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Specificity

Specificity of an appearance model defines its ability to generate realistic, new examples of the modelled class. A model that correctly describes the variation within an object class should be able to produce new examples of the class that would appear realistic compared to the original training set used to create the model. Conversely, a degraded model would be unable to articulate the main modes of object appearance and would only produce new examples disparate from the original training set. This definition is used to practically measure Specificity. Specificaly, given { $I_{j}:j=1..m\}$ as a large set of synthetic example images sampled from the model and having the same distribution, Specificity $S$ is defined as the average distance between each of the synthetic examples and it closest neighbour in the original training set:

$$S=\frac{1}{m}\begin{array}{c} m\\ \sum\\ j=1\end{array}min_{i}\,\vert I_{i}-I_{j}\vert.$$ (5)

where $I_{i}$ is the ith training image, $\vert\cdot\vert$ describes the distance between two images and SD is the standard deviation. Equivalently, the standard error in the measurement $\sigma_{S}$ is thus:

$$\mathbf{\sigma_{S}}=\frac{SD(min_{\, j}\,\vert I_{i}-I_{j}\vert)}{\sqrt{m-1}}.$$ (6)

Generally, for a good model the Specificity is low as the images generated by the model are similar (low distance) to original training examples. Conversely, as a model degrades the generated examples get further away from the training examples increasing the distance and consequently Specificity.