The medial axis transform has applications in numerous fields including visualization, computer graphics, and computer vision. Unfortunately, traditional medial axis transformations are usually brittle in the presence of outliers, perturbations and/o
r noise along the boundary of objects. To overcome this limitation, we introduce a new formulation of the medial axis transform which is naturally robust in the presence of these artifacts. Unlike previous work which has approached the medial axis from a computational geometry angle, we consider it from a numerical optimization perspective. In this work, we follow the definition of the medial axis transform as the set of maximally inscribed spheres. We show how this definition can be formulated as a least squares relaxation where the transform is obtained by minimizing a continuous optimization problem. The proposed approach is inherently parallelizable by performing independant optimization of each sphere using Gauss-Newton, and its least-squares form allows it to be significantly more robust compared to traditional computational geometry approaches. Extensive experiments on 2D and 3D objects demonstrate that our method provides superior results to the state of the art on both synthetic and real-data.
We propose ViewAL, a novel active learning strategy for semantic segmentation that exploits viewpoint consistency in multi-view datasets. Our core idea is that inconsistencies in model predictions across viewpoints provide a very reliable measure of
uncertainty and encourage the model to perform well irrespective of the viewpoint under which objects are observed. To incorporate this uncertainty measure, we introduce a new viewpoint entropy formulation, which is the basis of our active learning strategy. In addition, we propose uncertainty computations on a superpixel level, which exploits inherently localized signal in the segmentation task, directly lowering the annotation costs. This combination of viewpoint entropy and the use of superpixels allows to efficiently select samples that are highly informative for improving the network. We demonstrate that our proposed active learning strategy not only yields the best-performing models for the same amount of required labeled data, but also significantly reduces labeling effort. For instance, our method achieves 95% of maximum achievable network performance using only 7%, 17%, and 24% labeled data on SceneNet-RGBD, ScanNet, and Matterport3D, respectively. On these datasets, the best state-of-the-art method achieves the same performance with 14%, 27% and 33% labeled data. Finally, we demonstrate that labeling using superpixels yields the same quality of ground-truth compared to labeling whole images, but requires 25% less time.
We investigate the problem of learning category-specific 3D shape reconstruction from a variable number of RGB views of previously unobserved object instances. Most approaches for multiview shape reconstruction operate on sparse shape representations
, or assume a fixed number of views. We present a method that can estimate dense 3D shape, and aggregate shape across multiple and varying number of input views. Given a single input view of an object instance, we propose a representation that encodes the dense shape of the visible object surface as well as the surface behind line of sight occluded by the visible surface. When multiple input views are available, the shape representation is designed to be aggregated into a single 3D shape using an inexpensive union operation. We train a 2D CNN to learn to predict this representation from a variable number of views (1 or more). We further aggregate multiview information by using permutation equivariant layers that promote order-agnostic view information exchange at the feature level. Experiments show that our approach is able to produce dense 3D reconstructions of objects that improve in quality as more views are added.
