Entry requirements

90 ECTS credits in Mathematics.

Aims

The course offers knowledge about morphological mappings in

digital spaces

and vector spaces as well as about geometric and topological

concepts of

importance for digital geometry. The goals include both an

understanding

of the fundamental theoretical notions and a certain familiarity

with the

execution of operations on a computer.

Content

Morphological operations on sets and functions. Infimal

convolution.

Dilations, erosions and closure operators in vector spaces and

digital

spaces. Distance transforms. Complete lattices and operators

acting on

them. Continuity. Morphological filters. Skeletons.

Topological

concepts of importance for digital geometry. Khalimsky's topology

on the

integers. Topology and geometry in digital spaces. Straight

lines,

curves, and convex sets in digital geometry. Jordan's curve

theorem.

Fixed-point theorems.

Instruction

Lectures and lab sessions.

Assessment

Oral or written exam.