This thesis describes a novel and generic scheme, the trace model, for building invariant signal representations. The scheme is derived from first principles, leading to a "white box" representation that performs on par with or outperforms the state of the art in the respective domains. The construction of the trace model is based on the preservation of topology under homeomorphic transformations. Homeomorphisms comprise a large class of transformations and thus the trace model can fundamentally capture a wide range of common perturbations of sensor signals. Two applications of the trace model are described to demonstrate the range of its applicability. The first application addresses the representation and detection of structured patterns, i.e. patterns that follow a known pattern grammar, using the example of two-dimensional bar codes. The second application generalizes to the wider problem of modeling image patches under spatial perturbations and furthermore describes an extension of the patch model to the problem of incremental visual tracking. Implementations for all applications are described and it is shown that they all map to the well-known problem of finding paths in an attributed graph.
The trace model is not limited to patch modeling or visual tracking and it is specifically designed so that it may be easily transferred into other applications such as object recognition or domains outside image processing and computer vision.