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 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

Moment based method Moment: Advantage of moment based method: 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.

Moment invariants Moment invariants: DOH to DOM: 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.

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

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:

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 .

Combination of Five simple descriptors

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.