Intrinsic Features of Blobs
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==Glossary of Notation== | ==Glossary of Notation== | ||
| − | <math>p=(x,y,z)</math> - the coordinate of a voxel (three-dimensional point in a volume image)<br /> | + | <FONT SIZE="+1"><math>p=(x,y,z)</math></FONT> - the coordinate of a voxel (three-dimensional point in a volume image)<br /> |
| − | <math>N_p</math> - a neighbor voxel of <math>p</math><br /> | + | <FONT SIZE="+1"><math>N_p</math></FONT> - a neighbor voxel of <math>p</math><br /> |
| − | <math>l_p</math> - the segmentation label at <math>p</math><br /> | + | <FONT SIZE="+1"><math>l_p</math></FONT> - the segmentation label at <math>p</math><br /> |
| − | <math>I_i(p)</math> - the intensity value of <math>p</math> at <math>i^{th}</math> channel<br /> | + | <FONT SIZE="+1"><math>I_i(p)</math></FONT> - the intensity value of <math>p</math> at <math>i^{th}</math> channel<br /> |
| − | <math>\Omega = \{p|l_p = o\}</math> - the set of voxels of an object <math>o</math><br /> | + | <FONT SIZE="+1"><math>\Omega = \{p|l_p = o\}</math></FONT> - the set of voxels of an object <math>o</math><br /> |
| − | <math>\Omega_s = \{l_p = o; \exists N_p, l_{N_p} \neq o\}</math> - the set of surface voxels of the object<br /> | + | <FONT SIZE="+1"><math>\Omega_s = \{l_p = o; \exists N_p, l_{N_p} \neq o\}</math></FONT> - the set of surface voxels of the object<br /> |
| − | <math>\Omega_{in} = \Omega - \Omega_s</math> - the set of interior voxels of an object<br /> | + | <FONT SIZE="+1"><math>\Omega_{in} = \Omega - \Omega_s</math></FONT> - the set of interior voxels of an object<br /> |
| − | <math>G</math> - the magnitude of intensity gradient at <math>p</math><br /> | + | <FONT SIZE="+1"><math>G</math></FONT> - the magnitude of intensity gradient at <math>p</math><br /> |
| − | <math>\bar{p}</math> - the center of mass of the object<br /> | + | <FONT SIZE="+1"><math>\bar{p}</math></FONT> - the center of mass of the object<br /> |
| − | <math>P</math> - the normalized histogram of the intensities<br /> | + | <FONT SIZE="+1"><math>P</math></FONT> - the normalized histogram of the intensities<br /> |
| − | <math>P(I)</math> - normalized histogram of intensity values <math>I</math><br /> | + | <FONT SIZE="+1"><math>P(I)</math></FONT> - normalized histogram of intensity values <math>I</math><br /> |
==External Links== | ==External Links== | ||
Revision as of 15:48, 28 April 2009
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.
Volume
Number of voxels in the object. (Dirk)
Integrated Intensity
Sum of the intensities of all voxels in the object. (Dirk)
Centroid (unweighted and weighted)
The unweighted centroid calculates the center of the object. The weighted centroid uses the image intensity values to calculate the intensity center of the object. (Dirk)
Axes Lengths
The length of the axes of the ND hyper-ellipsoid fit to the object. (Dirk)
Eccentricity
Ratio of the distance between the foci of the best-fit hyper-ellipsoid to the length of its major axis. (2D) (Dirk)
Elongation
Ratio of the major axis length to minor axis length of the best-fit hyper-ellipsoid. (2D) (Dirk)
Orientation
Angle between the major axis of the best-fit hyper-ellipsoid and origin. (2D) (Dirk)
Bounding Box Volume
Number of voxels in the bounding box of the object. (Dirk)
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. (Dirk)
Sum
Same as integrated intensity (ITK statistics)
Mean
Average intensity of voxels in the object (ITK statistics)
Median
Middle intensity of voxels in the object (ITK statistics)
Minimum
Minimum intensity of voxels in the object (ITK statistics)
Maximum
Maximum intensity of voxels in the object (ITK statistics)
Sigma
Standard deviation of intensity of voxels in the object (ITK statistics)
Variance
Variance of intensity of voxels in the object (ITK statistics)
Radius Variation
Standard deviation of distance from surface voxels to centroid (Isaac)
Skew
Skew of the normalized intensity histogram (Isaac) (See Supplement B2)
Energy
Energy of the normalized intensity histogram (Isaac) (See Supplement B2)
Entropy
Entropy of the normalized intensity histogram (Isaac) (See Supplement B2)
Surface Gradient
Average of surface gradients (Isaac)
Interior Gradient
Average of interior gradients (Isaac)
Interior Intensity
Average of interior intensities (Isaac)
Surface Intensity
Average of surface intensities (Isaac)
Intensity Ratio
Ratio of surface intensity to interior intensity (Isaac)
Ratio of surface area that touches another object to total surface area (Isaac)
Surface Area
Number of voxels on surface of the object (Isaac)
Shape
Ratio of surface voxels to total voxels - compactness or thinness of object (Isaac) (See Supplement B2)
Glossary of Notation
p = (x,y,z) - the coordinate of a voxel (three-dimensional point in a volume image)
Np - a neighbor voxel of p
lp - the segmentation label at p
Ii(p) - the intensity value of p at ith channel
Ω = {p | lp = o} - the set of voxels of an object o
- the set of surface voxels of the object
Ωin = Ω − Ωs - the set of interior voxels of an object
G - the magnitude of intensity gradient at p
- the center of mass of the object
P - the normalized histogram of the intensities
P(I) - normalized histogram of intensity values I
