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# Objects in binary images

Objects in a binary image should be either connected black regions surrounded by white background, or connected white regions surrounded by blackbackground. We choose the former.

Objects are connected black regions surrounded by white background with white holes in them.

The area, or simply size, of an object includes the holes (the area of the hole is not subtracted). The decision to exclude the holes is justified by the idea that object's size is supposed to measure its importance. If we have a thin curve that encircles a large region, the area of the region reflects the importance of the curve.

The perimeter can be easily computed by traversing around the object. It can also be computed indirectly during merging and splitting. The areas and centroids are computed either directly by means of Green's Theorem while traversing the cycle or indirectly during merging and splitting.

Another characteristics is compactness or roundness computed as 4π*area divided by perimeter squared.

For more see Measuring objects.

Note: Keep in mind that this article only introduces some concepts and provides justification for them. More precisely these concepts (such as 0- and 1-cycles) are defined elsewhere.

Continue to Binary Images.