Understanding texture regularity in real images is a challenging computer vision task. We propose a higher-order feature matching algorithm to discover the lattices of near-regular textures in real images. The underlying lattice of a near-regular texture identifies all of the texels as well as the global topology among the texels. A key contribution of this paper is to formulate lattice-finding...

We discuss thick regular near 2d-gons with a Q-polynomial collinearity graph. For d ≥ 4, we show that apart from Hamming near polygons and dual polar spaces there are no thick Q-polynomial regular near polygons. We also show that no regular near hexagons exist with parameters (s, t2, t) equal to (3, 1, 34), (8, 4, 740), (92, 64, 1314560), (95, 19, 1027064) or (105, 147, 2763012). Such regular n...

Texture synthesis is widely used in the field of computer graphics, vision, and image processing. In the present paper, a texture synthesis algorithm is proposed for near-regular natural textures with the help of a representative periodic pattern extracted from the input textures using distance matching function. Local texture statistics is then analyzed against global texture statistics for no...

Hindman and Leader first investigated Ramsey theoretic properties near 0 for dense subsemigroups of (R,+). Following them, the notion of image partition regularity near zero for matrices was introduced by De and Hindman. It was also shown there that like image partition regularity over N, the main source of infinite image partition regular matrices near zero are Milliken–Taylor matrices. But ex...

The inequality of Higman for generalized quadrangles of order (s, t) with s > 1 states that t ≤ s. We will generalize this by proving that the intersection number ci of a regular near 2d-gon of order (s, t) with s > 1 satisfies the tight bound ci ≤ (s − 1)/(s − 1), and we give properties in case of equality. It is known that hemisystems in generalized quadrangles meeting the Higman bound induce...

In unpublished work, Geelen proved that a matroid is nearregular if and only if it has no minor isomorphic to U2,5, U3,5, F7, F ∗ 7 , F− 7 , (F − 7 ) ∗, AG(2, 3)\e, (AG(2, 3)\e)∗, ∆T (AG(2, 3)\e), or P8. We provide a proof of this characterization.