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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/or 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 artefacts. 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 independent 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. [ABSTRACT FROM AUTHOR]

Augmented reality (AR) for smartphones has matured from a technology for earlier adopters, available only on select high-end phones, to one that is truly available to the general public. One of the key breakthroughs has been in low-compute methods for six degree of freedom (6DoF) tracking on phones using only the existing hardware (camera and inertial sensors). 6DoF tracking is the cornerstone of smartphone AR allowing virtual content to be precisely locked on top of the real world. However, to really give users the impression of believable AR, one requires mobile depth. Without depth, even simple effects such as a virtual object being correctly occluded by the real-world is impossible. However, requiring a mobile depth sensor would severely restrict the access to such features. In this article, we provide a novel pipeline for mobile depth that supports a wide array of mobile phones, and uses only the existing monocular color sensor. Through several technical contributions, we provide the ability to compute low latency dense depth maps using only a single CPU core of a wide range of (medium-high) mobile phones. We demonstrate the capabilities of our approach on high-level AR applications including real-time navigation and shopping. [ABSTRACT FROM AUTHOR]