RLE sparse level sets

Houston, Ben; Wiebe, Mark; Batty, C.J.

doi:10.1145/1186223.1186394

Cited by 27 publications

(21 citation statements)

References 3 publications

(3 reference statements)

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“…Color and normal info ( b ) ehicle moves forward, the uncertainty increases thus the distance field is control input to determine how each grid point is changing relative to th xt grid location you can see the map has deformed to accommodate the u face), blue represents the interior of the object (negative distance) green ent the laser line scan data. The red dots represent the locations in whic represents the current location of the sensor for this set of measurement d, they are constant for a p. This can be alleviated e field appropriately with n [16] which used a o represent the level-set le high amounts of detail ents. Similarly, adaptive ees [24], or simply using [21] reduces the memory ing the computational since we must solve an e grid for each prediction tage.…”

Section: Discussionmentioning

confidence: 99%

A Variational Approach to Mapping and Localization

Hogue

Khattak

2012

2012 Ninth Conference on Computer and Robot Vision

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A fundamental open problem in SLAM is the effective representation of the map in unknown, ambiguous, complex, dynamic environments. Representing such environments in a suitable manner is a complex task. Existing approaches to SLAM use map representations that store individual features (range measurements, image patches, or higher level semantic features) and their locations in the environment. The choice of how we represent the map produces limitations which in many ways are unfavourable for application in real-world scenarios. In this paper, we explore a new approach to SLAM that redefines sensing and robot motion as acts of deformation of a differentiable surface. Distance fields and level set methods are utilized to define a parallel to the components of the SLAM estimation process and an algorithm is developed and demonstrated. The variational framework developed is capable of representing complex dynamic scenes and spatially varying uncertainty for sensor and robot models.

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Section: Discussionmentioning

confidence: 99%

A Variational Approach to Mapping and Localization

Hogue

Khattak

2012

2012 Ninth Conference on Computer and Robot Vision

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“…To the best of our knowledge, the only work directly related to ours is the work by Bridson [4] and Houston et al [14]. Bridson [4] suggests to store the level set in a sparse block grid which is a coarse uniform grid with finer uniform grids nested in the coarse grid cells that intersect the interface.…”

Section: Previous Workmentioning

confidence: 99%

“…Bridson also suggests a solution based on a hashtable to allow the grid to expand, but does not demonstrate it. The method of Houston et al [14] was described in a technical sketch (one page abstract) recently presented at a graphics conference, where we concurrently summarized the main features of DTGrid [3]. Their work primarily focuses on fluid simulations, and they propose a data structure based on Run-Length-Encoding which decouples the storage of the elements from the actual encoding.…”

Section: Previous Workmentioning

confidence: 99%

Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets

Nielsen

Museth

2006

J Sci Comput

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Level set methods [Osher and Sethian. Fronts propagating with curvaturedependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 (1988) 12] have proved very successful for interface tracking in many different areas of computational science. However, current level set methods are limited by a poor balance between computational efficiency and storage requirements. Tree-based methods have relatively slow access times, whereas narrow band schemes lead to very large memory footprints for high resolution interfaces. In this paper we present a level set scheme for which both computational complexity and storage requirements scale with the size of the interface. Our novel level set data structure and algorithms are fast, cache efficient and allow for a very low memory footprint when representing high resolution level sets. We use a time-dependent and interface adapting grid dubbed the "Dynamic Tubular Grid" or DT-Grid. Additionally, it has been optimized for advanced finite difference schemes currently employed in accurate level set computations. As a key feature of the DT-Grid, the associated interface propagations are not limited to any computational box and can expand freely. We present several numerical evaluations, including a level set simulation on a grid with an effective resolution of 1024 3 .

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“…In addition, for the eikonal equation used to maintain the signed distance property of the level set function, [19] used some special treatment at T-junctions in the context of the fast marching spirit [37]. There have been other local level set methods [20], [35], [5], [14], [4] proposed which range from variants of AMR to using tubes of uniformly spaced grid points near the interface. Some of the methods approach the complexity of [26], eliminating the need to store the unused grid points away from the interface of interest.…”

Section: Performing Organization Report Numbermentioning

confidence: 99%

Simplex Free Adaptive Tree Fast Sweeping and Evolution Methods for Solving Level Set Equations in Arbitrary Dimension

Cecil¹,

Osher²,

Qian³

2005

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We introduce simplex free adaptive tree numerical methods for solving static and time dependent Hamilton-Jacobi equations arising in level set problems in arbitrary dimension. The data structure upon which our method is built is a generalized n-dimensional binary tree, but it does not require the complicated splitting of cubes into simplices (aka generalized n-dimensional triangles or hypertetrahedrons) that current tree based methods require. It has enough simplicity that minor variants of standard numerical Hamiltonians developed for uniform grids can be applied, yielding consistent, monotone, convergent schemes. Combined with the fast sweeping strategy, the resulting tree based methods are highly efficient and accurate. Thus, without changing more than a few lines of code when changing dimension, we have obtained results for calculations in up to n = 7 dimensions.

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RLE sparse level sets

Cited by 27 publications

References 3 publications

A Variational Approach to Mapping and Localization

A Variational Approach to Mapping and Localization

Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets

Simplex Free Adaptive Tree Fast Sweeping and Evolution Methods for Solving Level Set Equations in Arbitrary Dimension

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