Konstantinos A. Raftopoulos

The Global-Local transformation for noise resistant shape representation

The use of smoothing kernels in boundary curvature calculations, affects both object shape and the localization of edges. The Global-Local transformation (GLT), addresses this issue by providing a framework for shape representation, such that local and global features are simultaneously represented, even in noisy shapes, without the need for smoothing. By means of two-dimensional manifolds (surfaces), embedded into the unit cube, useful properties of the transform space are explored. The expressive power of the GLT is demonstrated by means of a global descriptor, called View Area Representation (VAR). VAR is an intuitive and physically meaningful shape descriptor which is robust to noise, captures curvature and leads to the introduction of novel and hybrid (global/local) shape features. A series of proofs is presented that link VAR and its derivatives to those shape features, providing the basis for shape representation involving global and local features in the presence of noise. The theoretical results are shown to be effective in matching noisy shapes by improving the recognition capability, of Local Area Integral Invariant (LAII), a relevant state of the art method of low complexity. A combination of GLT with VAR is used to define a new matching method certain advantages of which, in recognition ability and execution time, renders the intuitive properties of VAR significant for complexity reduction.

Visual pathways for shape abstraction

The Medial Axis Transform (MAT) (or skeleton transform) is one of the most studied shape representation techniques with established advantages for general 2D shape recognition. Embedding local boundary information in the skeleton, in particular, has been shown to improve 2D shape recognition capability to state of the art levels. In this paper we present a visual pathway for extracting an analogous to the MAT skeleton abstraction of shape that also contains local boundary curvature information. We refer to this structure with the term curvature-skeleton. The proposed architecture is inspired by the biological findings regarding the cortical neurons of the visual cortex and their special purpose Receptive Fields (RFs). Points of high curvature are initially identified and subsequently combined by means of a visual pathway that achieves an analogous to the MAT abstraction of shape but also embeds in the skeleton local curvature information of the shapes boundary. We present experimental results illustrating that such an abstraction can improve the recognition capability of multi layered neural network classifiers.

The global-local transformation for invariant shape representation

We present the GlobalLocal (GL) transformation for closed planar curves. With this new transformation we can represent shape by means of two dimensional manifolds (surfaces) embedded into the unit cube. We explore some useful properties of the transform space and we demonstrate its high expressive power. We justify the high potential of the resulting invariant shape representations in object recognition by providing experimental results using the Kimia silhouette database.

Global Vertices and the Noising Paradox.

A theoretical and experimental analysis related to the effect of noise in the task of vertex identification in unknown shapes is presented. Shapes are seen as real functions of their closed boundary. An alternative global perspective of curvature is examined providing insight into the process of noise-enabled vertex localization. The analysis reveals that noise facilitates in the localization of certain vertices. The concept of noising is thus considered and a relevant global method for localizing Global Vertices is investigated in relation to local methods under the presence of increasing noise. Theoretical analysis reveals that induced noise can indeed help localizing certain vertices if combined with global descriptors. Experiments with noise and a comparison to localized methods validate the theoretical results.

Incremental Noising and its Fractal Behavior.

A theoretical and experimental analysis related to the effect of noise in the task of vertex identification in unknown shapes is presented. Shapes are seen as real functions of their closed boundary. An alternative global perspective of curvature is examined providing insight into the process of noise-enabled vertex localization. The analysis reveals that noise facilitates in the localization of certain vertices. The concept of noising is thus considered and a relevant global method for localizing Global Vertices is investigated in relation to local methods under the presence of increasing noise. Theoretical analysis reveals that induced noise can indeed help localizing certain vertices if combined with global descriptors. Experiments with noise and a comparison to localized methods validate the theoretical results.