Affordance is a feature of an object or environment that implies how to interact with it. Based on affordance theory, humans are said to perceive invariant structures for cognizing the object/environment for generating behaviors. In this paper, the authors present a method to extract invariant structures of objects from visual raw images, based on object manipulation experiences using a humanoid robot. The method consists of two training phases. The first phase utilizes Recurrent Neural Network with Parametric Bias (RNNPB) to self-organize dynamical object features extracted during active sensing with objects. The second phase trains a hierarchical neural network attached to RNNPB for associating object images and robot motions with self-organized object features. Analysis of the model has uncovered static objects features that are closely related to dynamic object motions, such as round or stable.