Measure Distance To Parent

Measure Distance To Parent measures how far each child (e.g. a spot) lies from the parent Relate Objects linked it to (e.g. its cell): from the child’s centre to the parent’s centre, and from the child’s centre to the nearest pixel of the parent’s edge. These are the child-parent distances of CellProfiler’s RelateObjects.

Use it, for example, to tell spots near the nucleus from spots near the cell membrane. It needs a Relate Objects step before it in the pipeline.

Parameters

Parameter	Description
ID	The step’s ID, unique in the project. Its values’ names in the results start with it (e.g. parent_distance_01).
Children	The children measured (e.g. spots).
Parent	The class of their parent, as linked by Relate Objects (e.g. Cell).

Measurements

Two values per child, in pixels:

Measurement	Description
Distance to parent centre	From the child’s centre to the parent’s centre.
Distance to parent edge	From the child’s centre to the nearest edge pixel of the parent.

Each value also names the parent it was measured to: in the List View, the column … · object next to it holds the parent’s object ID.

How it works

The centre of an object is its centre of mass: the mean position of its pixels, not weighted by intensity.

$$d_{\text{centre}} = \sqrt{(x_c - x_p)^2 + (y_c - y_p)^2}$$

with $(x_c, y_c)$ the child’s centre and $(x_p, y_p)$ the parent’s.

The parent’s edge pixels are its pixels with at least one of their 4 neighbours (up, down, left, right) outside the parent. A neighbour beyond the image border doesn’t count, so a parent cut off by the border has no edge along it. The distance to the edge is the shortest straight-line distance from the child’s centre to the centre of an edge pixel.

The distance to the edge has no sign: it is the same whether the child’s centre lies inside or outside the parent.

A child without a parent of the chosen class (not linked, or its parent no longer exists) has no value.