orientation matrix is an orthonormal matrix.
p
3
×1
represents the position vector of the ori-
gin of the rotated coordinate system with re-
spect to the reference system. 0
1
×3
is 1
× 3
zero vector.
homojunction
a junction between regions
of the same bulk material that differs in the
concentration of dopants. The typical exam-
ple is the n-p diode.
homomorphic filter
an image enhance-
ment technique based upon the illumination-
reflectance model.
The homomorphic fil-
ter assumes the image function
f (x, y) is
the combination of two functions
i(x, y) and
r(x, y). By taking the natural log of the im-
ages the components are separated and can
be processed separately; the reflectance of an
image usually contains high frequency com-
ponents while the illumination component
tends to vary slowly (the low frequencies);
thus, the filter applied to the logarithm im-
age should affect the low and high frequency
components differently. The most common
use for the filter is to enhance images by com-
pressing the brightness range while increas-
ing contrast; the filter applied in this case is
a circularly symmetric high pass filter with
the stop band magnitude
< 1 and pass band
magnitude
> 1.
homomorphic signal processing
the pro-
cessing of signals from a nonadditive model
under a tranformation which renders the
model additive. For example, a logarithmic
transformation may be used to transform a
multiplicative noise model into an additive
noise model.
homopolar generator
an electromag-
netic generator in which the magnetic flux
passes in the same direction from one mag-
netic member to the other over the whole of
a single air gap area. Such generators have
been built to supply very large pulsed cur-
rents.
homopolar machine
See
homopolar
generator
.
homopolar magnetic bearing
a magnetic
bearing in which the rotating member always
experiences a magnetic field of the same po-
larity.
homothetic
a copy of a signal that retains
the original shape, but is scaled in size. For
a signal
x(t), the homothetic x
λ
(t) = x(λt)
retains the shape of
x(t) but is scaled along
the
t axis as a function of the parameter λ.
Typically used in association with structuring
elements in mathematical morphology.
homotopy method
a technique for solv-
ing nonlinear algebraic equations
F (x) = 0
based on higher-dimensional function em-
bedding and curve tracing. The idea is to
construct a parameterized function such that
at one parameter value, say
λ = λ
0
, the sys-
tem of equations is easy to solve or has one
or more known solutions, and at another pa-
rameter value, say
λ = λ
f
, the system of
equations is identical to that of the system
of interest,
F (x) = 0. A homotopy method
may then be interpreted as geometric curve
following through solution space from the
known solutions of the “easy” problem to the
unknown solutions of
F (x) = 0.
Hopfield memory
See
Hopfield model
.
Hopfield model
a neural algorithm capa-
ble of recognizing an incomplete input. Also
known as Hopfield memory.
Hopfield suggested that an incomplete in-
put can be recognized in an iterative process,
in which the input is gradually recognized
in every cycle of the iteration. The iteration
is completed when the input finally matches
with a stored memory. The Hopfield model
is a sort of associative memory.
A holo-
gram can also be directly used as associative
memory. The main difference of the non-
neural holographic associative memory and
the Hopfield model is as follows. The di-
rect holographic associative memory is one
c
2000 by CRC Press LLC