circularity

cellseg_gsontools.geometry.circularity(polygon, **kwargs)

Compute the circularity of a polygon.

Note

Circularity (sometimes roundness) is the ratio of the area of an object to the area of a circle with the same convex perimeter. Circularity equals 1 for a circular object and less than 1 for non-circular objects. Note that circularity is insensitive to irregular boundaries. - Wirth

Circularity: $$ \frac{4 \times \pi A_{poly}}{P_{convex}^2} $$

where \(A_{poly}\) is the area of the polygon and \(P_{convex}\) is the perimeter of the convex hull.

Parameters:

Name	Type	Description	Default
polygon	Polygon	Input shapely polygon object.	required

Returns:

Name	Type	Description
float	float	The circularity value of a polygon between 0-1.

Source code in cellseg_gsontools/geometry/shape_metrics.py

def circularity(polygon: Polygon, **kwargs) -> float:
    """Compute the circularity of a polygon.

    Note:
        Circularity (sometimes roundness) is the ratio of the area of
        an object to the area of a circle with the same convex perimeter.
        Circularity equals 1 for a circular object and less than 1 for
        non-circular objects. Note that circularity is insensitive to
        irregular boundaries.
        - [Wirth](http://www.cyto.purdue.edu/cdroms/micro2/content/education/wirth10.pdf)

    **Circularity:**
    $$
    \\frac{4 \\times \\pi A_{poly}}{P_{convex}^2}
    $$

    where $A_{poly}$ is the area of the polygon and $P_{convex}$ is the perimeter of
    the convex hull.

    Parameters:
        polygon (Polygon):
            Input shapely polygon object.

    Returns:
        float:
            The circularity value of a polygon between 0-1.
    """
    convex_perimeter = polygon.convex_hull.length
    area = polygon.area

    circularity = (4 * np.pi * area) / convex_perimeter**2

    return circularity