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Weighting

In (Eq. [*]), the output from each cue is weighted. Four different weighting methods are evaluated:
1. Uniform weights - Outputs of all cues are weighted equally: $ w_i=1/n$, where $ n$ is the number of cues.
2. Texture based weighting - Weights are estimated experimentally and depend on the spatial content of the region. For a highly textured region, we use: color (0.25), image differencing (0.3), correlation (0.25), intensity variation (0.2). For uniform regions: color (0.45), image differencing (0.2), correlation (0.15), intensity variation (0.2).
3. One-step distance weighting - Weighting factor, $ w_i$, of a cue, $ c_i$, at time step $ k$ depends on the distance from the predicted image position, $ \hat{\textbf{z}}_{k\vert k-1}$. Initially, the distance is estimated as $ d_i = \vert\vert\textbf{z}^i_{k} - \hat{\textbf{z}}_{k\vert k-1}\vert\vert$ and errors are estimated as $ e_i=d_i/\sum_{i=1}^{n} d_i$. Weights are than inversely proportional to the error with $ \sum^{n}_{i=1}w_i=1$.
4. History-based distance weighting - Weighting factor of a cue depends on its overall performance during the tracking sequence. The performance is evaluated by observing how many times the cue was in an agreement with the rest of the cues. The strategy is:
1. For each cue, $ c_i$, examine if $ \vert\vert\textbf{z}^i_{k} - \textbf{z}^j_{k}\vert\vert < d_T$   where
$ i,j=1,\dots,n~$and$ ~i \ne j$. If this is true, $ a_{ij}$=1, otherwise $ a_{ij}$=0. Here, $ a_{ij}$=1 means there is an agreement between the outputs of cues $ i$ and $ j$ at that voting cycle and $ d_T$ represents a distance threshold which is set in advance.
2. Build $ (n-1)$ value set for each cue: $ c_i: \left\{ a_{ij} \vert j=1, \dots, n~\text{and}~i~\ne~j~\right\}$. Find sum $ s_i=\sum_{j=1}^{n}a_{ij}$.
3. The accumulated values during $ N$ tracking cycles, $ S_i=\sum_{k=1}^{N}s_i^k$, indicate how many times a cue, $ c_i$, was in the agreement with other cues. Weights are then simply proportional to this value: $ w_i=\frac{S_i}{\sum_{i=1}^{n}S_i}~~$with$ ~~\sum^{n}_{i=1}w_i=1$.


next up previous
Next: Implementation Up: Background and Theory Previous: Visual Cues
Danica Kragic 2002-12-06