A Presentation on
MINING SPATIAL ASSOCIATION RULES IN IMAGE
DATABASES USING 9

DLT AND ITS COMPARISON WITH
MINING VIWEPOINT PATTERNS IN IMAGE DATABASES
Submitted By:
KUSUM LATA
College Roll No: 24/CTA/07
University Roll No. 8833
under the Guidance of:
Dr. RAJNI JINDAL
Dept. of Computer Engineering
Delhi College of Engineering, Delhi
Introduction
Many data mining methods have been proposed such as
association rule mining, Sequence pattern mining, Text mining
,Temporal data mining etc.
Because of advances in Information technology vast number
of images have accumulated on the internet, in entertainment,
education and in other multimedia applications
So how to mine spatial patterns from image database has
attracted attention these days.
What is spatial data mining?
I
Spatial
data
mining
refers
to
the
extraction
of
implicit
knowledge
relationships,
or
other
interesting
patterns
stored
in
spatial
databases
.
Applications
:
Geographic
information
system
Architectural
images
Medical
images
Multimedia
information
system
etc
.
Image
representation
Many
image
representation
methods
has
been
proposed
such
as
attribute
relationship
graph
in
which
object
are
represented
by
a
node
and
relation
ship
b/w
nodes
is
represented
by
a
arc
.
Another
representation
is
9
DLT
representation
.
Directional
information
is
one
of
the
most
important
types
of
information
in
an
image
database,
and
the
9
DLT
representation
is
fundamental
in
this
method
.
Here
I
will
discuss
a
DLT
mining
algorithm
to
mine
spatial
association
rule
where
every
image
is
represented
by
a
9
DLT
representation
.
The 9DLT mining Algorithm
The algorithm consists of two phases
.
1. In the first phase, we find all frequent patterns of length one.
2. In the second phase, we use the frequent k

patterns,whose lengths are equal to k,
to generate all candidate (k + 1)

patterns. For each candidate (k + 1)

pattern
generated, we scan the database to count the pattern’s support and check
whether it is frequent. The steps in the second phase are repeated until no
more frequent patterns can be found.
Let I=(i
1
,i
2
……i
w
) be a set of items each of which is an object in an image.
An item set is a subset of I.
A spatial relation between two objects is one of the 9 directional codes
defined in 9DLT representation. A spatial relation is defined on the basis of
this representation.
Example demonstrating how a
symbolic image is transformed
to a 9DLT string:
First the symbolic image is
converted to 9DLT matrix, which
a lower triangular matrix,
Then the 9DLT matrix is
represented in the 9DLT string as
shown in figure.
So (A,B,C,D,5,6,6,7,6,6) is the
9DLT string representation of the
given symbolic image which
consists of two parts: item
(objects) and spatial relations.
Given two frequent 2

patterns (A,B,3) AND (A,C,4) as shown in above figure. We
can generate a candidate 3
–
pattern by joining them. That is we have (A,B,C,3,4,?),
where relation b/w (A,B) and (A,C) are known, but relation b/w (B,C) is unknown .
We need to find possible relations between B and C from (A, B, 3) and (A, C, 4).
The possible relations between (B
,
C), as shown in above figure are 4, 5, and 6. So,
we can obtain three candidate 3

patterns:
(A
,
B
,
C
,
3
,
4
,
4
)
,
(
A
,B,C,3,4,
5
), and
(A
,
B
,
C
,
3
,
4
,
6
), where the
underlined relations are the possible relations between B
and C
•
In General the possible relation
derived by joining two joinable
2 patterns (A,B,X) and (A,B,Y)
to generate a candidate 3

pattern (A,B,C,X,Y,Z). The
matrix hence derived is the
complementary matrix.
•
In this matrix the Z values of an
entry are complementary to
those of its symmetric entry.
•
For example the Z values of
entry[1,2] are equal to (6,7,8)
and the Z value of its symmetric
entry are [2,1] is equal to (2,3,4)
The Mining Algorithm
The 9DLT

