Given a complete nonsingular algebraic variety X and a divisor D with normal crossings, we say that X is log homogeneous with boundary D if the logarithmic tangent bundle TX(− log D) is generated by its global sections. Then the Albanese morphism α turns out to be a fibration with fibers being spherical (in particular, rational) varieties. It follows that all irreducible components of D are non...

In this paper, linear local tangent space alignment (LLTSA), as a novel linear dimensionality reduction algorithm, is proposed. It uses the tangent space in the neighborhood of a data point to represent the local geometry, and then aligns those local tangent spaces in the low-dimensional space which is linearly mapped from the raw high-dimensional space. Since images of faces often belong to a ...

Frenet-Serret and Bishop rigid-body motions have many potential applications in robotics, graphics and computer aided design. In order to study these motions new characterisations in terms of their velocity twists are derived. This is extended to general motions based on any moving frame to a space curve. Further it is shown that any such general moving frame motion is the product of a Frenet-S...

Recall that our mechanical worm (MW) model used in the simulation portion of our study is constructed from a chain of spherical beads of radius a. Each bead, indexed by n, is centered at Yn, and has an orientation vector t̂n. The vector t̂n is also used as the unit tangent to the worm’s centerline. Each bead is also subject to several forces and torques which sum to zero at each moment in the dyn...

An isometric immersion f : Mn → M̃n from a Riemannian nmanifold Mn into a Kähler n-manifold M̃n is called Lagrangian if the complex structure J of the ambient manifold M̃n interchanges each tangent space of Mn with the corresponding normal space. In this paper, we completely classify spherical Lagrangian submanifolds in complex Euclidean spaces. In this paper, we also provide two corresponding cla...

We discuss properties of a generalized Minkowski-Funk transform de…ned for a family of hypersurfaces. We prove two-side estimates for the integral operator and show that the range conditions can be written in terms of the reciprocal Funk transform. Some applications to the spherical mean transform are considered. 1 Families of hypersurfaces Let X and be smooth manifolds of dimension n > 1 and F...

The input of Multi-H are point correspondences with local affine transformations and the epipolar geometry. We use Matching On Demand with view Synthesis (MODS) method [3] since it provides accurate local affinities, the fundamental matrix F and point correspondences consistent with F. Using Homography from Affine transformation and Fundamental matrix (HAF) method [1] a homography is estimated ...

A closed κ0-curve is a closed regular curve of class C r (r ≥ 2) in the Euclidean 3-space having constant curvature κ0 > 0. We present various examples of nonplanar closed κ0-curves of class C , which are composed of n arcs of circular helices. The construction of c starts from the spherical image (= tangent indicatrix) c of c, which then has to be a closed regular curve of class C on the unit ...

We prove that every C closed curve immersed on an ellipsoid has a pair of parallel tangent lines. This establishes the optimal regularity for a phenomenon first observed by B. Segre. Our proof uses an approximation argument with the aid of an estimate for the size of loops in the tangential spherical image of a spherical curve. A skew loop is a C closed curve without parallel tangent lines imme...

In this paper, the spatial property of the magneto-static field generated by the stable current is discussed and exploited in image analysis. The region-division feature of the magnetic field generated by a current element on 2D plane is investigated experimentally for some simple test images. The virtual edge current in gray-scale images is presented by a magneto-static analogy, which is compo...