Digital Signal Processing Reference
In-Depth Information
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Figure 4.1. The lifting scheme with two iterations: (left) predict-
first approach; (right) update-first approach.
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grayscale images as a special case, based on complete lattices (Serra 1982). Arising
from this theoretical framework, Matheron and Serra formulated a theory of mor-
phological nonlinear filtering. Mathematical morphology is based on two operators:
the
infimum
(denoted
). The basic morphological
transformations are erosion, dilation, opening, and closing. For grayscale images,
they can be defined in the following way:
Dilation
consists of replacing each pixel of an image
f
by the supremum
2
of its
neighbors within the structuring element
∧
) and the
supremum
(denoted
∨
B
:
=
f
b
,
D
B
(
f
)
b
∈B
2
For discrete grayscale levels, the supremum is replaced by the pointwise maximum.
