Yann Strozecki

Patch reprojections for Non-Local methods

Since their introduction in image denoising, the family of non-local methods, whose Non-Local Means (NL-Means) is the most famous member, has proved its ability to challenge other powerful methods such as wavelet based approaches or variational techniques. Though simple to implement and efficient in practice, the classical NL-Means algorithm suffers from several limitations: noise artifacts are created around edges and regions with few repetitions in the image are not treated at all. In this paper, we present an easy to implement and time efficient modification of the NL-Means based on a better reprojection from the patches space to the original pixel space, specially designed to reduce the artifacts due to the rare patch effect. We compare the performance of several reprojection schemes on a toy example and on some classical natural images.

From patches to pixels in Non-Local methods: Weighted-average reprojection

Since their introduction in denoising, the family of non local methods, whose Non-Local Means (NL-Means) is the most famous member, has proved its ability to challenge other powerful methods such as wavelet based approaches or variational techniques. Though simple to implement and efficient in practice, the classical NL-Means suffers from ringing artifacts around edges. In this paper, we present an easy to implement and time efficient modification of the NL-means based on a better reprojection from the patches space to the original (image) pixel space. We illustrate the performance of our method on a toy example and on some classical images.

Enumeration Complexity of Logical Query Problems with Second-order Variables

We consider query problems defined by first order formulas of the form F(x,T) with free first order and second order variables and study the data complexity of enumerating results of such queries. By considering the number of alternations in the quantifier prefixes of formulas, we show that such query problems either admit a constant delay or a polynomial delay enumeration algorithm or are hard to enumerate. We also exhibit syntactically defined fragments inside the hard cases that still admit good enumeration algorithms and discuss the case of some restricted classes of database structures as inputs.

Enumeration of the monomials of a polynomial and related complexity classes

We study the problem of generating monomials of a polynomial in the context of enumeration complexity. We present two new algorithms for restricted classes of polynomials, which have a good delay between two generated monomials and the same global running time as the classical ones. Moreover they are simple to describe, use small evaluation points and one of them is parallelizable. We introduce TotalPP, IncPP and DelayPP, which are probabilistic counterparts of the most common classes for enumeration problems, hoping that randomization will be a tool as strong for enumeration as it is for decision. Our interpolation algorithms prove that a few interesting problems are in these classes like the enumeration of the spanning hypertrees of a 3-uniform hypergraph. Finally we give a method to interpolate degree 2 polynomials with an acceptable (incremental) delay. We also prove that finding a specified monomial in a degree 2 polynomial is hard unless RP = NP. It suggests that there is no algorithm with a delay as good (polynomial) as the one we achieve for multilinear polynomials.

Monadic second-order model-checking on decomposable matroids

A notion of branch-width, which generalizes the one known for graphs, can be defined for matroids. We first give a proof of the polynomial time model-checking of monadic second-order formulas on representable matroids of bounded branch-width, by reduction to monadic second-order formulas on trees. This proof is much simpler than the one previously known. We also provide a link between our logical approach and a grammar that allows to build matroids of bounded branch-width. Finally, we introduce a new class of non-necessarily representable matroids, described by a grammar and on which monadic second-order formulas can be checked in linear time.

Efficient Generation of Stable Planar Cages for Chemistry

In this paper we describe an algorithm which generates all colored planar maps with a good minimum sparsity from simple motifs and rules to connect them. An implementation of this algorithm is available and is used by chemists who want to quickly generate all sound molecules they can obtain by mixing some basic components.

Approximate verification and enumeration problems

We study enumeration problems using probabilistic methods, with application to verification problems. We consider the enumeration of monomials of a polynomial given as a black box, and the enumeration of discrete points which separate two polytopes in a space of dimension n, using a random walk which provides witnesses if the volume of the difference of the polytopes is large enough. The first method allows to enumerate all words of a given size which distinguish two probabilistic automata with a polynomial delay. The second method enumerates words which e-distinguish two nondeterministic finite automata.We also enumerate strategies which e-distinguish two Markov Decision Processes in time polynomial in the dimension of their statistical representation.

Finding Optimal Strategies of Almost Acyclic Simple Stochastic Games

The optimal value computation for turned-based stochastic games with reachability objectives, also known as simple stochastic games, is one of the few problems in NP ∩ coNP which are not known to be in P. However, there are some cases where these games can be easily solved, as for instance when the underlying graph is acyclic. In this work, we try to extend this tractability to several classes of games that can be thought as ”almost” acyclic. We give some fixed-parameter tractable or polynomial algorithms in terms of different parameters such as the number of cycles or the size of the minimal feedback vertex set.

The complexity of acyclic subhypergraph problems

We investigate the computational complexity of two decision problems concerning the existence of certain acyclic subhypergraphs of a given hypergraph, namely the SPANNING ACYCLIC SUBHYPERGRAPH problem and the MAXIMUM ACYCLIC SUBHYPERGRAPH problem. The former is about the existence of an acyclic subhypergraph such that each vertex of the input hypergraph is contained in at least one hyperedge of the subhypergraph. The latter is about the existence of an acyclic subhypergraph with k hyperedges where k is part of the input. For each of these problems, we consider different notions of acyclicity of hypergraphs: Berge-acyclicity, γ-acyclicity, β-acyclicity and α-acyclicity. We are also concerned with the size of the hyperedges of the input hypergraph. Depending on these two parameters (notion of acyclicity and size of the hyperedges), we try to determine which instances of the two problems are in P ∩ RNC and which are NP-complete.