Vladimir (Vova) Kim will present his preFPO on Wednesday October 17 at 4PM in room 402. The members of his committee are: Tom Funkhouser, advisor; Szymon Rusinkiewicz and Wilmot Li (Adobe), readers; Adam Finkelstein and David Dobkin, nonreaders. Everyone is invited to attend his talk. His abstract follows below. ---------------- TITLE: Establishing Correspondences in Collections of Diverse 3D Shapes ABSTRACT: Large repositories of 3D models have become available in recent years. These repositories include scans of everyday objects and outdoor environments, CAD models created by engineers, and computer graphics models created by artists and casual users. Establishing corresponding points allows reasoning about functional and semantic similarities between models in a collection, and opens space for many applications like transferring properties, classifying and segmenting new data and exploring 3D collections. Scale of these collections necessitates development of automatic algorithms for computing such correspondences. Much of the previous work concentrates on matching pairs of shapes with limited geometric diversity. Our work addresses several challenges related to finding and representing correspondences in large collections where models exhibit substantial geometric variations including non-uniform deformations, or have different multiplicities, complexities and styles of parts. We develop algorithms that (i) handle such variations robustly, (ii) represent semantic ambiguity due to diversity of the data, and (iii) efficiently process large collections. First, to address the challenge of matching models with non-uniform deformations, we propose a fully automatic pipeline for finding an intrinsic map between two non-isometric, genus zero surfaces. Our approach is based on the observation that efficient methods exist to search for nearly isometric maps, but no single solution found with these methods provides low-distortion everywhere for pairs of surfaces differing by large deformations. To address this problem, we suggest using a weighted combination of these maps to produce a “blended map.” This approach enables algorithms that leverage efficient search procedures, yet can provide the flexibility to handle large deformations. During experiments with these methods, we find that our algorithm produces blended maps that align semantic features better than alternative approaches over a variety of data sets. Second, we propose an automatic analysis method for computing similarity relationships between points on 3D shapes across a relatively homogeneous and small collection (order of hundreds of models). Our method is robust to general geometric variations, including non-uniform deformations, and partial similarity (e.g. due to different part multiplicities or styles). We encode the inherent ambiguity in similarity relationships using fuzzy point correspondences and propose a robust and efficient computational framework that estimates fuzzy correspondences using only a sparse set of pairwise model alignments. We evaluate our analysis method on a range of correspondence benchmarks and report substantial improvements in both speed and accuracy over existing alternatives. Finally, we address the challenge of establishing correspondences in large and diverse collections (order of tens of thousands of models) efficiently and robustly. We concentrate on models that can be represented as part-wise assemblies, and our goal is to compute consistent segmentation of models along with aligning transformations between all parts, (i.e. providing a representation that can directly define point-to-point or fuzzy correspondences). We propose a method that relies on fitting a deformable template that explicitly models class-specific geometric variations. The key contribution of our approach is in iterative learning of these variations from large collections with unreliable and noisy labels, (as they appear in public repositories, such as Google Warehouse). Resulting deformable template and consistent segmentations can be used in several applications including exploring collections of shapes, synthesizing new shapes by part-wise assembly and interpreting (classifying, segmenting and reconstructing) noisy 3D scans.