Mathematical morphology is an image analysis subject based on lattice theory and topology, and it is the basic theory of mathematical morphology image processing. Its basic operations include: binary corrosion and expansion, binary opening and closing operation, skeleton extraction, extreme corrosion, hit-and-miss transformation, morphological gradient, top hat transformation, particle analysis, watershed transformation, gray corrosion and expansion, gray opening and closing operation, gray morphological gradient and so on.

Expansion expansion

Consider two binary images a and b. Their foreground is black and their background is white. In addition, fA and fB respectively represent the collection of scenic spots in front of them. Expansion operation is defined as: expansion (a, B) = {a+b| a∈A, b∈B}. For example: A = {(2,8), (3,6), (4,4), (5,6), (6,4), (7,6), (8,8)} B = {(0,0), (0,65438+.

Corrosion erosion

Considering two images A and B, the erosion operation is defined as: erosion (a, b) = {a | (a+b) ∈ a, a ∈ a, b ∈ b}.

Characteristics of expansion corrosion operation

Commutative expansion (a, B) = expansion (b, a) associative expansion (a, b), c) = expansion (a, expansion (b, c)) and expansion (a, b ∪ c) = expansion (a, b ∪). C) growth if a belongs to b, then dilution (a, k) belongs to dilution (b, k)

history

Mathematical morphology was born in 1964, and its theoretical basis was laid by G. Matheron and J. Serra of French Mining Institute at that time. 1968 In April, the French Fontainebleau Mathematical Morphology Research Center was established, and the Paris Institute of Mining provided the research base for the center.

The development process of mathematical morphology in the 20th century can be roughly divided into:

The gestation and formation period in the 1960s.

The period of richness and development in the 1970s.

The mature and open period in the 1980s.

The expansion period from the 1990s to the present.