Supplementary morphometrics from the convex hull and bounding circle.

Hull and Circle Morphometrics

This page explains features returned when the convex hull and minimum bounding circle are calculated in FracLac (during box counting, sub scans, and LCFD scans). The illustration below shows the convex hull and radii for a binarized image of a neuron.
Click on a column heading in the screen shots of the Hull and Circle Results file below or read through the list below the screen shots to find out about each column in the file.See the Glossary and Morphometrics page for background.

#### Circularity

Circularity of the convex hull = 4π×areaperimeter2; for a circle it is 1

#### Perimeter

The perimeter in pixels of the convex hull.

#### Area

The area, in pixels2, of the convex hull.

#### Maximum Span Across Hull

The maximum distance in pixels between points across the convex hull.

#### Hull's Centre of Mass

X,Y coordinates of the convex hull's centre of mass calculated in ImageJ.

#### Span Ratio (major/minor axis)

The ratio of the major over the minor axes of the convex hull.

#### Density

Foreground Pixels/Hull Area; the unit is pixels/pixels2 or pixels-1

#### Total Pixels

The total pixels (foreground and background) in the part of the image that was analyzed.

#### Total Foreground Pixels

The total pixels deemed foreground in the part of the image that was analyzed. See glossary also.

#### File/Slice/Roi

Tells which part of the image was analyzed; see explanation of the file name in the tutorial for details.

The mean length in pixels from the centre of mass of the convex hull to an exterior point.

The relative variation in the length of radii from the centre of mass of the convex hull to an exterior point.

The ratio of the largest to the smallest radius from the centre of mass of the convex hull to an exterior point.

#### Maximum Radius from Hull's Centre of Mass

The maximum radius from the centre of mass for the convex hull to an exterior point.

#### Height

The height in pixels of the bounding box (the rectangle enclosing the foreground pixels of the image as oriented on the computer screen).

#### Width

The width in pixels of the bounding box (the rectangle enclosing the foreground pixels of the image as oriented on the computer screen).

#### Method

The method used to find the bounding circle, calculated using the maximum span across or else the three points defining the smallest circle around the convex hull.

#### Mean Radius from Circle's Centre

The mean radius from the circle's centre to the points of the convex hull.

#### CV for all Radii from Circle's Centre

The cv for all radii from the circle's centre to the points of the convex hull.

#### Max/Min Radii from Circle's Centre

The ratio of the maximum over the minimum radii from the circle's centre to a point on the convex hull.

#### Maximum Radius from Circle's Centre

The maximum radius (in pixels) from the circle's centre to a point on the convex hull.

#### Diameter of the Bounding Circle

The diameter in pixels of the smallest circle enclosing the convex hull enclosing the foreground pixels of an image. This is a measure of cell size for biological cells. Compare the area of this circle with the area of the convex hull.

#### Circle's Centre

The centre x,y coordinates of the bounding circle.