We introduce a differentiable moving particle representation based on the multi-level partition of unity (MPU) to represent dynamic implicit geometries. At the core of our representation are two groups of particles, n...
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We introduce a differentiable moving particle representation based on the multi-level partition of unity (MPU) to represent dynamic implicit geometries. At the core of our representation are two groups of particles, named feature particles and sample particles, which can move in space and produce dynamic surfaces according to external velocity fields or optimization gradients. These two particle groups iteratively guide and correct each other by alternating their roles as inputs and outputs. Each feature particle carries a set of coefficients for a local quadratic patch. These particle patches are assembled with partition-of-unity weights to derive a continuous implicit global shape. Each sampling particle carries its position and orientation, serving as dense surface samples for optimization tasks. Based on these moving particles, we develop a fully differentiable framework to infer and evolve highly detailed implicit geometries, enhanced by a multi-level background grid for particle adaptivity, across different inverse tasks. We demonstrated the efficacy of our representation through various benchmark comparisons with state-of-the-art neural representations, achieving lower memory consumption, fewer training iterations, and orders of magnitude higher accuracy in handling topologically complex objects and dynamic tracking tasks.
This paper presents a novel facial localization method for 3D face in the presence of facial pose and expression variation. An idea of using multi-level partition of unity (MPU) Implicits in a hierarchical way is prop...
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This paper presents a technique for creating a smooth, closed surface from a set of 2D contours, which have been extracted from a 3D scan. The technique interprets the pixels that make up the contours as points in R-3...
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This paper presents a technique for creating a smooth, closed surface from a set of 2D contours, which have been extracted from a 3D scan. The technique interprets the pixels that make up the contours as points in R-3 and employs multi-level partition of unity (MPU) implicit models to create a surface that approximately fits to the 3D points. Since MPU implicit models additionally require surface normal information at each point, an algorithm that estimates normals from the contour data is also described. Contour data frequently contains noise from the scanning and delineation process. MPU implicit models provide a superior approach to the problem of contour-based surface reconstruction, especially in the presence of noise, because they are based on adaptive implicit functions that locally approximate the points within a controllable error bound. We demonstrate the effectiveness of our technique with a number of example datasets, providing images and error statistics generated from our results. (c) 2006 Elsevier Inc. All rights reserved.
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