In this work we investigate techniques for embedding domain-specific spatial invariances into highly-constrained neural networks. This information is used to drastically reduce the number of weights which have to be determined during the learning phase, thus allowing us to apply artificial neural networks to problems characterized by a relatively small number of available examples. As an application of the proposed methodology, we study the problem of optical inspection of machined parts. More specifically, we have characterized the performance of a network created according to this strategy, which accepts images of parts under inspection at its input and issues a flag at its output which states whether the part is defective. The results obtained so far show that the proposed methodology provides a potentially relevant approach for the quality control of industrial parts, as it offers both accuracy and short software development time, when compared with a classifier implemented using a standard approach.