2D Measurements
The 2D measurements for multi-ROIs that are available in the Compute Measurements dialog include areas, major and minor axis lengths, form factor, aspect ratio, and many others. These measurements are shown in the Compute Measurements dialog below and are described in the following table.
2D measurements
| Measurement | Description | Unit |
|---|---|---|
| 2D Area | Is the projected 2D area of the labeled pixels belonging to a discrete object, and is calculated as the sum of the areas of each labeled pixel within the borders of the object. | (default units)2 |
| 2D Bounding Area Box | Is the area of the bounding box that encloses a discrete object. | (default units)2 |
| 2D Convex Area | Is the area of the convex hull of a discrete object, which is the smallest convex polygon that can enclose the object. | (default units)2 |
| 2D Eccentricity | Is the eccentricity of the ellipse that has the same second-moments as a discrete object. Eccentricity is the ratio of the focal distance (distance between focal points) over the major axis length. The value is in the interval [0, 1]. When it is 0, the ellipse becomes a circle. | none |
| 2D Equivalent Diameter | The 2D equivalent diameter, or area-equivalent diameter, is the diameter of a circle with the same area as a discrete object and is computed as sqrt(4*area/pi). | default units |
| 2D Euler Number | This simple topological descriptor is computed as the number of components minus the number of holes and is invariant to translation, rotation, and scaling. | none |
| 2D Extent | Is the ratio of labeled pixels in an object to pixels in the bounding box. Computed as: 2D Area / 2D Bounding Box Area. | none |
| 2D Filled Area | Is the area of all pixels — both labeled and unlabeled — in a discrete object. | (default units)2 |
| 2D Major Axis Length | Is the length of the primary axis of the best fitting ellipse. | default units |
| 2D Minor Axis Length | Is the length of the secondary axis of the best fitting ellipse. | default units |
| 2D Orientation | Is the angle between the 0th axis (rows) and the major axis of the ellipse that has the same second moments as an object, ranging from -pi/2 to pi/2 counter-clockwise. | degrees/radians |
| 2D Perimeter | Is the length of the outside boundary of the object, which is approximated as a line drawn through the centers of border pixels. | default units |
| 2D Solidity |
Is the ratio of the pixels in an object to the pixels of the object's convex hull. Solidity is a dimensionless value that measures the density of an object and is computed as: (2D area)/(2D convex area).
Note A value of signifies a solid object, while values less than 1 signify objects having irregular boundaries or containing holes. |
none |
| 2D Form Factor |
This dimensionless quantity represents the degree of deviation from an ideal shape, such as a circle or square, and is computed as: 4*pi*area/perimeter2.
Note A 2D form factor approaching 1.0 would represent maximum symmetry, such as a circle or square. |
none |
| 2D Roundness |
Is a measure of both the form and roughness of an object and is computed as 4*area/pi*(major axis length)2.
Note As an object becomes more round and smooth, roundness would approach 1. Conversely, as an object becomes more elongated and rougher, roundness should approach 0. |
none |
| 2D Compactness |
Is a measure of the compactness of an object and is computed as sqrt((4/pi)*area)/major axis length.
Note The compactness of a circle is 1.0, and much less for very elongated objects. |
none |
| 2D Aspect Ratio |
The 2D aspect ratio is computed as: (major axis length)/(minor axis length).
Note A perfect square or circle would have an aspect ratio of 1.0 and would approach 0 for a very elongated object. |
none |
| 2D Area/2D Perimeter | Is the ratio of the 2D area of an object to its 2D perimeter. | none |
| 2D Max Fereta | Is the longest distance between any two parallel tangents along each distinct object’s convex hull. Can also be referred to as the maximum caliper diameter. | default units |
| 2D Min Fereta | Is the shortest distance between any two parallel tangents along each distinct object’s convex hull. Can also be referred to as the minimum caliper diameter. | default units |
| 2D Feret Anglea | Is the angle (0 to 180 degrees) of the 2D max Feret. | degrees/radians |
a Ferets are computed from the center of the pixels that comprise the generated convex hull of each labeled object. These measurements are not available in the Object Analysis dialog.
