This paper describes a new approach for training generative adversarial networks (GAN) to understand the detailed 3D shape of objects. While GANs have been used in this domain previously, they are notoriously hard to train, especially for the complex joint data distribution over 3D objects of many categories and orientations. Our method extends previous work by employing the Wasserstein distance normalized with gradient penalization as a training objective. This enables improved generation from the joint object shape distribution. Our system can also reconstruct 3D shape from 2D images and perform shape completion from occluded 2.5D range scans. We achieve notable quantitative improvements in comparison to existing baselines
The pioneering work of Roberts @cite_19 and Marr @cite_18 exemplify early shape models composed of 3D geometric primitives with recognizable 2D properties. Similarly intuitive properties are still in common use, such as symmetric parts @cite_21 , skeletons @cite_0 and CAD wire-frames @cite_22 .
@cite_18 @cite_22 @cite_21 @cite_0 @cite_19
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In this paper, we present a two-level generative model for representing the images and surface depth maps of drapery and clothes. The upper level consists of a number of folds which will generate the high contrast (ridge) areas with a dictionary of shading primitives (for 2D images) and fold primitives (for 3D depth maps). These primitives are represented in parametric forms and are learned in a supervised learning phase using 3D surfaces of clothes acquired through photometric stereo. The lower level consists of the remaining flat areas which fill between the folds with a smoothness prior (Markov random field). We show that the classical ill-posed problem-shape from shading (SFS) can be much improved by this two-level model for its reduced dimensionality and incorporation of middle-level visual knowledge, i.e., the dictionary of primitives. Given an input image, we first infer the folds and compute a sketch graph using a sketch pursuit algorithm as in the primal sketch (, 2003). The 3D folds are estimated by parameter fitting using the fold dictionary and they form the "skeleton" of the drapery cloth surfaces. Then, the lower level is computed by conventional SFS method using the fold areas as boundary conditions. The two levels interact at the final stage by optimizing a joint Bayesian posterior probability on the depth map. We show a number of experiments which demonstrate more robust results in comparison with state-of-the-art work. In a broader scope, our representation can be viewed as a two-level inhomogeneous MRF model which is applicable to general shape-from-X problems. Our study is an attempt to revisit Marr's idea (Marr and Freeman, 1982) of computing the 2frac12D sketch from primal sketch. In a companion paper (Barbu and Zhu, 2005), we study shape from stereo based on a similar two-level generative sketch representation. A novel self-adaptive geometric primitive for functional geometric shape synthesis is presented. This novel geometric primitive, for CAD use, is specifically designed to reproduce geometric shapes with functional requirements, such as the aerodynamic and hydrodynamic ones, once the functional parameters are furnished. It produces a typical CAD representation of a functional profile: a set of Bezier curves. The proposed primitive follows a generate-and-test approach and takes advantage of the use of a properly designed artificial neural network (BNN). It combines the properties of a geometric primitive and the capability to manage the engineering knowledge in a specific field of application. The proposed evolutionary primitive is applied to a real engineering application: the automatic synthesis of airfoils. Some examples are simulated in order to test the effectiveness of the proposed method. The results obtained by an original prototypal software are presented and critically discussed. We propose models of 3D shape which may be viewed as deformable bodies composed of simulated elastic material. In contrast to traditional, purely geometric models of shape, deformable models are active—their shapes change in response to externally applied forces. We develop a deformable model for 3D shape which has a preference for axial symmetry. Symmetry is represented even though the model does not belong to a parametric shape family such as (generalized) cylinders. Rather, a symmetry-seeking property is designed into internal forces that constrain the deformations of the model. We develop a framework for 3D object reconstruction based on symmetry-seeking models. Instances of these models are formed from monocular image data through the action of external forces derived from the data. The forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2D silhouette of an object of interest. The effectiveness of our approach is demonstrated using natural images. We present an image-based approach to infer 3D structure parameters using a probabilistic "shape+structure" model. The 3D shape of an object class is represented by sets of contours from silhouette views simultaneously observed from multiple calibrated cameras, while structural features of interest on the object are denoted by a number of 3D locations. A prior density over the multiview shape and corresponding structure is constructed with a mixture of probabilistic principal components analyzers. Given a novel set of contours, we infer the unknown structure parameters from the new shape's Bayesian reconstruction. Model matching and parameter inference are done entirely in the image domain and require no explicit 3D construction. Our shape model enables accurate estimation of structure despite segmentation errors or missing views in the input silhouettes, and it works even with only a single input view. Using a training set of thousands of pedestrian images generated from a synthetic model, we can accurately infer the 3D locations of 19 joints on the body based on observed silhouette contours from real images.