http://leda.univ-lyon1.fr

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Note that all along this paper the optical densities are defined according to the DSS documentation as $d_{\rm c}=6553.4 \log(S_{\rm o} / S)$ , where $S_{\rm o}$ is the intensity of light transmission through an unexposed part of the plate and S is the transmitted intensity through the considered exposed part. We frequently use the term of pixel "intensity" for $d_{\rm c}$ instead of the proper term of pixel optical "density" which could lead to a confusion with the density in the sense of number of pixels per area unit.

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... $500 \times 500$ pixels

Except for the last row which is $500 \times 499$ .

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... $\log N(D>D_{\rm lim})=-3 \log D_{\rm lim}+ cst$

The completeness curve expressed in apparent magnitude m can be written similarly as: $\log N(m<m_{\rm lim})=0.6 m_{\rm lim} +cst$ . We will use this form in Sect. 5.4 when apparent magnitudes will be calibrated. It was used by Hubble (1934). A demonstration is given, e.g., by Zwicky (1957).

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... function

The choice of a sigmoid function is justified by the fact that we are looking for a bimodal answer. Note that this sigmoid function is not applied on inputs P_i which are not considered as neurones.

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