Skip to content

compactness

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

Compute the compactness of a polygon.

Note

Compactness is defined as the ratio of the area of an object to the area of a circle with the same perimeter. A circle is the most compact shape. Objects that are elliptical or have complicated, irregular (not smooth) boundaries have larger compactness. - Wirth

Compactness: $$ \frac{4\pi A_{poly}}{P_{poly}^2} $$

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

Parameters:

Name Type Description Default
polygon Polygon

Input shapely polygon object.

 required

Returns:

Name Type Description
float float

The compactness value of a polygon between 0-1.
Source code in cellseg_gsontools/geometry/shape_metrics.py 
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
def compactness(polygon: Polygon, **kwargs) -> float:
    """Compute the compactness of a polygon.

    Note:
        Compactness is defined as the ratio of the area of an object
        to the area of a circle with the same perimeter. A circle is the
        most compact shape. Objects that are elliptical or have complicated,
        irregular (not smooth) boundaries have larger compactness.
        - [Wirth](http://www.cyto.purdue.edu/cdroms/micro2/content/education/wirth10.pdf)

    **Compactness:**
    $$
    \\frac{4\\pi A_{poly}}{P_{poly}^2}
    $$

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

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

    Returns:
        float:
            The compactness value of a polygon between 0-1.
    """
    perimeter = polygon.length
    area = polygon.area

    compactness = (4 * np.pi * area) / perimeter**2

    return compactness