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

Generalized Extended Pseudo-Symbolic Pictures(GEP-Symbolic Pictures)

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

Algorithms for Generating GP-2D Strings

Algorithms for Generating GP-2D Strings

Algorithms for Generating GP-2D Strings

Algorithms for Generating GP-2D Strings

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

Algorithm for Generating GEP-2D Strings

Algorithm for Generating GEP-2D Strings

Algorithm for Generating GEP-2D Strings

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

Conclusion

Presented an efficient algorithm.Proved the upper bound of the lost ratio.Developed “the generalized combined 2D string representation”

They have proposed a unified framework to index images in image database based on image content.