Affinity graph-based segmentation methods have become a major trend in computer vision. The performance of these rely on the constructed affinity graph, with particular emphasis neighborhood topology and pairwise affinities among superpixels. However, ignore noisy data from images, that influence accuracy similarities. Multiscale combinatorial grouping graph fusion also generate higher computat...

We determine the p-rank of the incidence matrix of hyperplanes of PG(n, p) and points of a nondegenerate Hermitian variety. As a corollary, we obtain new bounds for the size of caps and the existence of ovoids in finite unitary spaces. This paper is a companion to [2], in which Blokhuis and this author derive the analogous p-ranks for quadrics.

Recovering intrinsic low-dimensional subspaces from data distributed on them is a key preprocessing step to many applications. In recent years, a lot of work has modeled subspace recovery as low-rank minimization problems. We find that some representative models, such as robust principal component analysis (R-PCA), robust low-rank representation (R-LRR), and robust latent low-rank representatio...

LetG be a Polish group, τ a Polish topology on a spaceX, G acting continuously on (X, τ), with B ⊂ X G-invariant and in the Borel algebra generated by τ . Then there is a larger Polish topology τ ⊃ τ on X so that B is open with respect to τ, G still acts continuously on (X, τ), and τ has a basis consisting of sets that are of the same Borel rank as B relative to τ . 1

We prove that the smallest degree of an apolar 0-dimensional scheme to a general cubic form in n+ 1 variables is at most 2n+ 2, when n ≥ 8, and therefore smaller than the rank of the form. When n = 8 we show that the bound is sharp, i.e. the smallest degree of an apolar subscheme is 18.

We consider the problem of finding for a given N -tuple of polynomials (real or complex) the closest N -tuple that has a common divisor of degree at least d. Extended weighted Euclidean seminorm of the coefficients is used as a measure of closeness. Two equivalent representations of the problem are considered: (i) direct parameterization over the common divisors and quotients (image representat...

We show that if G is a stable group of finite weight with no infinite, infinite-index, chains of definable subgroups, then G is superstable of finite U rank. Combined with recent work of Palaćın and Sklinos, we conclude that (Z,+, 0) has no proper stable expansions of finite weight. A corollary of this result is that if P ⊆ Zn is definable in a finite dp-rank expansion of (Z,+, 0), and (Z,+, 0,...

In this paper, we study VC-density over indiscernible sequences (denoted VCind-density). We answer an open question in [1], showing that VCind-density is always integer valued. We also show that VCind-density and dp-rank coincide in the natural way.

Let k be a field of characteristic q, C a smooth connected curve defined over k with function field K := k(C). Let A/K be a non constant abelian variety defined over K of dimension d. We assume that q = 0 or > 2d + 1. Let p 6= q be a prime number and C → C a finite geometrically Galois and étale cover defined over k with function field K ′ := k(C). Let (τ , B) be the K /k-trace of A/K. We give ...