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: C3 → C2. 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.

Jirik, M., Dicarlo, A., Liska, V., Paoluzzi, A. (2020). Algebraic filtering of surfaces from 3d medical images with julia. COMPUTER-AIDED DESIGN AND APPLICATIONS, 18(3), 468-485 [10.14733/cadaps.2021.468-485].

### Algebraic filtering of surfaces from 3d medical images with julia

#### Abstract

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: C3 → C2. 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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2020
Jirik, M., Dicarlo, A., Liska, V., Paoluzzi, A. (2020). Algebraic filtering of surfaces from 3d medical images with julia. COMPUTER-AIDED DESIGN AND APPLICATIONS, 18(3), 468-485 [10.14733/cadaps.2021.468-485].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11590/379175`
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