Miner Algorithm consists of two phases.
In the First phase ,we find all frequent patterns of length one.
In the second phase, we find use the frequent k

patterns (k>=2) to generate
all candidate (k+1)

patterns. For each (k+1) pattern generated ,we scan the
database to count its support and check if it frequent. the steps in phase 2
are repeated until no more frequent patterns can be found.
The 9DLT
–
Miner algorithm consists of one procedure GenCandidates
which is used to generates possible
candidate patterns.
Mining Viewpoint Patterns in Image Databases
•
Viewpoint patterns refer to patterns that capture the invariant relationships of
one object from the point of view of another object.
•
These patterns are unique and significant in
images because the absolute
positional information of objects for most images is not important, but rather, it
is the relative distance and orientation of the objects from each other that is
meaningful. Analyzing large set of images, we find that the absolute positional
information of objects do not convey critical perceptual information, but rather,
it is the invariant relationships , in the form of the relative spatial relationships
among the objects in images, that are important.
Above
relationship a
viewpoint pattern
.
Such patterns are insensitive to
translational operations, and in some applications, rotational operations too.
The figure 2 shows the possible 2

objects pairs in the plan_1.
Setting the minimum support to 3 , the
frequent 2

object patterns generated from
the images in figure 1 are given be
The 2

objects table is scanned to determine the frequent 2

objects patterns.
Based on 2

object table we build the 3

object table. For each pair of the object in
the 2

object table we adda new object that can be found in the same image to form
a 3

object group
.
When scanning a 3

object table candidates whose count is greater than or equal
to three are output as 3

object viewpoint patterns. This process is repeated until
no more frequent patterns can be found.
A Comparison
As directional information is one of the most important types of information in an
image database, and the 9

DLT representation is fundamental in this method. The
9DLT

Miner is a spatial mining algorithm, called 9

DLT

Miner, to mine spatial
association rules in an image database, where every image is represented by the 9

DLT representation.
While on the other hand the Viewpoint Miner Algorithm uses another image
representation approach. Viewpoint patterns refer to patterns that capture the
invariant relationships of one object from the point of view of another object.
The viewpoint patterns are unique and significant in images because the absolute
positional information of objects for most images is not important, but rather, it is
the relative distance and orientation of the objects from each other that is
meaningful.. Analyzing large set of images, the absolute positional information of
objects do not convey critical perceptual information, but rather, it is the invariant
relationships , in the form of the relative spatial relationships among the objects in
images is important. Again the Viewpoint Miner is able to mine rotational

invariant
patterns while 9

DLT not.
17

DLT Method
•
9

DLT algorithm is designed to mine for frequent patterns of images represented by
the 9

DLT representation, it is extended to mining frequent patterns for images
represented by the other directional representation i.e. 17

DLT. The 17

DLT is
more direction specific than 9

DLT. The complementary matrix for this
representation is derived. For the 17

DLT representation, each directional code (not
including 0) in the 9

DLT representations divided into two sub

directional codes.
B
A
C
F
D
E
(A,B,C,D,E,F,9,3,12,11,13,5,6,5,4,5,3,1
)
CONCLUDING REMARKS AND FUTURE WORK
In this project 9

DLT

Miner for mining spatial association rules in image databases
discussed in which every image is represented by a

9DLT representation. The
algorithm consists of two phases. In the first phase, we find all frequent patterns of
length one. In the second phase, we use the frequent k

patterns (k >= 1), whose
lengths are equal to k, to generate all candidate (k + 1)

patterns and then scan the
database to count the support and check if a pattern is frequent for each candidate (k
+ 1)

pattern generated. The steps in phase 2 are repeated until no more frequent
patterns can be found. Another
algorithm
discussed and
compared with 9

DLT is Viewpoint miner.
•
Viewpoint patterns refer to patterns that capture the invariant relationships of one
object from the point of view of another object. These patterns are unique and
significant in images because the absolute positional information of objects for
most images is not important, but rather, it is the relative distance and orientation of
the objects from each other that is meaningful.
•
Further 9

DLT is extended to 17

DLT to mine frequent patterns of images
represented by the 17

DLT representation. The complementary matrix for 17

DLT
is derived.
•
There are a number of possible future research directions .We can work for mining
association rules for an image database in which images are represented by other
representations Attribute Relationship Graph.
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Min Ko,Wen

Kwang Tsao,Hsiu

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±
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