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Specificity

The Specificity of a generative appearance model measures the extent to which images generated by the model are similar to those in the training set. A specific model should generate a distribution of images that overlaps the training distribution as completely as possible. If we take a synthetic image set such as that defined previously, $\{I_{\alpha}:\alpha=1,\ldots m\}$, each synthetic image should be close to an image in the training set. We define the Specificity, $S$, and its standard error, $\sigma_{S}$, as follows:

$$S=\frac{1}{m} \sum\limits_{\alpha=1}^{m}{\bf min}_{i}\vert I_{i}-I_{\alpha}\vert,$$ (5)

$$\mathbf{\sigma_{S}}=\frac{SD({\bf min}_{i}\vert I_{i}-I_{\alpha}\vert)}{\sqrt{m-1}}.$$ (6)

That is, Specificity is the average distance from each synthetic image to the nearest training image. A good model exhibits a low value of Specificity, indicating that it generates synthetic images, all of which are similar to those in the training set.