We propose a non-iterative, globally optimal dense motion field estimation technique based on a multiresolutional probability model. We consider the field to be estimated in terms of its wavelet coefficients and carry out the estimation in the field’s wavelet transform domain. Our approach models interscale dependencies of the wavelet coefficients and allows for smooth, edge, and occluded regions in the field. We obtain segmentations of the field and our results show that the field estimates yield accurate depictions of scene motion. The globally optimal nature of our estimation framework allows it to be applicable in scenes exhibiting large motion and in settings of ill-posed motion. Hence, our algorithms can also be used to determine accurate initializations for optical flow type estimation techniques, which use more sophisticated models but can only obtain locally optimal solutions that are heavily dependent on initial conditions. The performance is illustrated on several examples.
This paper takes up the design of wavelet tight frames that are analogous to Daubechies orthonormal wavelets - that is, the design of minimal length wavelet filters satisfying certain polynomial properties, but now in the oversampled case. The oversampled dyadic DWT considered in this paper is based on a single scaling function and tow distinct wavelets. Having more wavelets than necessary gives a closer spacing between adjacent wavelets within the same scale. As a result, the transform is nearly shift-invariant, and can be used to improve denoising. Because the associated time- frequency lattice preserves the dyadic structure of the critically sampled DWT it can be used with tree-based denoising algorithms that exploit parent-child correlation.
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