Intrinsic Features of Blobs

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Intrinsic Features for Blobs

These features can be calculated with two input images (Data Image and Label Image). They are most commonly used for blob-like regions, such as cell nuclei. Equations are shown for 3-dimensional space unless otherwise noted.

Name	Description	Formula
Volume	Number of voxels in the object [1]	$\| Ω \|$ or $M 000 \| {I = b i n a r y}$
Integrated Intensity	Sum of the intensities of all voxels in the object [1]	$\sum I(\Omega)$ or $M 000 \| {I = i n t e n s i t y}$
Centroid	Center of the object [1]	$\left [ \begin{array}{ccc} \frac{M_{100}}{M_{000}}, & \frac{M_{010}}{M_{000}}, & \frac{M_{001}}{M_{000}} \end{array} \right ]\|\{I=binary\}$
Weighted Centroid	Uses the image intensity values to calculate the center of mass of the object [1]	$\left [ \begin{array}{ccc} \frac{M_{100}}{M_{000}}, & \frac{M_{010}}{M_{000}}, & \frac{M_{001}}{M_{000}} \end{array} \right ]\|\{I=intensity\}$
Axes Lengths	The length of the axes of the ND hyper-ellipsoid fit to the object [1]	$\| Ω \|$
Eccentricity	Ratio of the distance between the foci of the best-fit hyper-ellipsoid to the length of its major axis. (2D) [1]
Elongation	Ratio of the major axis length to minor axis length of the best-fit hyper-ellipsoid. (2D) [1]
Orientation	Angle between the major axis of the best-fit hyper-ellipsoid and origin. (2D) [1]
Bounding Box Volume	Number of voxels in the bounding box of the object [1]
Oriented Bounding Box Volume	Number of voxels in the oriented bounding box of the object. The oriented bounding box is defined as the bounding box aligned along the axes of the object. [1]
Sum	Same as integrated intensity [2]
Mean	Average intensity of voxels in the object [2]
Median	Middle intensity of voxels in the object [2]
Minimum	Minimum intensity of voxels in the object [2]
Maximum	Maximum intensity of voxels in the object [2]
Sigma	Standard deviation of intensity of voxels in the object [2]
Variance	Variance of intensity of voxels in the object [2]
Radius Variation	Standard deviation of distance from surface voxels to centroid
Skew	Skew of the normalized intensity histogram
Energy	Energy of the normalized intensity histogram
Entropy	Entropy of the normalized intensity histogram
Surface Gradient	Average of surface gradients
Interior Gradient	Average of interior gradients
Interior Intensity	Average of interior intensities
Surface Intensity	Average of surface intensities
Intensity Ratio	Ratio of surface intensity to interior intensity
Shared Boundary	Ratio of surface area that touches another object to total surface area
Surface Area	Number of voxels on surface of the object
Shape	Ratio of surface voxels to total voxels - compactness or thinness of object

Glossary of Notation

$p = (x, y, z)$ - the coordinate of a voxel (three-dimensional point in a volume image)
$N p$ - a neighbor voxel of $p$
$l p$ - the segmentation label at $p$
$I i (p)$ - the intensity value of $p$ at $i t h$ channel
$Ω = {p | l p = o}$ - the set of voxels of an object $o$
$\Omega_s = \{l_p = o; \exists N_p, l_{N_p} \neq o\}$ - the set of surface voxels of the object
$Ω i n = Ω - Ω s$ - the set of interior voxels of an object
$G$ - the magnitude of intensity gradient at $p$
$\bar{p}$ - the center of mass of the object
$P$ - the normalized histogram of the intensities
$P (I)$ - normalized histogram of intensity values $I$
$M_{p,q,r} = \sum_{z=0}^{Z-1}\sum_{y=0}^{Y-1}\sum_{x=0}^{X-1}x^p y^q z^r I(x,y,z)$ - Raw Moment of discrete image $I$
$λ i$ - $i t h$ eigenvalue of covariance matrix

External Links

[1] itkLabelGeometryImageFilter
[2] itkLabelStatisticsImageFilter
[3] Kitware Source Newsletter

Intrinsic Features of Blobs

Intrinsic Features for Blobs

Glossary of Notation

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