Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Computational geometry in C
On the complexity of optimization problems for 3-dimensional convex polyhedra and decision trees
Computational Geometry: Theory and Applications
Surface Approximation and Geometric Partitions
SIAM Journal on Computing
Polyhedral surface approximation of non-convex voxel sets through the modification of convex hulls
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Convex hulls in a 3-dimensional space
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Algorithms in digital geometry based on cellular topology
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Cup products on polyhedral approximations of 3D digital images
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
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In this paper we introduce an algorithm for the creation of polyhedral approximations for certain kinds of digital objects in a three-dimensional space. The objects are sets of voxels represented as strongly connected subsets of an abstract cell complex. The proposed algorithm generates the convex hull of a given object and modifies the hull afterwards by recursive repetitions of generating convex hulls of subsets of the given voxel set or subsets of the background voxels. The result of this method is a polyhedron which separates object voxels from background voxels. The objects processed by this algorithm and also the background voxel components inside the convex hull of the objects are restricted to have genus 0. The second aim of this paper is to present some practical improvements to the discussed convex hull algorithm to reduce computation time.