Properties of simple sets in digital spaces. Contractions of simple sets preserving the homotopy type of a digital space
This incremental work addresses topology preservation in digital spaces for applications like medical imaging and computer graphics.
The paper tackles the problem of compressing digital spaces while preserving topology by introducing simple sets of points that can be contracted without altering homotopy type, showing that this method can substantially reduce the number of points.
A point of a digital space is called simple if it can be deleted from the space without altering topology. This paper introduces the notion simple set of points of a digital space. The definition is based on contractible spaces and contractible transformations. A set of points in a digital space is called simple if it can be contracted to a point without changing topology of the space. It is shown that contracting a simple set of points does not change the homotopy type of a digital space, and the number of points in a digital space without simple points can be reduces by contracting simple sets. Using the process of contracting, we can substantially compress a digital space while preserving the topology. The paper proposes a method for thinning a digital space which shows that this approach can contribute to computer science such as medical imaging, computer graphics and pattern analysis.