Images of a single object, varying the capture position, can generate smooth deformations in their selfrepresentation. In an image plane, these deformations can be approximated by affine transformations, making it useful to recognize the same object in different angles. We present the RHO-Affine-ORB, an affine invariant feature detector, based on original ORB algorithm adapted to be affine inva...

Affine invariant functions are constructed in spatial domain. Unlike the previous affine representation functions in transform domain, these functions are constructed directly on the object contour without any transformation. To eliminate the effect of the choice of points on the contour, an affine invariant function using seven points on the contour is constructed. For objects with several sep...

Affine-invariant properties are an abstract class of properties that generalize some central algebraic ones, such as linearity and low-degree-ness, that have been studied extensively in the context of property testing. Affine invariant properties consider functions mapping a big field Fqn to the subfield Fq and include all properties that form an Fq-vector space and are invariant under affine t...

Classical designs and their (projective) q-analogs can both be viewed as designs in matroids, using the matroid of all subsets of a set and the matroid of linearly independent subsets of a vector space, respectively. Another natural matroid is given by the point sets in general position of an affine space, leading to the concept of an affine design. Accordingly, a t-(n, k, λ) affine design of o...

We describe a linear algorithm to recover 3D affine shape/motion from line correspondences over three views with uncalibrated affine cameras. The key idea is the introduction of a one-dimensional projective camera. This converts the 3D affine reconstruction of “lines” into 2D projective reconstruction of “points”. Using the full tensorial representation of three uncalibrated 1D views, we prove ...

Affine transformations are a well-known robustness issue in many multimedia fingerprinting systems. Since it is quite easy with modem computers to apply affine transformations to audio, image and video content, there is an obvious necessity for affine transformation resilient fingerprinting. In this paper we present a new method for affine transformation resilient fingerprints that is based upo...

In this paper we discuss planar quadrilateral (PQ) nets as discrete models for convex affine surfaces. As a main result, we prove a necessary and sufficient condition for a PQ net to admit a Lelieuvre co-normal vector field. Particular attention is given to the class of surfaces with discrete harmonic co-normals, which we call discrete affine minimal surfaces, and the subclass of surfaces with ...