Structural analysis of patterns and shapes using hierarchical vibrations

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The structural representation of shapes and pattern spaces is crucial in computer vision and image analysis, particularly for classifying and segmenting images and for multi-modal data fusion. Image segmentation poses challenges as an ill-posed, inverse problem with multiple potential solutions that may not depend continuously on the data. This complexity arises from the noise and incompleteness of images, along with significant variations in texture and shape due to articulation, occlusion, and changes in perspective and lighting. A common top-down approach involves creating a manually labeled training set to learn shape and texture variations, but probabilistic graphical models can require extensive training to distinguish valid from invalid non-linear variations, which is not always feasible. To address this, a structural decomposition approach is introduced for model-based analysis of visual shapes and patterns in images without training. The finite element shape decomposition principle has been adapted to describe and match deformable visual objects at various levels of abstraction. By employing knowledge-based a-priori constraints and general heuristics, the model generates anatomically plausible shapes. This hierarchical shape decomposition provides a comprehensive characterization of fitted shapes, demonstrating effectiveness in representing diverse object categories and allowing for interpolation between exemplar conf