Distance Sets for Shape Filters and Shape Recognition

圖形識別期末報告 Distance Sets for Shape Filters and Shape Recognition 資 碩一 M 9415027 王敬堯 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 12, NO. 10, OCTOBER 2003

Outline • • • Introduction (Labeled) Distance Sets of (Labeled) Distance Sets Distance Set Shape Filter Shape Comparison Conclusion

Introduction • Using a new local image descriptor, namely the (labeled) distance set for shape filters and shape recognition. • Scheme – distance set shape filter

Definition • Feature points: the spatial interrelations between perceptually significant points • Local image descriptor: A number which characterizes the image content in the surroundings of a point • Rich descriptor: a set of number or a data structure computed on the neighborhood of a point and presents a more informative characteristic of the local image contents

Local descriptors They are used for different purposes: 1. Select only those points whose local descriptors fulfill a certain condition. 2. Solving the correspondence problem.

Distance Sets • feature points For a given point one can select only a subset of N ≦ n nearest neighboring points. • distance set where be the distance between point p and its i-nearest neighbor form S, 1≦i ≦N

Distance Sets – Cont. • relation difference between i-neighbor and j-neighbor distances of p and q: • dissimilarity between two distance sets and : where is a one-to-one mapping and Πis the set of all such mappings

Distance Sets – Cont. • (a) A point from the printed character “a” together with its set of distances to the first nearest neighbors within. (b) The points in the word “alphabet” which have 5 -distance sets (within ) identical with that of p, (c) Points for which , the same points are obtained also for

Labeled Distance Sets • Let L be the set of possible feature labels and let l∊ L be one such label. We define the labeled distance subset of a point p to its first neighbor feature points of type l: A labeled distance set is the set of tuples of labeled distance subsets:

Labeled Distance Sets – Cont.

(Labeled) Distance Sets Implementation • Advanced data structures which can be used to efficiently search nearest neighbors in higher dimensional spaces include quad-trees, K-d trees, range trees, lookup maps, etc. • In this paper, it uses semidynamic binary search tree (SD tree). The time complexity is O(nlog(n)) to build a SD tree and find the N-nearest neighbors of a point p is Θ(N)

Sets of (labeled) Distance Sets distance set . The set of distance sets of S:

Sets of (Labeled) Distance Sets Dissimilarity • two sets of points and , • dissimilarity measure between their associate sets of N-distance sets and where is the cost of a mapping -one mapping from to , M is the set of all one-to

Sets of (Labeled) Distance Sets Implementation • Using Hungarian method to find optimal solution of dissimilarity. • The time complexity is O( v*( e + vlog(v) ) ) • The time complexity can reduce to because within a distance set, the distances are ordered increasingly • Dynamic programming can be used and the time complexity is

Distance Set Shape Filter • is reference image and where applied is test image is the number of times F has to be recursively

Distance Set Shape Filter – Printed Character Recognition

Distance Set Shape Filter – Continuous Handwritten Text

Shape Comparison

Conclusion • Using dissimilarity measure between two (labeled) distance sets to define a shape filter and the reduced computational complexity. • Application: character recognition、object recognition based on 2 D、MPEG-7 shape database retrieval.