Ng}\sum_{j=1}^{Ng}{ij\mathbf{P}\(i j)} Cluster Prominence: A measure of the skewness and asymmetry of the GLCM. A higher values implies more asymmetry about the mean value while a lower value indicates a peak around the mean value and less variation about the mean. Cluster Shade: A measure of the skewness and uniformity of the GLCM. A higher cluster shade implies greater asymmetry. Cluster Tendency: Indicates the number of potential clusters present in the image. Contrast: A measure of the local intensity variation, favoring P(i,j) values away from the diagonal (i != j), with a larger value correlating with larger image variation. Correlation: A value between 0 (uncorrelated) and 1 (perfectly correlated) showing the linear dependency of gray level values in the GLCM. For a symmetrical GLCM, ux = uy (means of px and py) and sigx = sigy (standard deviations of px and py). Difference Entropy: Dissimilarity: Energy (GLCM): Also known as the Angular Second Moment and is a measure of the homogeneity of an image. A homogeneous image will contain less discrete gray levels, producing a GLCM with fewer but relatively greater values of P(i,j), and a greater sum of the squares. Entropy(GLCM): Indicates the uncertainty of the GLCM. It measures the average amount of information required to encode the image values. Homogeneity 1: A measure of local homogeneity that increases with less contrast in the window. Homogeneity 2: A measure of local homogeneity. Informational Measure of Correlation 1 (IMC1): Informational Measure of Correlation 2 (IMC2): Inverse Difference Moment Normalized (IDMN): A measure of the local homogeneity of an image. IDMN weights are the inverse of the Contrast weights (decreasing exponentially from the diagonal i=j in the GLCM). Unlike Homogeneity 2, IDMN normalizes the square of the difference between values by dividing over the square of the total number of discrete values. Inverse Difference Normalized (IDN): Another measure of the local homogeneity of an image. Unlike Homogeneity 1, IDN normalizes the difference between the values by dividing over the total number of discrete values. Inverse Variance: Maximum Probability: Sum Average: Sum Entropy: Sum Variance: Weights elements that differ from the average value of the GLCM. Variance (GLCM): The dispersion of the parameter values around the mean of the combinations of reference and neighborhood pixels, with values farther from the mean weighted higher. A high variance indicates greater distances of values from the mean.

 Texture: Gray-Level Run Length Matrix (GLRL) Short Run Emphasis (SRE): A measure of the distribution of short run lengths, with a greater value indicative of shorter run lengths and more fine textural textures. Long Run Emphasis (LRE): A measure of the distribution of long run lengths, with a greater value indicative of longer run lengths and more coarse structural textures. Gray Level Non-Uniformity (GLN): Measures the similarity of gray-level intensity values in the image, where a lower GLN value correlates with a greater similarity in intensity values. Run Length Non-Uniformity (RLN): Measures the similarity of run lengths throughout the image, with a lower value indicating more homogeneity among run lengths in the image. Run Percentage (RP): Measures the homogeneity and distribution of runs of an image for a certain direction Low Gray Level Run Emphasis (LGLRE): Measures the distribution of low gray-level values, with a higher value indicating a greater concentration of low gray-level values in the image. High Gray Level Run Emphasis (HGLRE): Measures the distribution of the higher gray-level values, with a higher value indicating a greater concentration of high gray-level values in the image. Short Run Low Gray Level Emphasis (SRLGLE): Measures the joint distribution of shorter run lengths with lower gray-level values. Short Run High Gray Level Emphasis (SRHGLE): Measures the joint distribution of shorter run lengths with higher gray-level values. Long Run Low Gray Level Emphasis (LRLGLE): Measures the joint distribution of long run lengths with lower gray-level values. Long Run High Gray Level Emphasis (LRHGLE)Measures the joint distribution of long run lengths with higher gray-level values.

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