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an innovative algorithm for key frame extraction in video ...

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histogram. The threshold has been heuristically set at the 4% of the gradientmaximum value <strong>in</strong> order to remove from the histogram computation edgesderived from background noise.Multiresolution wavelet <strong>an</strong>alysis provides representations of image data <strong>in</strong>which both spatial <strong>an</strong>d frequency <strong>in</strong><strong>for</strong>mation are present [33]. In multiresolutionwavelet <strong>an</strong>alysis we have four b<strong>an</strong>ds <strong>for</strong> each level of resolution result<strong>in</strong>g fromthe application of two filters, a low-pass filter (L) <strong>an</strong>d <strong>an</strong> high-pass filter (H). Thefilters are applied <strong>in</strong> pairs <strong>in</strong> the four comb<strong>in</strong>ations, LL, LH, HL <strong>an</strong>d HH, <strong>an</strong>dfollowed by a decimation phase that halves the result<strong>in</strong>g image size. The f<strong>in</strong>alimage, of the same size as the orig<strong>in</strong>al, conta<strong>in</strong>s a smoothed version of the orig<strong>in</strong>alimage (LL b<strong>an</strong>d) <strong>an</strong>d three b<strong>an</strong>ds of details (see Fig. 5a).F oLHF vF Horizontalo=filter<strong>in</strong>g <strong>an</strong>d decimationF Verticalv=filter<strong>in</strong>g <strong>an</strong>d decimationLLHLLHHHa) b)Fig. 5. The filter<strong>in</strong>g <strong>an</strong>d decimation of the image along the horizontal <strong>an</strong>d vertical directions. Fourb<strong>an</strong>ds are created each a quarter the size of the whole image. b) The tree-step application of themultiresolution wavelet. The wavelet filters are applied to the top left b<strong>an</strong>d conta<strong>in</strong><strong>in</strong>g the resizedimage.Each b<strong>an</strong>d corresponds to a coefficient matrix that c<strong>an</strong> be used to reconstructthe orig<strong>in</strong>al image. These b<strong>an</strong>ds conta<strong>in</strong> <strong>in</strong><strong>for</strong>mation about the content of theimage <strong>in</strong> terms of general image layout (the LL b<strong>an</strong>d) <strong>an</strong>d <strong>in</strong> terms of details(edges, textures, etc..). In our procedure the features are extracted from thelum<strong>in</strong><strong>an</strong>ce image us<strong>in</strong>g a three-step Daubechies multiresolution waveletdecomposition that uses 16 coefficients <strong>an</strong>d produc<strong>in</strong>g ten sub-b<strong>an</strong>ds [34] (Fig.5b). Two energy features, the me<strong>an</strong> <strong>an</strong>d st<strong>an</strong>dard deviation of the coefficients, arethen computed <strong>for</strong> each of the 10 sub-b<strong>an</strong>d obta<strong>in</strong>ed, result<strong>in</strong>g <strong>in</strong> a 20-valueddescriptor.To compare two <strong>frame</strong> descriptors, a difference measure is used to evaluatethe color histograms, wavelet statistics <strong>an</strong>d edge histograms. There are severaldist<strong>an</strong>ce <strong>for</strong>mulas <strong>for</strong> measur<strong>in</strong>g the similarity of color histograms. Techniques <strong>for</strong>compar<strong>in</strong>g probability distributions are not appropriate because it is visualperception that determ<strong>in</strong>es the similarity, rather th<strong>an</strong> the closeness of theprobability distributions. One of the most commonly used measures is thehistogram <strong>in</strong>tersection [29]. The dist<strong>an</strong>ce between two color histograms (dH)us<strong>in</strong>g the <strong>in</strong>tersection measure is given by:63t+ −∑j=0( H , H ) = 1 ( H (j),H (j))dH t 1m<strong>in</strong>t t+1(10)where H t <strong>an</strong>d H t+1 are the color histograms <strong>for</strong> <strong>frame</strong> F(t) <strong>an</strong>d <strong>frame</strong> F(t+1)respectively.9

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