Integral-geometry morphological image analysis

Michielsen, Kristel; Raedt, de Hans

doi:10.1016/s0370-1573(00)00106-x

Cited by 245 publications

(255 citation statements)

References 90 publications

(110 reference statements)

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“…The Euler characteristic χ, though proportional to the surface integral of the Gaussian curvature (κ 1 · κ 2 ), is related to the number of structures in the system. In the three dimensional case it can be shown to be given by the number of connected components plus the number of cavities minus the number of tunnels in the system [34], that is…”

Section: B Topologymentioning

confidence: 99%

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Nuclear “pasta” formation

et al. 2013

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The formation of complex nonuniform phases of nuclear matter, known as nuclear pasta, is studied with molecular dynamics simulations containing 51 200 nucleons. A phenomenological nuclear interaction is used that reproduces the saturation binding energy and density of nuclear matter. Systems are prepared at an initial density of 0.10 fm −3 and then the density is decreased by expanding the simulation volume at different rates to densities of 0.01 fm −3 or less. An originally uniform system of nuclear matter is observed to form spherical bubbles ("swiss cheese"), hollow tubes, flat plates ("lasagna"), thin rods ("spaghetti") and, finally, nearly spherical nuclei with decreasing density. We explicitly observe nucleation mechanisms, with decreasing density, for these different pasta phase transitions. Topological quantities known as Minkowski functionals are obtained to characterize the pasta shapes. Different pasta shapes are observed depending on the expansion rate. This indicates non equilibrium effects. We use this to determine the best ways to obtain lower energy states of the pasta system from MD simulations and to place constrains on the equilibration time of the system.

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Section: B Topologymentioning

confidence: 99%

“…This can be achieved by making use of integral-geometric formulae [33] often referred to as Minkowski functionals [34]. Minkowski functionals are a robust way to describe complex structures.…”

Section: Introductionmentioning

confidence: 99%

Nuclear “pasta” formation

et al. 2013

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“…MIA is easy to use. Results of applications to perfect and imperfect SC, FCC and BCC lattice structures, to triply periodic minimal surfaces and to three-dimensional structures formed in polymer solutions will be published elsewhere [6,8]. nfaces=0 nedges=0 nvert=0 do i=-1,1,2 jxi=jx+i jyi=jy+i jzi=jz+i kc1=1-lattice(jxi+Lx*(jy+Ly*jz)) kc2=1-lattice(jx+Lx*(jyi+Ly*jz)) kc3=1-lattice(jx+Lx*(jy+Ly*jzi)) nfaces=nfaces+kc1+kc2+kc3 do j=-1,1,2 jyj=jy+j jzj=jz+j k4=Lx*(jyj+Ly*jz) k7=Lx*(jy+Ly*jzj) kc7=1-lattice(jx+k7) kc1kc4kc5=kc1*(1-lattice(jxi+k4))*(1-lattice(jx+k4)) nedges=nedges+kc1kc4kc5+kc2*(1-lattice(jx+Lx*(jyi+Ly*jzj)))*kc7 1 +kc1*(1-lattice(jxi+k7))*kc7 if(kc1kc4kc5.ne.0) then do k=-1,1,2 jzk=jz+k k9=Lx*(jy+Ly*jzk) k10=Lx*(jyj+Ly*jzk) nvert=nvert+(1-lattice(jxi+k9))*(1-lattice(jxi+k10)) 1 *(1-lattice(jx+k10))*(1-lattice(jx+k9)) enddo !…”

Section: Discussionmentioning

confidence: 99%

“…In order to calculate the morphological properties of P(x) in an efficient way we consider each pixel ( (d) for the building blocks Q ν of a 2D square and a 3D cubic lattice can easily be calculated [6] and are listed in Tables 1 and 2, respectively. For the whole image P = P(x) these functionals can be calculated using…”

Section: Morphological Propertiesmentioning

confidence: 99%

Morphological image analysis

Michielsen

Raedt

2000

Computer Physics Communications

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“…image retrieval, object classification, object recognition, object identification, etc). Different mathematical tools have been used to define the shape descriptors: algebraic invariants [14], Fourier analysis [6], morphological operations [26], integral transformations [23], statistical methods [17], fractal techniques [15], logic [27], combinatorial methods [1], multiscale approaches [9], integral invariants [16], multi-scale integral geometry [3,4,18], etc. Generally speaking, shape descriptors can be classified into two groups: area based descriptors and boundary based ones.…”

Section: Introductionmentioning

confidence: 99%

Measuring linearity of curves in 2D and 3D

Rosin

Pantović

Žunić

2016

Pattern Recognition

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In this paper we define a new linearity measure for open curve segments in 2D and 3D. The measure considers the distance of the curve end points to the curve centroid. It is simple to compute and has the basic properties that should be satisfied by any linearity measure. The new measure ranges over the interval (0, 1], and produces the value 1 if and only if the measured curve is a perfect straight line segment. Also, the new linearity measure is invariant with respect to translations, rotations and scaling transformations. The new measure is theoretically well founded and, because of this, its behaviour can be well understood and predicted to some extent. This is always beneficial because it indicates the suitability of the new measure to the desired application.Several experiments are provided to illustrate the behaviour and to demonstrate the efficiency and applicability of the new linearity measure.

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Integral-geometry morphological image analysis

Cited by 245 publications

References 90 publications

Nuclear “pasta” formation

Nuclear “pasta” formation

Morphological image analysis

Measuring linearity of curves in 2D and 3D

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