Dept. of Computer and Information Sciences Vantage Objects Dr. Rolf Lakaemper Dept. of Computer and Information Sciences Temple University

The Application: ISS Database Task: Create Image Database Problem: Response Time Comparison of 2 Shapes: 23ms on Pentium1Ghz ISS contains 15,000 images: Response Time about 6 min. Clustering not possible (not a metric)

Vantage Objects Solution: Full search on entire database using a simpler comparison Vantage Objects (Vleugels / Veltkamp, 1999) provide a simple comparison of n- dimensional vectors (n typically < 100) Paper: Vleugels/Veltkamp: Efficient Image Retrieval through Vantage Objects (1999)

Vantage Objects The Idea: Compare the query-shape q to a predefined subset S of the shapes in the database D The result is an n-dimensional Vantage Vector V, n = |S| s1 v1 s2 v2 q s3 v3 … sn vn

Vantage Objects - Each shape can be represented by a single Vantage Vector - The computation of the Vantage Vector calls the ASR – comparison only n times - ISS uses 54 Vantage Objects, reducing the comparison time (needed to create the Vantage Vector) to < 1.5s - How to compare the query object to the database ?

Vantage Objects - Create the Vantage Vector vi for every shape di in the database D - Create the Vantage Vector vq for the query-shape q - compute the euclidean distance between vq and vi - best response is minimum distance Note: computing the Vantage Vectors for the database objects is an offline process !

How to define the set S of Vantage Objects ?

k=1..i-1 e(di , sk) maximal. (e = eucl. dist.) Vantage Objects Algorithm 1 (Vleugels / Veltkamp 2000): Predefine the number n of Vantage Objects S0 = { } Iteratively add shapes di  D\Si-1 to Si-1 such that Si = Si-1  di and k=1..i-1 e(di , sk) maximal. (e = eucl. dist.) Stop if i = n.

Vantage Objects Result: Did not work for ISS.

Algorithm 2 (Latecki / Henning / Lakaemper): Vantage Objects Algorithm 2 (Latecki / Henning / Lakaemper): Def.: A(s1,s2): ASR distance of shapes s1,s2 q: query shape ‘Vantage Query’ : determining the result r by minimizing e(vq , vi ) vi = Vantage Vector to si ‘ASR Query’: determining the result r by minimizing A(q,di ) Vantage Query has certain loss of retrieval quality compared to ASR query. Define a loss function l to model the extent of retrieval performance

Vantage Objects Given a Database D and a set V of Vantage Vectors, the loss of retrieval performance for a single query by shape q is given by: lV,D (q) = A(q,r), Where r denotes the resulting shape of the vantage query to D using q. Property: lV,D (q) is minimal if r is the result of the ASR-Query.

L(S) = 1/n  lS,D\{si} (si) Vantage Objects Now define retrieval error function L(S) of set S={s1 ,…, sn }  D of Vantage Vectors of Database D: L(S) = 1/n  lS,D\{si} (si) Task: Find subset S  D such that L(S) is minimal.

Vantage Objects Algorithm: V0={ } iteratively determine sj in D\Sj-1 such that Sj =Sj-1  sj and L(Vj) minimal. Stop if improvement is low

Number of Vantage Objects Result: Worked fine for ISS, though handpicked objects stil performed better. Handpicked Algorithm 2 L(S) Number of Vantage Objects

Vantage Objects …some of the Vantage Objects used in ISS:

Vantage Objects helped in times of need, but discussion is required !