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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.
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Mapping and coverage with a particle swarm controlled by uniform inputs
We propose an approach to mapping tissue and vascular systems without the use of contrast agents, based on moving and measuring magnetic particles. To this end, we consider a swarm of particles in a 1D or 2D grid that can be tracked and controlled by an external agent. Control inputs are applied uniformly so that each particle experiences the same applied forces. We present algorithms for three tasks: (1) Mapping, i.e., building a representation of the free and obstacle regions of the workspace; (2) Subset Coverage, i.e., ensuring that at least one particle reaches each of a set of desired locations; and (3) Coverage, i.e., ensuring that every free region on the map is visited by at least one particle. These tasks relate to a large body of previous work from robot navigation, both from theory and practice, which is based on individual control. We provide theoretical insights that have potential relevance for fast MRI scans with magnetically controlled contrast media. In particular, we develop a fundamentally new approach for searching for an object at an unknown distance D, where the search is subject to two different and independent cost parameters for moving and for measuring. We show that regardless of the relative cost of these two operations, there is a simple O(log D/log log D)-competitive strategy, which is the best possible. Also, we provide practically useful and computationally efficient strategies for higher-dimensional settings. These algorithms extend to any number of particles and show that additional particles tend to reduce the mean and the standard deviation of the time required for each task.
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- PAR ID:
- 10048942
- Date Published:
- Journal Name:
- Intelligent Robots and Systems (IROS), 2017 IEEE/RSJ International Conference on
- Page Range / eLocation ID:
- 1097 to 1104
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/IROS.2017.8202280
