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A Unified Approach to Iconic Indexing, Retrieval and Maintenance of Spatial Relationships in Image Databases
Reporter : Cindy Liu
Outline
IntroductionBackground WorkGP-Symbolic PicturesGEP-Symbolic PicturesAlgorithmsMaintainance of Lost Absolute Spatial RelationshipsThe GC-2D String RepresentationRetrievalConclusion
Introduction
One of the most important portant problems in the design of image database systems is how images are stored in the image databases.Efficient 、 economic storage 、 flexible retrieval 、 the manipulation of vast amounts of image information.
Background Work-Symbolic Pictures
: Relative spatial relationships : Absolute spatial relationshipsV : A given set V of symbolsƒ : A symbolic picture over V is and mn matrix (u,v) : A (reduced) 2D string over V is defined as a pair of strings
ra
)...,...( )(12)2(1)1(12211 tptpptt xzzxzxxyyxyx
and where Vxi and symbols nullor either are , rii zy functionn permutatio a is },...,2,1{},...,2,1{: ttp
Background Work-Symbolic Pictures
Problem : The possibility of multiple occurrences of a given symbol.Using “augmented 2D string” to solve this problem.A definition of nonredundant 2D string is given by Costagliola et al.
Background Work-The types of 2D String
t).rscs,cr(ct:string 2Dnt Nonredunda
t,13452),rsccs,cr(ct :string 2D Augmented
,13452 wheret),rsccs,cr(ct:String D2
p
Background Work-Absolute Spatial Relationships
Sistla et al. developed a rule System .There are three obvious distinctions between the work of Sistla et al. and the work mentioned in other studies.Some semantic definitions of various absolute spatial relationships
Background Work-Absolute Spatial Relationships
p be a picture in which objects A and B are definedA left-of B 、 A below B 、 A in-front-of BA inside B : p(A) p(B)A outside B : p(A) p(B)= A overlaps B : p(A) p(B) right-of 、 above 、 behind are duals of left-of 、 below 、 in-front-of .
Background Work-A System of Rules , rules I-III
Transitivity of left-of, below, in-front-of, and inside. I : For each x{left-of, below, in-front-of,
inside}, we have A x C :: A x B, B x C. II : For each x{left-of, below, in-front-
of}, we have A x D :: A x B, B overlaps C, C x D.
III : For each x{left-of, below, in-front-of, outside}, we have the following two types of rules : (a) A x C :: A inside B, B x C; (b) A x C :: A x B, C inside B.
Background Work-A System of Rules , rules IV-VIII
Symmetry of overlaps and outside. IV : For each x{overlaps, outside},
we have A x B ::B x A. V : For each x{left-of, below, in-
front-of}, we have A outside B :: A x B VI : A overlaps B ::A inside B VII : A overlaps B :: C inside A, C
overlaps B. VII : A inside A ::.
Background Work-Minimal and Maximal Set of Spatial Relationships
Two problems in general-purpose picture retrieval systems : The deduction problem
A left-of B,B left-of CA left-of C. The reduction problem.
A left-of B,B left-of C,A left-of C A left-of B,B left-of C
Background Work-Two efficiently decidable classes of planar pictures
Yau and Zhang used two efficiently decidable classes of planar pictures. Pseudo-symbolic pictures. Extended pseudo-symbolic pictures.
To avoid ambiguity, they associate multiple occurrences of the same object with different nonnegative integers starting at zero.
Background Work-Pseudo-Symbolic Pictures
A local scene plays a key role.Super-symbol :
."r" and ",c" t}, {
r}, s{},c {c sences local thepoint to
,,,, where),(),(
121
1
432101423043210
outsides
insideoverlaps
eeeeeeeeeeeeeeevu
)0( iei
Background Work-Extended Pseudo-Symbolic Pictures
T : A regular partition on an mn matrix is a collection of sets of slot.T=The numbers of rows and columns are minimal.
}|{ IiTi
Background Work-Combined 2D String Representation
Zhang and Yau proposed this new iconic indexing.There are never left-of or below relationships among objects in the same local scene.
Combined 2D String Representation-Fig.2.
The combined 2D string representation : the pseudo-2D string representation (u,v), associated with their corresponding 2D strings.
)r,r(
),c,c(),st,s(t
sr),sr,(),cc,cc(
11
2211
11
Generalized Pseudo-Symbolic Pictures(GP-Symbolic Pictures)
There are possible left-of and below relationships among objects in each slot of the matrix
Algorithms for Generating GP-2D Strings
ƒ : a planar picture : the sets of all objects : absolute spatial relationships in ƒ.
fO
fR
Algorithms for Generating GP-2D Strings-Steps
Encode Generalized Local Scenes by Super-Symbols. Spatial-Comparable & Spatial-Incomparable
Define left-of and below Relationships among Super-Symbols.Find Local Substrings of Super-SymbolsProduce the Generalized Pseudo-2D String Representation
Algorithm for Generating GEP-2D Strings-Steps
1 and 2 same as 1 and 2 in the case of generalized pseudo-symbolic pictures.Produce the Generalized Extended Pseudo-2D String Representation
Maintenance of Lost Absolute Spatial Relationships
Two absolute spatial relationships “ “ and “ “ are satisfied in the FIG. 5.I(ƒ) : the set of all absolute spatial relationshipsD(ƒ) : the set of all absolute spatial relationships derived from the GEP-symbolic picture.L(ƒ)=I(ƒ)-D(ƒ) : the missing set.r(ƒ)= : the lost ratio of ƒ.
cbelowc 1 31 cofleftt
)(/)( fIfL
Maintenance of Lost Absolute Spatial Relationships
How big is r(ƒ) ?If each generalized local scene of an image ƒ contains exactly one object r(ƒ) =0Theorem 5.1 : r(ƒ) cannot exceed 1/3=33.4% for every 2D image ƒ.
The GC-2D String Representation
The information about relative spatial relationships left-of and below in the generalized local scene is still of critical importance.
The GC-2D String Representation-FIG.4.
The GC-2D string : the generalized GP-2D string representation (u,v), associated with their corresponding 2D strings.
),(),(
),(
),,(),,(
1133
1221
11
rrcc
stccst
srsrcccc
Picture Retrieval by GEP-2D Strings and GC-2D Strings
Change et al. defined type-0, type-1, type-2 picture matching
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