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We calculate the histogram
from the sensed subsample of features
analogously to Section 3.
The first criterion for comparison with a database histogram
is the
intersection
![\begin{displaymath}
\bigcap(H_O,H_{O'}) =
\sum \limits_{i=1}^d \min(H_{O}(i), H_{O'}(i))\ ,
\end{displaymath}](img74.png) |
(11) |
often used with fuzzy-set techniques and previously applied to color-histogram
classification [10].
It is very fast to compute, because, apart from summation, no arithmetic
operations are needed.
Another straightforward criterion is the squared Euclidian distance
![\begin{displaymath}
{\cal{E}}(H_O,H_{O'}) =
\sum \limits_{i=1}^d (H_{O}(i) - H_{O'}(i))^2\ ,
\end{displaymath}](img75.png) |
(12) |
which is known to be sensitive to noise and does not generalize very well.
Next, the statistical
-test is examined in its two forms
![\begin{displaymath}
\chi_1^2(H_O,H_{O'}) =
\sum \limits_{i=1}^d \frac{(H_{O}(i) - H_{O'}(i))^2} {H_{O}(i)}
\end{displaymath}](img77.png) |
(13) |
and
![\begin{displaymath}
\chi_2^2(H_O,H_{O'}) =
\sum \limits_{i=1}^d \frac{(H_{O}(i) - H_{O'}(i))^2}
{H_{O}(i) + H_{O'}(i)}\ .
\end{displaymath}](img78.png) |
(14) |
Finally, we test the symmetric form of the Kullback-Leibler divergence
![\begin{displaymath}
{\cal{K}}(H_O,H_{O'}) =
\sum \limits_{i=1}^d (H_{O'}(i) - H_{O}(i))\ln
\frac{H_{O'}(i)}{H_{O}(i)}\ .
\end{displaymath}](img79.png) |
(15) |
Because of the logarithmic operation, it is the computationally most expensive
of all six criteria.
Next: Likelihood criterion
Up: Recognition phase
Previous: Recognition phase
Eric Wahl
2003-11-06