A neural network-based approach is proposed for invariant recognition of two-dimensional objects. The industrial tools to be recognized have one degree of freedom, the dynamic range of their shapes leads the feature vector not uniquely defined even for a single object. The Fourier descriptors of objects boundary are taken as the features being invariant to translation, rotation and scale changes. A multilayer feedforward neural net with two hidden layer classifiers is utilized. The experimental studies involving four sorts of mechanical tools are carried out. The performance is compared to a nearest neighbor rule. It is shown that the approach is robust to not only noisy but also varying feature vector, and the neural network can recognize some untrained objects.