Page 328 - Electrical Engineering Dictionary

f (x, y), the gradient is grammar an ordered 4-tuple (G =
T, V, P, S), where T is said to be the set of
 
∂f terminals, V is the set of variables or non-
∂x
∇f =   terminals, P a set of production rules and
∂f
∂y S ∈ V is called the start symbol. Terminals
are the symbols with which the strings of the
The magnitude of this gradient is
language are made. For example, T may be
s the English alphabet, the ASCII character set,
2 2
∂f ∂f or the set {0, 1}. Non-terminals are symbols
|∇f |= + .
∂x ∂y that are replaced by a string of zero or more
terminals and non-terminals. The production
In image processing, the term gradient often rules specify which strings can be used to re-
refers to the magnitude of the gradient. See place non-terminals. The symbol S is the first
also Sobel operator. symbol with which every production starts.
All the strings that can be generated from S
gradient descent a method for finding using rules in P are said to be in L(G), the
the minimum of a multidimensional function language of G.
f(x). The technique starts at some point and
example: LetGbethegrammar(T,V,P,S)
advances towards the minimum by iteratively
such that
moving in a direction opposite to that of the
gradient:
T ={a, b}
∂f V ={S}
x i+1 = x i − α
∂x
where S is the start symbol and
where α is some scalar, usually set empiri-
cally. See also gradient, optimization.
P ={S → aSb, S → }
gradient edge detector an edge detec-
where is the empty string. The language
tor that defines an edge to be present at a
L(G) is the set of all strings of the form
pixel only if the magnitude of the gradient at n n
a b . The → symbol signifies that S can
that pixel is greater than some threshold. See
be replaced with whatever follows the arrow.
also edge, edge detection, gradient, Sobel
operator.
grant signal a control signal on a bus that
gradient index optics optical compo- gives permission to control the bus to another
nents, e.g., optical fibers, within which the module.
refractive index changes gradually between
two extremes. graph a couple G = (E, V ) where V is
a set of nodes and E ⊆ V × V is a set of
gradientspace a2-Drepresentationofthe edges. Graphs are widely used in modeling
orientationofa3-Dsurfaceinspace, inwhich networks, circuits, and software.
thetwocomponentsofapointP ≡ (p, q)are
the first-order partial derivatives of a surface graph search an optimization technique
of the form z = f (x, y). used to find the minimum cost path from a
starting point to a goal point, through a graph
Gram-Schmidt orthogonalization a re- of interconnected nodes. Each link between
cursive procedure for whitening (decorrelat- nodeshasanassociatedpathcost, whichmust
ing) a sequence of random vectors. See also be selected based on the problem of interest.
whitening filter. See also optimization.

c
2000 by CRC Press LLC