We present a deformation-driven approach to topology-varying 3D shape correspondence. In this paradigm, the best correspondence between two shapes is the one that results in a minimal-energy, possibly topology-varying, deformation that transforms one shape to conform to the other while respecting the correspondence. Our deformation model, called GeoTopo transform , allows both geometric and topological operations such as part split, duplication, and merging, leading to fine-grained and piecewise continuous correspondence results. The key ingredient of our correspondence scheme is a deformation energy that penalizes geometric distortion, encourages structure preservation, and simultaneously allows topology changes. This is accomplished by connecting shape parts using structural rods , which behave similarly to virtual springs but simultaneously allow the encoding of energies arising from geometric, structural, and topological shape variations. Driven by the combined deformation energy, an optimal shape correspondence is obtained via a pruned beam search. We demonstrate our deformation-driven correspondence scheme on extensive sets of man-made models with rich geometric and topological variation and compare the results to state-of-the-art approaches.

Abstract In the field of computer vision, the introduction of a low‐level preprocessing step to oversegment images into superpixels – relatively small regions whose boundaries agree with those of the semantic entities in the scene – has enabled advances in segmentation by reducing the number of elements to be labeled from hundreds of thousands, or millions, to a just few hundred. While some recent works in mesh processing have used an analogous oversegmentation, they were not intended to be general and have relied on graph cut techniques that do not scale to current mesh sizes. Here, we present an iterative superfacet algorithm and introduce adaptations of undersegmentation error and compactness, which are well‐motivated and principled metrics from the vision community. We demonstrate that our approach produces results comparable to those of the normalized cuts algorithm when evaluated on the Princeton Segmentation Benchmark, while requiring orders of magnitude less time and memory and easily scaling to, and enabling the processing of, much larger meshes.

We present a sparse analytic representation for spherical functions, including those expressed in a Spherical Harmonic (SH) expansion, that is amenable to fast and accurate rotation on the GPU. Exploiting the fact that each band- l SH basis function can be expressed as a weighted sum of 2 l + 1 rotated band- l Zonal Harmonic (ZH) lobes, we develop a factorization that significantly reduces this number. We investigate approaches for promoting sparsity in the change-of-basis matrix, and also introduce lobe sharing to reduce the total number of unique lobe directions used for an order- N expansion from N 2 to 2 N -1. Our representation does not introduce approximation error, is suitable for any type of spherical function (e.g., lighting or transfer), and requires no offline fitting procedure; only a (sparse) matrix multiplication is required to map to/from SH. We provide code for our rotation algorithms, and apply them to several real-time rendering applications.

Abstract Shape segmentations designed for different applications show significant variation in the composition of their parts. In this paper, we introduce the segmentation and labeling of shape based on the simultaneous optimization of multiple heterogenous objectives that capture application‐specific segmentation criteria. We present a number of efficient objective functions that capture useful shape adjectives (compact, flat, narrow, perpendicular, etc.) Segmentation descriptions within our framework combine multiple such objective functions with optional labels to define each part. The optimization problem is simplified by proposing weighted Voronoi partitioning as a compact and continuous parametrization of spatially embedded shape segmentations. Separation of spatially close but geodesically distant parts is made possible using multi‐dimensional scaling prior to Voronoi partitioning. Optimization begins with an initial segmentation found using the centroids of a k‐means clustering of surface elements. This partition is automatically labeled to optimize heterogeneous part objectives and the Voronoi centers and their weights optimized using Generalized Pattern Search. We illustrate our framework using several diverse segmentation applications: consistent segmentations with semantic labels, bounding volume hierarchies for path tracing, and automatic rig and clothing transfer between animation characters.

This article presents a method for real-time line drawing of deforming objects. Object-space line drawing algorithms for many types of curves, including suggestive contours, highlights, ridges, and valleys, rely on surface curvature and curvature derivatives. Unfortunately, these curvatures and their derivatives cannot be computed in real-time for animated, deforming objects. In a preprocessing step, our method learns the mapping from a low-dimensional set of animation parameters (e.g., joint angles) to surface curvatures for a deforming 3D mesh. The learned model can then accurately and efficiently predict curvatures and their derivatives, enabling real-time object-space rendering of suggestive contours and other such curves. This represents an order-of-magnitude speedup over the fastest existing algorithm capable of estimating curvatures and their derivatives accurately enough for many different types of line drawings. The learned model can generalize to novel animation sequences and is also very compact, typically requiring a few megabytes of storage at runtime. We demonstrate our method for various types of animated objects, including skeleton-based characters, cloth simulation, and blend-shape facial animation, using a variety of nonphotorealistic rendering styles. An important component of our system is the use of dimensionality reduction for differential mesh data. We show that Independent Component Analysis (ICA) yields localized basis functions, and gives superior generalization performance to that of Principal Component Analysis (PCA).