Abstracting complex 3D shapes with parsimonious part-based representations has been a long standing goal in computer vision. This paper presents a learning-based solution to this problem which goes beyond the traditional 3D cuboid representation by exploiting superquadrics as atomic elements. We demonstrate that superquadrics lead to more expressive 3D scene parses while being easier to learn than 3D cuboid representations. Moreover, we provide an analytical solution to the Chamfer loss which avoids the need for computational expensive reinforcement learning or iterative prediction. Our model learns to parse 3D objects into consistent superquadric representations without supervision. Results on various ShapeNet categories as well as the SURREAL human body dataset demonstrate the flexibility of our model in capturing fine details and complex poses that could not have been modelled using cuboids.
Superquadrics are a parametric family of surfaces that can be used to describe cubes, cylinders, spheres, octahedra, ellipsoids @cite_28 . In contrast to geons @cite_44 , superquadric surfaces can be described using a fairly simple parameterization. In contrast to generalized cylinders @cite_44 , superquadrics are able to represent a larger variety of shapes. See fig:superquadrics for an illustration of the shape space.
@cite_28 @cite_44
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We present a new approach to the problem of modeling smoothly deformable shapes with convex polyhedral bounds. Our hyperquadric modeling primitives, which include superquadrics as a special case, can be viewed as hyperplanar slices of deformed hyperspheres. As the original hypersphere is deformed to its bounding hypercube, the slices undergo corresponding smooth deformations to convex polytopes. The possible shape classes include arbitrary convex polygons and polyhedra, as well as taperings and distortions that are not naturally included within the conventional superquadric framework. By generalizing Blinn's “blobby” approach to modeling complex objects, we construct single equations for nonconvex, composite shapes starting with our basic convex primitives. Hyperquadrics are of potential interest for the generation of synthetic images, for automated image interpretation and for psychological models of geometric shape representation, manipulation, and perception. A physically-based approach is presented to fitting complex 3D shapes using a novel class of dynamic models. These models can deform both locally and globally. The authors formulate deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline. The local global representational power of a deformable superquadric simultaneously satisfies the conflicting requirements of shape reconstruction and shape recognition. The model's six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models. Model fitting experiments involving 2D monocular image data and 3D range data are reported. > Abstracting complex 3D shapes with parsimonious part-based representations has been a long standing goal in computer vision. This paper presents a learning-based solution to this problem which goes beyond the traditional 3D cuboid representation by exploiting superquadrics as atomic elements. We demonstrate that superquadrics lead to more expressive 3D scene parses while being easier to learn than 3D cuboid representations. Moreover, we provide an analytical solution to the Chamfer loss which avoids the need for computational expensive reinforcement learning or iterative prediction. Our model learns to parse 3D objects into consistent superquadric representations without supervision. Results on various ShapeNet categories as well as the SURREAL human body dataset demonstrate the flexibility of our model in capturing fine details and complex poses that could not have been modelled using cuboids. Generalized cylinder (GC) is a class of parametric shapes that is very flexible and capable of modeling many different types of real-world objects, and have subsequently been the focus of considerable research in the vision community. Most of the related works proposed previously have dealt with the recovery of 3D shape description of objects based on the GC representation from one or more 2D image data. Different from the objective of the previous works, in this paper, we will propose a new approach to obtain a GC-based shape description of 3D objects. The proposed approach of deriving the GC axis is a further extension of the potential-based skeletonization approach presented in (IEEE Trans. Pattern Anal. Mach. Intell. 22(11) (2000) 1241). Simulation results demonstrate that the derived GC representation will yield better approximation of object shape than that based on simpler subclasses of GC since there is, in principle, no restriction on the topology of the GC axis and the shape of the cross-sections.