MODELS OF IMAGES AND IMAGE OPERATIONS - Fundamentals of Three-Dimensional Digital Image Processing - page 34

Fig. 2.10. Binary operation among images.

Table 2.2. Examples of pointwise operations among images.
Definition

Notation

(1) Addition φ ( x, y )= x + y = F

F
F
F
F
F
F
F
F

+ G

H

(2) Subtraction φ ( x, y )= x − y H = − G

(3) Multiplication φ ( x, y )= x × y = × G

H

(4) Division φ ( x, y )= x ÷ y H = ÷ G

(5) Max φ ( x, y )=max( x, y ) H = ∧ G

(6) Min φ ( x, y )=min( x, y ) H = ∨ G

(7) Logical sum φ ( x, y )= x ⊕ y H = ⊕ G

(8) Logical product φ ( x, y )= x ⊗ y H = ⊗ G

(9) Logical difference φ ( x, y )= x y H = G

∗ (7)(8) and (9) in the table are binary image operators applied to binary images
and

F

G ,and x and y are binary variables

commutative law: F + G = G + F , F × G = G × F (2.16)

right distributive law: ( F + G ) × H =( F × H )+( G × H ) (2.17)

associative law: ( F + G )+ H = F +( G + H ) ,

( F × G ) × H = F × ( G × H ) (2.18)

2.3.4 Composition of image operations

Let us consider generating a new image operation by composing or combin-
ing two or more procedures. This process is formulated as operations among