Three-dimensional (3D) analysis is an essential tool to obtain quantitative results from 3D datasets. Considerable progress has been made in 3D imaging techniques, resulting in a growing need for more flexible, complete analysis packages containing advanced algorithms. At the Centre for X-ray Tomography of the Ghent University (UGCT), research is being done on the improvement of both hardware and software for high-resolution X-ray computed tomography (CT). UGCT collaborates with research groups from different disciplines, each having specific needs. To meet these requirements the analysis software package, Morpho+, was developed in-house. Morpho+ contains an extensive set of high-performance 3D operations to obtain object segmentation, separation, and parameterization (orientation, maximum opening, equivalent diameter, sphericity, connectivity, etc.), or to extract a 3D geometrical representation (surface mesh or skeleton) for further modeling. These algorithms have a relatively short processing time when analyzing large datasets. Additionally, Morpho+ is equipped with an interactive and intuitive user interface in which the results are visualized. The package allows scientists from various fields to obtain the necessary quantitative results when applying high-resolution X-ray CT as a research tool to the nondestructive investigation of the microstructure of materials.

Three-dimensional analysis of high-resolution X-ray computed tomography data with Morpho+.

Algebraic geometry : an introduction to birational geometry of algebraic varieties

Let (X, L) be a quasi-polarized variety of dim X = n. In this paper we give a new invariant (the i-th sectional geometric genus) of (X, L), which is a generalization of the degree and the sectional genus of (X, L). Furthermore we study some properties of the sectional geometric genus.

On the Sectional Geometric Genus of Quasi-Polarized Varieties. I

Algebraic geometry and commutative algebra in honor of Masayoshi Nagata

Let (X,L) be a quasi-polarized variety of dimension n. In this paper we investigate a lower bound for the sectional genus g(L) for the following types; (1) A lower bound for the sectional genus of the case in which (f,X,C,L )i s a quasi-polarized fiber space, where C is a smooth curve. (2) Non-negativity of te sectional genus of the case where (X,L) is a quasi-polarized manifold or (X,L) is a polarized variety with some singularities. (3) A lower bound for the sectional genus of the case where dimX =3 .

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A lower bound for sectional genus of quasi-polarized manifolds

Let (X,L) be a quasi-polarized variety, i.e. X is a smooth projective variety over the complex numbers \(\mathbb{C}\) and L is a nef and big divisor on X. Then we conjecture that g(L) = q(X), whereg(L) is the sectional genus of L and \(q(X) = \dim H^1 (\mathcal{O}_X )\). In this paper, we treat the case \(\dim X = 2\). First we prove that this conjecture is true for \(\kappa (X) \leqslant 1\), and we classify (X,L) withg(L)=q(X), where \(\kappa (X)\) is the Kodaira dimension of X. Next we study some special cases of\(\kappa (X) = 2\).

A Lower Bound for the Sectional Genus of Quasi-Polarized Surfaces

Let (X, L) be a polarized manifold of dimension 3. In this paper, we consider a lower bound for h0(KX + 2L). We prove that h0(KX + 2L) > 0 if KX + 2L is nef, which is a conjecture of Beltrametti–Sommese for polarized 3-folds. Moreover we classify polarized 3-folds (X, L) with h0(KX + 2L) = 1 under the assumption that KX + 2L is nef.

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Yoshiaki Fukuma

Papers

On the Sectional Geometric Genus of Quasi-Polarized Varieties. I

A Lower Bound for the Sectional Genus of Quasi-Polarized Surfaces

A lower bound for sectional genus of quasi-polarized manifolds

On a conjecture of beltrametti–sommese for polarized 3-folds

On the dimension of global sections of adjoint bundles for polarized 3-folds and 4-folds