CAD models from medical images using LAR

Paoluzzi, Alberto; DiCarlo, Antonio; Furiani, Francesco; Jiřík, Miroslav

doi:10.1080/16864360.2016.1168216

Cited by 5 publications

(11 citation statements)

References 39 publications

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“…Arrangements of cellular complexes 1:3 e problem studied in this paper has a number of useful geometric applications, including the motion planning of robots, the variadic 1 computation of Boolean operations (union, intersection, di erence, symmetric di erence), and the topology repair of graphical meshes, all starting from a set of cellular complexes embedded in the same Euclidean space. In particular, we are currently using chain complexes and boundary operators to extract the models of neurons and vessels from extreme-resolution 3D images of brain tissue, and to dramatically reduce the complexity of their representation, while preserving the homotopy type, in order to piecewise compute the connectome of brain structures [11,33].…”

Section: Problem Statement and Resultsmentioning

confidence: 99%

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Regularized arrangements of cellular complexes

Paoluzzi¹,

Shapiro²,

DiCarlo³

2017

Preprint

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In this paper we propose a novel algorithm to combine two or more cellular complexes, providing a minimal fragmentation of the cells of the resulting complex. We introduce here the idea of arrangement generated by a collection of cellular complexes, producing a cellular decomposition of the embedding space. e algorithm that executes this computation is called Merge of complexes. e arrangements of line segments in 2D and polygons in 3D are special cases, as well as the combination of closed triangulated surfaces or meshed models.is algorithm has several important applications, including Boolean and other set operations over large geometric models, the extraction of solid models of biomedical structures at the cellular scale, the detailed geometric modeling of buildings, the combination of 3D meshes, and the repair of graphical models. e algorithm is e ciently implemented using the Linear Algebraic Representation (LAR) of argument complexes, i.e., on sparse representation of binary characteristic matrices of d-cell bases, well-suited for implementation in last generation accelerators and GPGPU applications.

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Section: Problem Statement and Resultsmentioning

confidence: 99%

“…e very general shape allowed for cells makes the LAR scheme notably appropriate for biomedical applications like the modeling of neuronal tissues [11,33] and the solid modeling of buildings and their components [31]. E.g., the whole facade of a building can be described by a single 3-cell in its solid model.…”

Section: Linear Algebraic Representationmentioning

confidence: 99%

Regularized arrangements of cellular complexes

Paoluzzi¹,

Shapiro²,

DiCarlo³

2017

Preprint

Self Cite

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“…Due to the simplicity of the cells (voxels = cubes), a sufficient (geom,top) pair is given below as (V,CV), where CV is an array of arrays of Int64 indices of vertices of grid cubes. [ 1,2,3,4,7,8,9,10], [ 3,4,5,6,9,10,11,12], [ 7,8,9,10,13,14,15,16], [ 9,10,11,12,15,16,17,18], [13,14,15,16,19,20,21,22], [15,16,17,18,21,22,23,24] Boundary matrices: The boundary matrices between non-oriented chain spaces are computed by sparse matrix multiplication followed by matrix filtering, produced in Julia by the broadcast of vectorized integer division (.÷):…”

Section: Discussion Of Methodsmentioning

confidence: 99%

“…In particular, a boundary representation provides a cellular decomposition of the object's boundary into cells of dimension zero (vertices), one (edges), and two (faces). Medical imaging can be classified as the enumerative representation of cellular decompositions of organs and tissues [16], in particular, as subsets of 3D volume elements (voxels) from 3D medical image.…”

Section: Representation Schemementioning

confidence: 99%

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Algebraic Filtering of Surfaces from 3D Medical Images with Julia

Jiřík¹,

Paoluzzi²

2020

Cad'20

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In this paper we introduce a novel algebraic filter, based on algebraic topology methods, to extract and smooth the boundary surface of any subset of voxels arising from the segmentation of a 3D medical image. The input of the Linear Algebraic Representation (lar) Surface extraction filter (lar-surf) is defined as a chain, i.e., an element of a linear space of chains here subsets of voxels represented in coordinates as a sparse binary vector. The output is produced by a linear mapping between spaces of 3-and 2-chains, given by the boundary operator ∂ 3 : C 3 → C 2 . The only data structures used in this approach are sparse arrays with one or two indices, i.e., sparse vectors and sparse matrices. This work is based on lar algebraic methods and is implemented in Julia language, natively supporting parallel computing on hybrid hardware architectures.

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Topological Computing of Arrangements with (Co)Chains

Paoluzzi

Shapiro

DiCarlo³

et al. 2020

ACM Trans. Spatial Algorithms Syst.

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In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences, adjacencies, and ordering of cells, generally using disparate and often incompatible data structures and algorithms. This article introduces computational topology algorithms to discover the two-dimensional (2D)/3D space partition induced by a collection of geometric objects of dimension 1D/2D, respectively. Methods and language are those of basic geometric and algebraic topology. Only sparse vectors and matrices are used to compute both spaces and maps, i.e., the chain complex, from dimension zero to three. The prototype software is written in Julia, the novel language for scientific computing. The applications may vary from 3D graphics to 3D printing, from images to scene understanding, and from games to building information modeling.

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CAD models from medical images using LAR

Cited by 5 publications

References 39 publications

Regularized arrangements of cellular complexes

Regularized arrangements of cellular complexes

Algebraic Filtering of Surfaces from 3D Medical Images with Julia

Topological Computing of Arrangements with (Co)Chains

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