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Fig. 6 Results of filtering of flat blocks and outliers. Sequence “Claire” c
LABRI.
Fig. 7 Object extraction at the top of the pyramid by merging frame segmentation and motion
masks. Sequence “Lance trousse” c
LABRI.
MRF based adjustment of object borders with LL and HF subbands
When projected between two successive levels of the pyramid, one wavelet coef-
ficient of a higher W k ( i , j ) level in each subband is transformed into four coef-
ficients W k 1 (2 i , 2 j ), W k 1 (2 i , 2 j + 1), W k 1 (2 i + 1 , 2 j ), W k 1 (2 i + 1 , 2 j + 1) of
lower level. To avoid this aliasing in resulting object border a morphological erosion
of the projected mask is performed thus defining an uncertainty area. Then pixel-
coefficients in it are assigned according to the minimal energy adapting the classical
MRF formulation with Maximal A posteriori Probability (MAP) criterion. Gaussian
multivariate distribution of LL coefficients in each segmented region is supposed.
For a coefficient in LL subband at position p the label l is assigned according to the
minimum of the energy:
[1 , L ] U 1 ( l , p )+ U 2 ( l , p )
l ( p )=arg min
l
(11)
The first potential U 1 expresses the Gaussian assumption of distribution of the coef-
ficients in LL subband:
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