3D shape models are naturally parameterized using vertices and faces, i.e., composed of polygons forming a surface. However, current 3D learning paradigms for predictive and generative tasks using convolutional neural networks focus on a voxelized representation of the object. Lifting convolution operators from the traditional 2D to 3D results in high computational overhead with little additional benefit as most of the geometry information is contained on the surface boundary. Here we study the problem of directly generating the 3D shape surface of rigid and non-rigid shapes using deep convolutional neural networks. We develop a procedure to create consistent `geometry images' representing the shape surface of a category of 3D objects. We then use this consistent representation for category-specific shape surface generation from a parametric representation or an image by developing novel extensions of deep residual networks for the task of geometry image generation. Our experiments indicate that our network learns a meaningful representation of shape surfaces allowing it to interpolate between shape orientations and poses, invent new shape surfaces and reconstruct 3D shape surfaces from previously unseen images. Our code is available at https://github.com/sinhayan/surfnet.

We propose DeepHand to estimate the 3D pose of a hand using depth data from commercial 3D sensors. We discriminatively train convolutional neural networks to output a low dimensional activation feature given a depth map. This activation feature vector is representative of the global or local joint angle parameters of a hand pose. We efficiently identify 'spatial' nearest neighbors to the activation feature, from a database of features corresponding to synthetic depth maps, and store some 'temporal' neighbors from previous frames. Our matrix completion algorithm uses these 'spatio-temporal' activation features and the corresponding known pose parameter values to estimate the unknown pose parameters of the input feature vector. Our database of activation features supplements large viewpoint coverage and our hierarchical estimation of pose parameters is robust to occlusions. We show that our approach compares favorably to state-of-the-art methods while achieving real time performance (≈ 32 FPS) on a standard computer.

Collaborative filtering is a popular technique to infer users' preferences on new content based on the collective information of all users preferences. Recommender systems then use this information to make personalized suggestions to users. When users accept these recommendations it creates a feedback loop in the recommender system, and these loops iteratively influence the collaborative filtering algorithm's predictions over time. We investigate whether it is possible to identify items affected by these feedback loops. We state sufficient assumptions to deconvolve the feedback loops while keeping the inverse solution tractable. We furthermore develop a metric to unravel the recommender system's influence on the entire user-item rating matrix. We use this metric on synthetic and real-world datasets to (1) identify the extent to which the recommender system affects the final rating matrix, (2) rank frequently recommended items, and (3) distinguish whether a user's rated item was recommended or an intrinsic preference. Our results indicate that it is possible to recover the ratings matrix of intrinsic user preferences using a single snapshot of the ratings matrix without any temporal information.

Collaborative filtering aims to predict unknown user ratings in a recommender system by collectively assessing known user preferences. In this paper, we first draw analogies between collaborative filtering and the pose estimation problem. Specifically, we recast the hand pose estimation problem as the cold-start problem for a new user with unknown item ratings in a recommender system. Inspired by fast and accurate matrix factorization techniques for collaborative filtering, we develop a real-time algorithm for estimating the hand pose from RGB-D data of a commercial depth camera. First, we efficiently identify nearest neighbors using local shape descriptors in the RGB-D domain from a library of hand poses with known pose parameter values. We then use this information to evaluate the unknown pose parameters using a joint matrix factorization and completion (JMFC) approach. Our quantitative and qualitative results suggest that our approach is robust to variation in hand configurations while achieving real time performance (≈ 29 FPS) on a standard computer.

Abstract We introduce novel multi‐scale kernels using the random walk framework and derive corresponding embeddings and pairwise distances. The fractional moments of the rate of continuous time random walk (equivalently diffusion rate) are used to discover higher order kernels (or similarities) between pair of points. The formulated kernels are isometry, scale and tessellation invariant, can be made globally or locally shape aware and are insensitive to partial objects and noise based on the moment and influence parameters. In addition, the corresponding kernel distances and embeddings are convergent and efficiently computable. We introduce dual Green's mean signatures based on the kernels and discuss the applicability of the multi‐scale distance and embedding. Collectively, we present a unified view of popular embeddings and distance metrics while recovering intuitive probabilistic interpretations on discrete surface meshes.