Medial descriptors for 3D shape segmentation, reconstruction, and analysis
Three dimensional shape analysis is an important component in several applications such as path planning, shape matching, or shape segmentation. Most methods in this area use, as input, a representation of the shape boundary or surface. However, such representations present several limitations when we are interested to reason about global shape properties.
An alternative shape representation was proposed in 1967 by Harry Blum, and is known under the names of medial representation, medial axis, or skeleton. Medial representation describe shapes in terms of their symmetry set, and allow a natural way to reason about both local and global shape properties. Such representations have been used in many 2D shape analysis problems. However, their extension to large and complex 3D (polygonal) shapes is far from trivial and poses several conceptual and computational challenges.
This thesis addresses several of the above challenges for computing 3D shape skeletons and next using these skeletons to support a range of shape analysis applications. We present a new robust, fast, and accurate method to extract multiscale medial representations from large polygonal models, and also explore the relationship between 3D skeletons and 2D skeletons of projections of the same shape.
Next, we show how we can enrich and adapt our medial representations with additional information, such as the relationships between medial points and surface points, to support a wide range of applications, including skeleton reconstruction, shape reconstruction, edge detection, and shape simplification and segmentation. We demonstrate our methods on a large collection of real-world 3D shapes.