Affine-invariant curvature estimators for implicit surfaces

Representation of Dupin cyclides using quaternions

Dupin cyclides are surfaces characterized by the property that all their curvature lines are circles or lines. Spheres, circular cylinders, cones and tori are particular examples. We introduce a bilinear rational Bézier-like formula with quaternion weights for parametrizing principal patches of Dupin cyclides. The proposed construction is not affine invariant but it is Möbius invariant, has low...

Learning Basic Patterns from Repetitive Texture Surfaces Under Non-rigid Deformations

In this paper, we approach the problem of determining the basic components from repetitive textured surfaces undergoing free-form deformations. Traditional methods for texture modeling are usually based on measurements performed on fronto-parallel planar surfaces. Recently, affine invariant descriptors have been proposed as an effective way to extract local information from non-planar texture s...

Discrete Affine Surfaces based on Quadrangular Meshes

In this paper we are interested in defining affine structures on discrete quadrangular surfaces of the affine three-space. We introduce, in a constructive way, two classes of such surfaces, called respectively indefinite and definite surfaces. The underlying meshes for indefinite surfaces are asymptotic nets satisfying a non-degeneracy condition, while the underlying meshes for definite surface...

Affine Invariant 3L Fitting of Implicit Polynomials

Combining implicit polynomials and algebraic invariants for representing and recognizing complicated objects proves to be a powerful technique. However, a basic requirement for using implicit polynomials for affine invariant recognition is to have an affine invariant fitting algorithm. In this paper, we study the problem of affine invariant fitting of an implicit polynomial to data. Received Ja...

Convergence of an Implicit Iteration for Affine Mappings in Normed and Banach Spaces