Hierarchy-of-Visual-Words: a Learning-based Approach for Trademark Image Retrieval

From the background, the procedure extracts the holes' shapes and associate them with the component shapes' list (lines 7 and 8). The foreground shapes are used in the next iterations (lines 5 and 9) until all component shapes have been extracted from the initial binary trademark image. Shape's feature extraction consists of building a feature vector for each component shape of a given trademark image (Figs. 1 (d) and (k)). These 29-dimension feature vectors combine region-based and contour-based descriptors. Shape's region is described by the 25 moments of the Zernike polynomials (ZM) of order p from 0 to 8: Z p,q= p + 1 π null ρ null θ V p,q(ρ,θ) I ( ρ,θ), (1) where ρ = null x 2 + y 2 is the length of vector from origin to pixel (x,y), θ is the angle between the vector defining ρ and the x -axis in the counter clockwise direction and V p,q(ρ,θ) is a Zernike polynomial of order p with repetition q that forms a complete set over the interior of the unit disk inscribing the component shape: V p,q( ρ,θ) = R p,q(ρ) exp ( i qθ) .