3D shape analysis based on feature curve networks

For high-level analysis of 3D shapes, we require an abstract representation of geometric data. Typically, this is achieved by developing descriptors on a local pointwise level or globally on the entire shape. Point based descriptors can be very sensitive to local changes of the shape (e.g. noise). In contrast, global descriptors tend to be too coarse, depending on the analysist ask. Hence, a desirable representation encodes different levels of abstraction, which range from a geometric point based description over intermediate topological information to high level structure and is flexible enough to be applied in various shape analysis tasks. In this thesis we show that networks consisting of feature curves are able to capture this information at various levels, and are therefore a well-suited representation for the challenging task of analysis of 3D shapes. Feature curves trace out salient creases and crests of 3D geometric data. Their computation has been studied intensively in the past and various directions such as patch layouts, slippage-based techniques, or crest line tracing have been established. They provide an abstract representation of salient parts of the geometry and contain topological and global structural information about the shape as well as geometric details. E.g., the geometric information can be exploited in low-level geometry processing tasks such as remeshing or smoothing, where geometric entities should align with surface features to obtain high quality output. In contrast, the more high-level structural information contained in the feature curve network provides important cues, which can be beneficial for the analysis of the geometric data. However, automatically computed feature curve networks on raw data can have various defects such as noise, fragmentation, or missing data. To make the feature curves applicable to downstream applications, we require a set of meaningful feature curves with low fragmentation and without misclassified feature curves (e.g. due to noise). First attempts to obtain a more relevant set of curves from the automatically computed feature curve networks resort to local solutions such as smoothing, filtering, or (curvature based) thre sholding of the curves. This however, also removes small-scale or weak feature curves from the network which might describe important details. In this thesis, we combine local (feature curve strength, length, parallelism, etc.) and global (density and symmetry) saliency measures to extract meaningful feature curve networks from raw potentially noisy input networks. While the pure geometric information from these meaningful feature curve networks can beused directly for downstream applications, the more high-level structural information is not aseasily accessible. However, for the analysis of the geometric data, more abstract information is required. Hence, in this thesis we present techniques to obtain structural information from symmetry, reoccurrence, and curve template membership, which can be exploited in shapeanalysis applications. Finally, we present several applications, which benefit from the use of meaningful feature curve networks. These range from low-level geometry processing (remeshing, smoothing) to high-level shape analysis (functional maps)