Fourier descriptors Ahmad Alkhodre Mostefa Belarbi Insa Lyon

Fourier descriptors Ahmad Alkhodre & Mostefa Belarbi Insa Lyon Georg Langs & Srdan Tosovic Vienna University Nicolas Sicard Pavia University Lecturer: Alberto Aguado University of Surrey ABi. Li. Tie. S Fourier Descriptors Analysis Team

Contents ® Introduction ® Fourier descriptors ® Classification ® Occlusion ® Suggestions ® Conclusion ABi. Li. Tie. S Fourier Descriptors Analysis Team

Introduction ®Image classification ®Different ® means Using shapes ® ® Advantages Drawbacks ? ABi. Li. Tie. S Fourier Descriptors Analysis Team

Fourier decomposition =. . . ABi. Li. Tie. S Fourier Descriptors Analysis Team

Fourier descriptors original picture border Fourier coefficients decomposed to real + imaginary part Fourier descriptors ABi. Li. Tie. S Fourier Descriptors Analysis Team

Fourier decomposition (of Nicolas) Processing ABi. Li. Tie. S Fourier Descriptors Analysis Team

Invariance (Rotation) work in progress ABi. Li. Tie. S Fourier Descriptors Analysis Team

Reconstruction (of Nicolas) ABi. Li. Tie. S Fourier Descriptors Analysis Team

Classification ® Database of Fourier descriptors with 14 airplanes and 1 Nicolas. ® Evaluation function for matching the test object with one object or Nicolas in the database. ® Astonishing results ABi. Li. Tie. S Fourier Descriptors Analysis Team

Occlusion problem ® Random results, when classifying occluded curves • How much is occluded? • Which part of the original curve? • Which airplane? ABi. Li. Tie. S Fourier Descriptors Analysis Team

database building Classification – occlusions Create databases of subcurves for each airplane: subcurves curve a b fourier descriptors Set of 200 -400 descriptorvectors per airplane, indexed by intervalborders Alpha-beta decomposition ABi. Li. Tie. S Fourier Descriptors Analysis Team

database building 1. Curve represented by subcurve descriptors 2. 3. 4. beta alpha 5. ABi. Li. Tie. S Fourier Descriptors Analysis Team

matching Processing of input b Process the curve as an interval from a to b, for every (a, b) couple present in the database a nx Store results in a datastructure similar to the database ABi. Li. Tie. S Fourier Descriptors Analysis Team

matching Matching Alpha-beta Descriptors Subcurves database Input image 1 2 Computation of distance between descriptors verto - = 3 ABi. Li. Tie. S Fourier Descriptors Analysis Team

matching Search for lowest point Lowest point a b ABi. Li. Tie. S Fourier Descriptors Analysis Team

matching Results match inputshape b a ABi. Li. Tie. S Fourier Descriptors Analysis Team

matching Problems, observations ® Symmetry ® Descriptors are invariant against mirroring ® Time for more testing Tests were performed on one airplane ® Matching is dependent on number of airplanes in the database ® ® Weigthing algorithm for lowest point search ® Robustness ABi. Li. Tie. S Fourier Descriptors Analysis Team

Conclusion ® What we have done: Shape extraction ® Fourier coefficients ® Invariant Fourier descriptors ® Shape reconstruction ® Classification ® Proposition for occlusion problem ® ® What ® we still need to do: Generalization of alpha-beta decomposition ABi. Li. Tie. S Fourier Descriptors Analysis Team