Representing Non-Rigid Objects with Neural Networks

Background

Self-organising maps, by means of a competitive learning, make an adaptation of the reference vectors of the neurons, as well as, of the interconnection network among them; obtaining a mapping that tries to preserve the topology of an input space. Besides, they are able of a continuous re-adaptation process even if new patterns are entered, with no need to reset the learning.

These capacities have been used for the representation of objects (Flórez, García, García & Hernández, 2001)] (Figure 1) and their motion (Flórez, García, García & Hernández, 2002) by means of the Growing Neural Gas (GNG) (Fritzke, 1995) that has a learning process more flexible than other self-organising models, like Kohonen maps (Kohonen, 2001).

Figure 1

These two applications, representation of objects and their motion, have in many cases temporal constraints, reason why it is interesting the acceleration of the learning process. In computer vision applications the condition of finalization for the GNG algorithm is commonly defined by the insertion of a predefined number of neurons. The election of this number can affect the quality of the adaptation, measured as the topology preservation of the input space (Martinetz & Schulten, 1994).

In this work GNG has been used to represent two-dimensional objects shape deformations in sequences of images, obtaining a topology representing graph that can be used for multiple tasks like representation, classification or tracking. When deformations in objects topology are small and gradual between consecutive frames in a sequence of images, we can use previous maps information to place the neurons without reset the learning process. Using this feature of GNG we achieve a high acceleration of the representation process.

One way of selecting points of interest in 2D shapes is to use a topographic mapping where a low dimensional map is fitted to the high dimensional manifold of the shape, whilst preserving the topographic structure of the data. A common way to achieve this is by using self-organising neural networks where input patterns are projected onto a network of neural units such that similar patterns are projected onto units adjacent in the network and vice versa. As a result of this mapping a representation of the input patterns is achieved that in post-processing stages allows one to exploit the similarity relations of the input patterns. Such models have been successfully used in applications such as speech processing (Kohonen, 2001), robotics (Ritter & Schulten, 1986), (Martinez, Ritter, & Schulten, 1990) and image processing (Nasrabati & Feng, 1988). However, most common approaches are not able to provide good neighborhood and topology preservation if the logical structure of the input pattern is not known a priori. In fact, the most common approaches specify in advance the number of neurons in the network and a graph that represents topological relationships between them, for example, a two-dimensional grid, and seek the best match to the given input pattern manifold. When this is not the case the networks fail to provide good topology preserving as for example in the case of Kohonen’s algorithm.