Zhisnyakov A.L., Fomin A.A.,
Privezencev D.G., Baranov A.A.
Murom Institute of Vladimir
State Univercity
STRUCTURE ANALYSIS OF IMAGES SEQUENCES
The work
purpose is approach construction to the description of the digital images,
based on analysis of sign group behavior on images sequence.
Image is a
function f(x,y), which is determined
on subset P of plane R2 and takes on a real
values.
Let's
consider we can compare each image f
to finite signs set X = {X1, X2, …Xn}, that unambiguously determines f
into multiple set of another images given on P.
We name
some ordered images sequence as {fn}
and set index for each element {fn}={f0, f1,… fn}.
(1)
We limit
all multiformity of existing sequences and view case that we can describe
sequence forming by some operator. Thus every image from sequence is a result
of influencing of operator T on the
previous one.
As each
image from initial set f is
unambiguously characterized by signs set X,
we can construct the set {Xn} = {X0, X1, X2
…} identical with (1).
Let's
consider if there is some images sequence {fn},
that is ordered by any signs set X, then adjoining images can have some
similarity degree. In other words if any sign presents on the image fk Î{fn}, probably it will presents on the neighbouring
images fk-1 Î{fn} è fk+1 Î{fn}, k = 1..N-2. Naturally the
images are more closely among themselves, the longer there is the images
sequence
{… fk-2, fk-1, fk,
fk+1, fk+2...}, k = 1..N-2, (2)
which
contains same sign.
Therefore we
can talk about sign inheriting factor on images sequence.
At the same
time it is obvious, as relationship between images in the sequence will
decrease depending on distance between ones (increasing image index difference),
some signs, that distinctly show on the one image, can be less visibly on the another
images or vanish quite.
It is
characterized as the signs mutability on the images sequence.
Let's
consider sequence consisted of elements {Xn} that define same sign (in example sign with index i) for
viewing all images from initial sequence
{x(i)n} = {x0(i), x1(i),… xn(i)}.
We named
operator that defines sign x(i) entry level into fuzzy set X(i) as sign of attribute operator.
It represents conformity degree of single sign realization to the limit
(etalon) value on the images sequence.
mi : mi[xj(i)]®[0,1].
Then we can
hold up as a conformity to each signs set Xj of image fjÎ{fn} the vector mÕj = (m1õ1, m2õ2, .. mkõk
)Ò where k is
signs amount.
For every
sign we can introduce the threshold operator
Ã: Ãmi[xj(i)]®{0,1}. (3)
As a result
of application of (3) to initial vector Xj that characterized image fi, we get some vector Wj consists of
ones and zeroes:
W = (w1, w2,… wê)Ò, wi Î {0,1}, i =
1, 2,…k.
Let we have
two neighboring images fm and
fm+1 from sequence {fn}. Vectors Wm and Wm+1 agree with them.
Let’s
consider pairs of elements (wmi, wm+1i), i = 1, 2,..k. Elements coincidence in
such pairs is there are same sign presented on both images or it is not presented
on ones.
Sequence
mutability is the process of old signs losing or new signs acquiring while
transiting to each next sequence image.
To get
mutability characteristic we can use the expression
,
where Å is inequivalence
operation (exclusive disjunction).
Inheriting of
images sequence is signs holding process while transiting to the next image of sequence.
Taking into
consideration relation between mutability and inheriting terms we can introduce
sign mutability characteristic in this view:
.
Sign x(i) distribution
curve on the images sequence {fn} is graph of function mi(j) º mi[xj(i)]
that takes on a discrete values on the points jÎ{0,1,..n}.
To
realization sequence of some sign on the images sequence the sequence consists
of ones and zeros agrees
Q = {q1, q2,… qn}, qj Î {0,1}, j = 1, 2,…n. (4)
Index i of
sequence Q element
for which condition (qi-1 = 0) Ù (qi = 1) is true we can name sign appearance
point.
Index j of
sequence Q element
for which condition (qj-1 = 1) Ù (qj = 0) is true we can name sign disappearance
point.
The result
of operator à application to sequence of function mi(j) values
we can name normed curve of sign x(i) distribution on the images sequence {fn}.
The part
length of normed curve of sign x(i) distribution on which the function Ãmi(j) takes
on value equal one we can name depth of sign x(i) enclosure on the images
sequence {fn}.
Hence we
can think image f can be characterized by both signs X set and mutability features of this
signs on the images sequence than derived from successive multiple application
of operator T to the analyzed image.
At that one sign that is congruous for two different images will behave on
their sequences differently, because of different mutability and inheritance
character that is defined by images features.
References
1.
Zhiznjakov A.L., Sadykov S.S.,Gai V.E. Analysis of impact behavior of feature’s
group at image sequence. 9th International Conference “Pattern
Recognition and Image Analysis: New Information Technologies” (PRIA-9-2008):
Conference Proceedings. Vol.2.-Nizhni Novgorod, 2008.-404 p.(pp.365-366)