# Measurement¶

Measurement modules produce measurements from either images or objects produced by prior modules.

## MeasureColocalization¶

MeasureColocalization measures the colocalization and correlation between intensities in different images (e.g., different color channels) on a pixel-by-pixel basis, within identified objects or across an entire image.

Given two or more images, this module calculates the correlation & colocalization (Overlap, Manders, Costes’ Automated Threshold & Rank Weighted Colocalization) between the pixel intensities. The correlation / colocalization can be measured for entire images, or a correlation measurement can be made within each individual object. Correlations / Colocalizations will be calculated between all pairs of images that are selected in the module, as well as between selected objects. For example, if correlations are to be measured for a set of red, green, and blue images containing identified nuclei, measurements will be made between the following:

• The blue and green, red and green, and red and blue images.
• The nuclei in each of the above image pairs.

A good primer on colocalization theory can be found on the SVI website.

Supports 2D? Supports 3D? Respects masks?
YES YES YES

### Measurements made by this module¶

• Correlation: The correlation between a pair of images I and J, calculated as Pearson’s correlation coefficient. The formula is covariance(I ,J)/[std(I ) × std(J)].
• Slope: The slope of the least-squares regression between a pair of images I and J. Calculated using the model A × I + B = J, where A is the slope.
• Overlap coefficient: The overlap coefficient is a modification of Pearson’s correlation where average intensity values of the pixels are not subtracted from the original intensity values. For a pair of images R and G, the overlap coefficient is measured as r = sum(Ri * Gi) / sqrt (sum(Ri*Ri)*sum(Gi*Gi)).
• Manders coefficient: The Manders coefficient for a pair of images R and G is measured as M1 = sum(Ri_coloc)/sum(Ri) and M2 = sum(Gi_coloc)/sum(Gi), where Ri_coloc = Ri when Gi > 0, 0 otherwise and Gi_coloc = Gi when Ri >0, 0 otherwise.
• Manders coefficient (Costes Automated Threshold): Costes’ automated threshold estimates maximum threshold of intensity for each image based on correlation. Manders coefficient is applied on thresholded images as Ri_coloc = Ri when Gi > Gthr and Gi_coloc = Gi when Ri > Rthr where Gthr and Rthr are thresholds calculated using Costes’ automated threshold method.
• Rank Weighted Colocalization coefficient: The RWC coefficient for a pair of images R and G is measured as RWC1 = sum(Ri_coloc*Wi)/sum(Ri) and RWC2 = sum(Gi_coloc*Wi)/sum(Gi), where Wi is Weight defined as Wi = (Rmax - Di)/Rmax where Rmax is the maximum of Ranks among R and G based on the max intensity, and Di = abs(Rank(Ri) - Rank(Gi)) (absolute difference in ranks between R and G) and Ri_coloc = Ri when Gi > 0, 0 otherwise and Gi_coloc = Gi when Ri >0, 0 otherwise. (Singan et al. 2011, BMC Bioinformatics 12:407).

(Jump to top)

## MeasureGranularity¶

MeasureGranularity outputs spectra of size measurements of the textures in the image.

Image granularity is a texture measurement that tries to fit a series of structure elements of increasing size into the texture of the image and outputs a spectrum of measures based on how well they fit. Granularity is measured as described by Ilya Ravkin (references below). The size of the starting structure element as well as the range of the spectrum is given as input.

Supports 2D? Supports 3D? Respects masks?
YES YES YES

### Measurements made by this module¶

• Granularity: The module returns one measurement for each instance of the granularity spectrum.