Digital Planar Segment Based Polyhedrization for Surface Area Estimation

Abstract. We present a method for estimating the surface volume of four-dimensional objects in discrete binary images. A surface volume weight is assigned to each 2 × 2 × 2 × 2 configuration of image elements. The total surface volume of a digital 4D object is given by a summation of the local volume contributions. Optimal volume weights are derived in order to provide an unbiased estimate with minimal variance for randomly oriented digitized planar hypersurfaces. Only 14 out of 64 possible boundary configurations appear on planar hypersurfaces. We use a marching hypercubes tetrahedrization to assign surface volume weights to the non-planar cases. The correctness of the method is verified on fourdimensional balls and cubes digitized in different sizes. The algorithm is appealingly simple; the use of only a local neighbourhood enables efficient implementations in hardware and/or in parallel architectures.

Section: Previous and Related Workmentioning

confidence: 99%

Surface Volume Estimation of Digitized Hyperplanes Using Weighted Local Configurations

Lindblad

2005

“…Even if these methods offer a good visualization, it does not provide a good data compression (huge number of facets) but we have a first reversible solution. Digital geometry solutions deal with a first step that segments the object boundary into pieces of digital plane [2,6,17,9,11,15]. The digital plane is a fundamental object for this problem because reversibility properties exist.…”

Section: Introductionmentioning

confidence: 99%

Optimization Schemes for the Reversible Discrete Volume Polyhedrization Using Marching Cubes Simplification

Cœurjolly

Dupont

Jospin

et al. 2006

“…One can also apply Fukuda's CDD algorithm for solving systems of linear inequalities by successive intersection of half-spaces defined by the inequalities. An efficient incremental algorithm based on a similar approach is proposed in [15]. In [8] Buzer presents an incremental linear time algorithm based on solving a linear program by appropriate modification of Megiddo's algorithm [18].…”

Section: Introductionmentioning

confidence: 99%

Complexity Analysis for Digital Hyperplane Recognition in Arbitrary Fixed Dimension

Brimkov

Dantchev

2005

Abstract. We consider the following problem. Given a set of pointswhether M is a portion of a digital hyperplane and, if so, determine its analytical representation. In our setting p 1 , p 2 , . . . , p m may be arbitrary points (possibly, with rational and/or irrational coefficients) and the dimension n may be any arbitrary fixed integer. We provide an algorithm that solves this digital hyperplane recognition problem by reducing it to an integer linear programming problem of fixed dimension within an algebraic model of computation. The algorithm performs O (m log D) arithmetic operations, where D is a bound on the norm of the domain elements.