| Περίληψη: | The objective of this thesis is to explore the potentiality of several methods on 2D and 3D shape database related applications, such as segmentation, retrieval, clustering to name a few.
For the shape segmentation problem all methods describe the shape using contour information for the 2D or the volume for the 3D case, respectively. This kind of information is mainly represented using the notion of visibility as a head-start, moving towards into more sophisticated methods and implementations. Several algorithms are introduced which aim to explore if the (contour) volumetric information is adequately captured by visibility-based transformations and additionally to explore the limits of volumetric methods in this application.
Each shape is modeled by exploiting its visibility context which is proved to be an effective and perceptual compatible way of representation \cite{visibility}. Using the visibility context indirectly implies that the convex parts of each shape are captured, which are known to imitate the human's way of partitioning. Although all mentioned methods are graph-based and use the visibility graph as a starting point, then this graph is appropriately modified to meet the needs of the segmentation issue, by using constraints, spectral techniques, or diffusion-based transformations. Extended experimental measurements revealed the highly discriminative nature of these methods and their capability of yielding meaningful shape partitions. Moving one step further, a novel method combines the complementary information provided by the mesh surface and its volume. The additional usage of geodesic measurements leaded to better results.
Another issue that this thesis deals with is the 2D shape retrieval by using multidimensional descriptors originating from simple 1D sequences that represent a shape and usually describe it by means of its centroid-to-contour distance and the angle-sequence-along-contour measurements. Specifically, the phase space and the scale space representation is investigated modifying the initial 1D sequence to a set of vectors in a higher dimension. Experimental results on several databases, including an application on leaf images, demonstrated the superiority of the proposed high dimensional description over conventional ones, especially when using fusion methods.
Finally, 3D shape clustering and classification is revisited from the view of Non-Negative Least Squares NNLS coding technique. The objective is to point out that NNLS as a graph encoding technique provides an effective solution to the mentioned applications. Sparse coding with L2 graph is also adopted for the fusion of multilayer graphs. Experimental results validate the excellent performance of this framework.
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