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outline. Two region based shape analysis approach Moment and moment invariants Wavelet based method combined with moment based method Combination of various shape descriptors Future work. Region based shape analysis.

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  1. outline • Two region based shape analysis approach • Moment and moment invariants • Wavelet based method combined with moment based method • Combination of various shape descriptors • Future work

  2. Region based shape analysis • Graphical: objects are represented by a planar graph with nodes representing sub-regions. • region skeleton • region decomposition • Scalar: computer scalar result based on global shape, global transform descriptors include: moments,Fourier, Walsh etc. • moment based method—most popular • shape Matrices and vector • mathematical morphology—suitable for shape related processing. • Shortcomings of global scalar transform: • can not measure the degree of similarity • can not match query with part of image • sensitive to noise and occlusion

  3. Moment based method • Moment: Moment is used to calculate statistical data of geometric properties of distribution such as area, centroid ,moment of inertia, skewness,… • Mathematical presentation: moment m of order of p+q of function f(x,y) is: • Advantage of moment based method: • information preserving---moment m is uniquely determined by f(x,y), vice versa, m can be used accurately reconstruct f(x,y) . • mathematically concise. • Disadvantage of moment based method: difficult to correlate high order moments with shape feature.

  4. Moment invariants • Moment invariants: • fundamental moment formula is not invariant to translation,rotation and scale—depending on position,orientation,or scale. • Hu’s 7 normalized central moment invariants is the foundation for latter application in 1961. • Orthogonal moments(Legendre,Zernike,etc.) is superior to regular moments, complex moments in terms information redundancy . Zernike moments have the the best overall performance. • Fuzzy moment : in order to separate object and background into different class ,apply fuzzy logic to obtain optimal parameter. • DOH to DOM: DOH(difference of histogram) : is suitable for real time (not sensitive to motion), but is sensitive to translation and scale. • DOM(difference of moments): moments invariants are giving good performance when lighting condition changes.

  5. Wavelet based method combined with moment method • Wavelet based method:wavelet transform can provide multiresolution capability and high compaction. wavelet based compressor and decompressor: Compressor Forward wavelet transform Original image Quantizer Encoder Decompressor Decompressed image Inverse Wavelet transform Dequantizer Decoder

  6. wavelet based illumination invariant indexing • TSI-LGM+WP: • M.K.mandal proposed TSI-LGM+WP—combine moment technique(TSI-LGM) with wavelet technique(WP) : • Indexing is performed directly on compressed data, moment is used to improve compression efficiency. • Image retrieval result:

  7. Combination of various descriptors • Fourier and moment descriptors: J.S.Park and colleagues use two stage scheme, 1. compute moments, 2. improved by Fourier descriptors, best result: Hu’s moment invariants + Fourier Zernike moment invariants + Fourier descriptor • Simple combined descriptors: Jukka and colleagues compared CCH, PGH and combined simple descriptors of convexity, principle axes, compactness, variance and elliptic variance . result: combined descriptors has medium performance on time and memory compared with the other two, but gives best recognition result when using small irregular objects as test .

  8. Combination of Five simple descriptors

  9. Future work • Combined descriptors: Human perceptual system compute similarity involves both region and boundary aspects. • Segmentation: extract only objects of interest • Shape matching for partially recovered or objects having occlusion. • Semantically meaningful retrieval:develop perceptually based image features.

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