Extracting Parts of 2d Shapes Using Local and Global Interactions Simultaneously

Abstract

Perception research provides strong evidence in favor of part based representation of shapes in human visual system. Despite considerable differences among different theories in terms of how part boundaries are found, there is substantial agreement on that the process depends on many local and global geometric factors. This poses an important challenge from the computational point of view. In the first part of the chapter, I present a novel decomposition method by taking both local and global interactions within the shape domain into account. At the top of the partitioning hierarchy, the shape gets split into two parts capturing, respectively, the gross structure and the peripheral structure. The gross structure may be conceived as the least deformable part of the shape which remains stable under visual transformations. The peripheral structure includes limbs, protrusions, and boundary texture. Such a separation is in accord with the behavior of the artists who start with a gross shape and enrich it with details. The method is particularly interesting from the computational point of view as it does not resort to any geometric notions (e.g. curvature, convexity) explicitly. In the second part of the chapter, I relate the new method to PDE based shape representation schemes.

On the Usefulness of the Vector Field Singular Points Shapes for Classification

“…In recent years, the VF applications to Image Processing and Analysis [5,6] as well as in computer vision and machine learning (ML) are gaining popularity [7][8][9][10][11]. Ma and Wang [12] used VFs on Manifolds to measure the correlations between VF trajectories.…”

“…The authors in [8] used the Hamilton-Jacobi equation to generate a vector flow that detects the skeletons of image objects. Object skeletons are also extracted in [9] where the authors built a field that captures region and boundary interaction among shape points. The field is generated by minimizing an energy functional.…”

Análise de formas usando wavelets em grafos

“…Ainda, a literatura reporta uma representação de formas por grafos, que estabelece relações entre as partes resultantes de um esquema de decomposição de formas baseado na operação morfológica abertura, uma abordagem que se mostrou robusta a transformações rígidas, ruído, deformação e oclusão (Kim et al, 2004). Outros esquemas de decomposição de formas por partes são propostos por Zeng et al (2008), Mi et al (2009, Luyuan et al (2010) e Tari (2011).…”