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Indexing Images with Multiple Regions
Euripides G.M. [email protected]
Dept. of Electronic and Computer EngineeringTechnical University
of Crete (TUC)
IR'2001 Oulu, 19-22 Sept. 2001
- Problem Definition:Given a database with N images.Retrieve
images similar to a query Q.Similar objects;Similar spatial
relationships.Respond faster than sequential scanning.Use an index
to answer two type of image queries.D(Q,I)
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Indexing ApproachEach object is represented by an n-dimensional
feature vector (v1v2vn).E.g., (size, orientation, roundness,
colour, texture).Distance between objects Df: any vector distance
like Euclidean, Manhattan etc.Map each vector to a n-dimensional
feature space.Each region one point;Image (query) with many regions
multiple points.Apply a SAM for indexing (R-tree, SR-tree etc)
.
IR'2001 Oulu, 19-22 Sept. 2001
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Mapping images I=(I1,I2,I3) and J=(J1,J2) and query Q=(Q1,Q2) Q1
Q2I1I2I3J1J2ttsizeroundness
IR'2001 Oulu, 19-22 Sept. 2001
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Problems with SAMsA SAM can treat only one point (region in our
case) per image or query.Existing algorithms can treat range or NN
queries for each Q1 or Q2 but not for Q as a whole.Eg., find the k
NNs of Q1 or Q2;Similarly for range queries.A SAM retrieves the
k-NNs with respect to Df not to D (distance between whole images).D
= function (Df)
IR'2001 Oulu, 19-22 Sept. 2001
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Our contributionsWe formulate the problem of image indexing as
one of spatial searching using existing SAMs.We show how a SAM can
be used treat images and queries with multiple objects and
answerNearest Neighbor queries;Range queries.Two algorithms are
proposed, one for each type of query.
IR'2001 Oulu, 19-22 Sept. 2001
- Range QueriesInput: query Q, distances D, Df, tolerance t.
Output: images I satisfying D(Q,I)
- Nearest Neighbor (NN) QueriesInput: query Q, distance D, Df,
number k.Output: the k images most similar to Q.Decompose Q =
(Q1,Q2,,Qn);Apply a k-NN query for each Qi.Retrieve k distinct
images (incremental k-NN search);Compute ti = their max distance
from Q;Compute t = min{ti};Apply a range query D(Q,I)
- Comments on the Two AlgorithmsAssumption: image distance
satisfies the Lower Bounding Principle Df(Q,I)
- Definition Image Distance (1)Image matching as an assignment
problem (Hungarian algorithm).D(Q,I) : cost of the best mapping of
objects of Q to objects in I.Cost of a mapping.C(Q,I) =
Df(i,j).D(Q,I) = min {C(Q,I)}.Df(Q,I)
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ExperimentsDataset: 13,500 synthetic images. each image contains
4-8 objects; 90,000 vectors are stored in an R-tree; search in the
main memory.The results are averages over 20 queries.Demonstrate
the superiority of the proposed approach over sequential scan
searching.
IR'2001 Oulu, 19-22 Sept. 2001
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Speed-up: Range Queries
IR'2001 Oulu, 19-22 Sept. 2001
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Speed-up: NN queries
IR'2001 Oulu, 19-22 Sept. 2001
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Scale-up: Range Queries
IR'2001 Oulu, 19-22 Sept. 2001
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Scale-up: NN Queries
IR'2001 Oulu, 19-22 Sept. 2001
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Conclusions Interesting problem. image, video retrieval, data
mining etc.Disadvantages of the proposed solution:Suitable for
small images with 4-8 objects;Require careful design of the
distance;Use of incremental NN search. More efficient algorithms
are necessary.
IR'2001 Oulu, 19-22 Sept. 2001
- Definition of Image Distance (2)Image matching as a
transformation of the ARG of I to the ARG of Q (A* algorithm).
D(Q,I): minimum cost transformation.Cost of a transformation C(Q,I)
= max {Df(i,j)}.Df(Q,I)
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Retrieval Example
IR'2001 Oulu, 19-22 Sept. 2001
