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Table 1 Morphometrical parameters used in the analysis of the theoretical cells.

From: Quantitative analysis of the epithelial lining architecture in radicular cysts and odontogenic keratocysts

Parameter

Units

Explanation

Perim

pixels

Perimeter calculated from the centres of the boundary pixels

Area

pixels2

The area inside the polygon defined by the perimeter

MinR

pixels

Radius of the inscribed circle centred at the centre of mass

MaxR

pixels

Radius of the enclosing circle centred at the centre of mass

Feret

pixels

Largest axis length

Breadth

pixels

The largest axis perpendicular to the Feret diameter

CHull

pixels

Convex Hull or convex polygon calculated from pixel centres

CArea

pixels2

Area of the Convex Hull polygon

MBCRadius

pixels

Radius of the Minimal Bounding Circle

AspRatio

none

Aspect Ratio = Feret/Breadth

Circ

none

Circularity = 4*Ï€*Area/Perimeter2, also called form factor

Roundness

none

Roundness = 4*Area/(Ï€*Feret2)

AreaEquivD

pixels

Area of circle with equivalent diameter = sqrt((4/Ï€)*Area)

PerimEquivD

none

Perimeter of circle with equivalent diameter = Area/Ï€

EquivEllipseAr

pixels2

Equivalent Ellipse Area = (Ï€*Feret*Breadth)/4

Compactness

none

Compactness: sqrt((4/Ï€)*Area)/Feret

Solidity

none

Solidity = Area/Convex_Area

Concavity

pixels2

Concavity = Convex_Area - Area

Convexity

none

Convexity = Convex_Hull/Perimeter

Shape

none

Shape = Perimeter2/Area

RFactor

none

RFactor = Convex_Hull/(Feret*Ï€)

ModRatio

none

Modification Ratio = (2*MinR)/Feret

Sphericity

none

Sphericity = MinR/MaxR

ArBBox

pixels2

ArBBox = Feret*Breadth, area of the box along Feret diameter

Rectang

none

Rectangularity = Area/ArBBox

  1. Here, the "pixel" units relate to length (the distance between the centre of one pixel and its neighbour), while pixels2 relate to area (the number of pixels). "None" are dimensionless values.