Abstract
By using affine-invariant shape descriptors, it is possible to recognize an unknown planar object from an image taken from an arbitrary view when standard view images of candidate objects exist in a database. In a previous study, an affine-invariant function calculated from the wavelet coefficients of the object boundary has been proposed. In this work, the invariant is constructed from the multiwavelet and (multi)scaling function coefficients of the boundary. Multiwavelets are known to have superior performance compared to scalar wavelets in many areas of signal processing due to their simultaneous orthogonality, symmetry, and short support properties. Going from scalar wavelets to multiwavelets is challenging due to the increased dimensionality of multiwavelets. This increased dimensionality is exploited to construct invariants with better performance when the multiwavelet "detail" coefficients are available. However, with (multi)scaling function coefficients, which are more stable in the presence of noise, scalar wavelets cannot be defeated.
Highlights
Object recognition is one of the most difficult problems in computer vision
When the depth of an object along the line of sight is small compared to the viewing distance of the camera, as its images are produced from different viewpoints, it seems to be going through an affine transformation
With MWjxi(t) denoting the multiwavelet coefficients of the x-coordinate function x(t) of the preprocessed boundary at the ith row and scale j, and taking the multiwavelet transform of (11), it is observed that multiwavelet coefficients at identical rows, which correspond to the same wavelet ψi(t), are related by an equation similar to the scalar wavelet case for the jth scale:
Summary
Object recognition is one of the most difficult problems in computer vision. if the problem definition includes only planar objects, which are to be viewed from arbitrary directions, it is possible to design recognition systems that have satisfactory performances. Recognition techniques are classified according to how the shape descriptors are calculated from the images of objects One such classification is based on whether the boundary or the region of the object is required. Analyzing only the boundary is advantageous compared to the region-based techniques in terms of computational complexity, since the amount of data to be processed substantially diminishes Another classification to discriminate between the shape descriptors is whether they are local or global. Multiwavelets, which are generalizations of wavelets, have shown superior performance compared to wavelets in such areas as image compression [8] and image denoising [9, 10] These application areas are related to object recognition, for they, too, require compact and accurate representations.
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