This article introduces the Hierarchical Run-Length Encoded (H-RLE) Level Set data structure. Thi... more This article introduces the Hierarchical Run-Length Encoded (H-RLE) Level Set data structure. This novel data structure combines the best features of the DT-Grid (of Nielsen and Museth [2004]) and the RLE Sparse Level Set (of Houston et al. [2004]) to provide both optimal efficiency and extreme versatility. In brief, the H-RLE level set employs an RLE in a dimensionally recursive fashion. The RLE scheme allows the compact storage of sequential nonnarrowband regions while the dimensionally recursive encoding along each axis efficiently compacts nonnarrowband planes and volumes. Consequently, this new structure can store and process level sets with effective voxel resolutions exceeding 5000 × 3000 × 3000 (45 billion voxels) on commodity PCs with only 1 GB of memory. This article, besides introducing the H-RLE level set data structure and its efficient core algorithms, also describes numerous applications that have benefited from our use of this structure: our unified implicit object r...
Page 1. Volume Graphics (2006) T. Möller, R. Machiraju, T. Ertl, M. Chen (Editors) Contour-Based ... more Page 1. Volume Graphics (2006) T. Möller, R. Machiraju, T. Ertl, M. Chen (Editors) Contour-Based Surface Reconstruction using Implicit Curve Fitting, and Distance Field Filtering and Interpolation Jeffrey Marker1 Ilya Braude1 Ken Museth2 David Breen1 ...
Level set methods, an important class of partial differential equation (PDE) methods, define dyna... more Level set methods, an important class of partial differential equation (PDE) methods, define dynamic surfaces implicitly as the level set (iso-surface) of a sampled, evolving nD function. The course begins with preparatory material that introduces the concept of using partial differential ...
Typically 3-D MR and CT scans have a relatively high resolution in the scanning X-Y plane, but mu... more Typically 3-D MR and CT scans have a relatively high resolution in the scanning X-Y plane, but much lower resolution in the axial Z direction. This non-uniform sampling of an object can miss small or thin structures. One way to address this problem is to scan the same object from multiple directions. In this paper we describe a method for deforming a level set model using velocity information derived from multiple volume datasets with non-uniform resolution in order to produce a single high-resolution 3D model. The method locally approximates the values of the multiple datasets by fitting a distance-weighted polynomial using moving least-squares. The proposed method has several advantageous properties: its computational cost is proportional to the object surface area, it is stable with respect to noise, imperfect registrations and abrupt changes in the data, it provides gain-correction, and it employs a distance-based weighting to ensures that the contributions from each scan are properly merged into the final result. We have demonstrated the effectiveness of our approach on four multi-scan datasets, a Griffin laser scan reconstruction, a CT scan of a teapot and MR scans of a mouse embryo and a zucchini.
This article introduces the Hierarchical Run-Length Encoded (H-RLE) Level Set data structure. Thi... more This article introduces the Hierarchical Run-Length Encoded (H-RLE) Level Set data structure. This novel data structure combines the best features of the DT-Grid (of Nielsen and Museth [2004]) and the RLE Sparse Level Set (of Houston et al. [2004]) to provide both optimal efficiency and extreme versatility. In brief, the H-RLE level set employs an RLE in a dimensionally recursive fashion. The RLE scheme allows the compact storage of sequential nonnarrowband regions while the dimensionally recursive encoding along each axis efficiently compacts nonnarrowband planes and volumes. Consequently, this new structure can store and process level sets with effective voxel resolutions exceeding 5000 × 3000 × 3000 (45 billion voxels) on commodity PCs with only 1 GB of memory. This article, besides introducing the H-RLE level set data structure and its efficient core algorithms, also describes numerous applications that have benefited from our use of this structure: our unified implicit object r...
Page 1. Volume Graphics (2006) T. Möller, R. Machiraju, T. Ertl, M. Chen (Editors) Contour-Based ... more Page 1. Volume Graphics (2006) T. Möller, R. Machiraju, T. Ertl, M. Chen (Editors) Contour-Based Surface Reconstruction using Implicit Curve Fitting, and Distance Field Filtering and Interpolation Jeffrey Marker1 Ilya Braude1 Ken Museth2 David Breen1 ...
Level set methods, an important class of partial differential equation (PDE) methods, define dyna... more Level set methods, an important class of partial differential equation (PDE) methods, define dynamic surfaces implicitly as the level set (iso-surface) of a sampled, evolving nD function. The course begins with preparatory material that introduces the concept of using partial differential ...
Typically 3-D MR and CT scans have a relatively high resolution in the scanning X-Y plane, but mu... more Typically 3-D MR and CT scans have a relatively high resolution in the scanning X-Y plane, but much lower resolution in the axial Z direction. This non-uniform sampling of an object can miss small or thin structures. One way to address this problem is to scan the same object from multiple directions. In this paper we describe a method for deforming a level set model using velocity information derived from multiple volume datasets with non-uniform resolution in order to produce a single high-resolution 3D model. The method locally approximates the values of the multiple datasets by fitting a distance-weighted polynomial using moving least-squares. The proposed method has several advantageous properties: its computational cost is proportional to the object surface area, it is stable with respect to noise, imperfect registrations and abrupt changes in the data, it provides gain-correction, and it employs a distance-based weighting to ensures that the contributions from each scan are properly merged into the final result. We have demonstrated the effectiveness of our approach on four multi-scan datasets, a Griffin laser scan reconstruction, a CT scan of a teapot and MR scans of a mouse embryo and a zucchini.
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Papers by Ken Museth