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The Fisher-Rao metric and its applications in computer vision| old_uid | 3898 |
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| title | The Fisher-Rao metric and its applications in computer vision |
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| start_date | 2008/01/24 |
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| schedule | 14h |
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| online | no |
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| location_info | couloir 55-65, salle 211 |
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| summary | Many computer vision algorithms involve measurements of distance. For
example, in a clustering algorithm it is of interest to measure the
distances between the different clusters. The measurement of distance is
made more complicated because the form of the data often depends on an
arbitrary choice of a coordinate system by the computer vision
practitioner. Under these circumstances it is necessary for the
measurements to be independent of the choice of coordinate system. This
requirement places a severe restriction on the choice of measurement.
If, in the above example, the clusters are modeled by probability
density functions, then a natural measurement of the distance between
two probability density functions is the Kullback-Leibler divergence,
which has the essential property that it is invariant under changes of
coordinate system. If the probability density functions belong to a
parameterised family of densities then the Kullback Leibler distance
defines a Riemannian metric on the parameter space. This metric is known
as the Fisher-Rao metric.
The Kullback-Leibler distance is widely used in computer vision, but
there have until now been very few applications of the Fisher-Rao
metric. It is shown how the Fisher-Rao metric is the basis of a new
approach to structure detection in which the parameter space for the
structures in question is sampled at a finite number of points and each
point is tested in turn to see if the presence of the corresponding
structure is supported by the measurements. The sample points are chosen
such that every point in the parameter space is near, under the
Fisher-Rao metric, to at least one sample point. The Fisher-Rao metric
is used to obtain an estimate of the number of sample points that are
required. The applications of this method to the detection of lines and
ellipses are described. |
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| oncancel | changement de lieu |
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| responsibles | Clady |
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