Visual Servoing using the Sum of Conditional Variance

International audienceIn this paper we propose a new way to achieve direct visual servoing. The novelty is the use of the sum of conditional variance to realize the optimization process of a positioning task. This measure, which has previously been used successfully in the case of visual tracking, has been shown to be invariant to non-linear illumination variations and inexpensive to compute. Compared to other direct approaches of visual servoing, it is a good compromise between techniques using the illumination of pixels which are computationally inexpensive but non robust to illumination variations and other approaches using the mutual information which are more complicated to compute but offer more robustness towards the variations of the scene. This method results in a direct visual servoing task easy and fast to compute and robust towards non-linear illumination variations. This paper describes a visual servoing task based on the sum of conditional variance performed using a Levenberg-Marquardt optimization process. The results are then demonstrated through experimental validations and compared to both photometric-based and entropy-based techniques

Dense non-rigid visual tracking with a robust similarity function

International audienceThis paper deals with dense non-rigid visual tracking robust towards global illumination perturbations of the observed scene. The similarity function is based on the sum of condi- tional variance (SCV). With respect to most approaches that minimize the sum of squared differences, which is poorly robust towards illumination variations in the scene, the choice of SCV as our registration function allows the approach to be naturally robust towards global perturbations. Moreover, a thin-plate spline warping function is considered in order to take into account deformations of the observed template. The proposed approach, after being detailed, is tested in nominal conditions and on scenes where light perturbations occur in order to assess the robustness of the approach

Tree Diet: Reducing the Treewidth to Unlock FPT Algorithms in RNA Bioinformatics

Hard graph problems are ubiquitous in Bioinformatics, inspiring the design of specialized Fixed-Parameter Tractable algorithms, many of which rely on a combination of tree-decomposition and dynamic programming. The time/space complexities of such approaches hinge critically on low values for the treewidth tw of the input graph. In order to extend their scope of applicability, we introduce the Tree-Diet problem, i.e. the removal of a minimal set of edges such that a given tree-decomposition can be slimmed down to a prescribed treewidth tw\u27. Our rationale is that the time gained thanks to a smaller treewidth in a parameterized algorithm compensates the extra post-processing needed to take deleted edges into account. Our core result is an FPT dynamic programming algorithm for Tree-Diet, using 2^{O(tw)}n time and space. We complement this result with parameterized complexity lower-bounds for stronger variants (e.g., NP-hardness when tw\u27 or tw-tw\u27 is constant). We propose a prototype implementation for our approach which we apply on difficult instances of selected RNA-based problems: RNA design, sequence-structure alignment, and search of pseudoknotted RNAs in genomes, revealing very encouraging results. This work paves the way for a wider adoption of tree-decomposition-based algorithms in Bioinformatics

A New Parametrization for Independent Set Reconfiguration and Applications to RNA Kinetics

International audienceIn this paper, we study the Independent Set (IS) reconfiguration problem in graphs. An IS reconfiguration is a scenario transforming an IS L into another IS R, inserting/removing vertices one step at a time while keeping the cardinalities of intermediate sets greater than a specified threshold. We focus on the bipartite variant where only start and end vertices are allowed in intermediate ISs. Our motivation is an application to the RNA energy barrier problem from bioinformatics, for which a natural parameter would be the difference between the initial IS size and the threshold. We first show the para-NP hardness of the problem with respect to this parameter. We then investigate a new parameter, the cardinality range, denoted by ρ which captures the maximum deviation of the reconfiguration scenario from optimal sets (formally, ρ is the maximum difference between the cardinalities of an intermediate IS and an optimal IS). We give two different routes to show that this problem is in XP for ρ: The first is a direct O(n 2)-space, O(n 2ρ+2.5)-time algorithm based on a separation lemma; The second builds on a parameterized equivalence with the directed pathwidth problem, leading to a O(n ρ+1)-space, O(n ρ+2)-time algorithm for the reconfiguration problem through an adaptation of a prior result by Tamaki [20]. This equivalence is an interesting result in its own right, connecting a reconfiguration problem (which is essentially a connectivity problem within a reconfiguration network) with a structural parameter for an auxiliary graph. We demonstrate the practicality of these algorithms, and the relevance of our introduced parameter, by considering the application of our algorithms on random small-degree instances for our problem. Moreover, we reformulate the computation of the energy barrier between two RNA secondary structures, a classic hard problem in computational biology, as an instance of bipartite reconfiguration. Our results on IS reconfiguration thus yield an XP algorithm in O(n ρ+2) for the energy barrier problem, improving upon a partial O(n 2ρ+2.5) algorithm for the problem

Visual Servoing using the Sum of Conditional Variance

International audienceIn this paper we propose a new way to achieve direct visual servoing. The novelty is the use of the sum of conditional variance to realize the optimization process of a positioning task. This measure, which has previously been used successfully in the case of visual tracking, has been shown to be invariant to non-linear illumination variations and inexpensive to compute. Compared to other direct approaches of visual servoing, it is a good compromise between techniques using the illumination of pixels which are computationally inexpensive but non robust to illumination variations and other approaches using the mutual information which are more complicated to compute but offer more robustness towards the variations of the scene. This method results in a direct visual servoing task easy and fast to compute and robust towards non-linear illumination variations. This paper describes a visual servoing task based on the sum of conditional variance performed using a Levenberg-Marquardt optimization process. The results are then demonstrated through experimental validations and compared to both photometric-based and entropy-based techniques

Dense non-rigid visual tracking with a robust similarity function

International audienceThis paper deals with dense non-rigid visual tracking robust towards global illumination perturbations of the observed scene. The similarity function is based on the sum of condi- tional variance (SCV). With respect to most approaches that minimize the sum of squared differences, which is poorly robust towards illumination variations in the scene, the choice of SCV as our registration function allows the approach to be naturally robust towards global perturbations. Moreover, a thin-plate spline warping function is considered in order to take into account deformations of the observed template. The proposed approach, after being detailed, is tested in nominal conditions and on scenes where light perturbations occur in order to assess the robustness of the approach

Automated Design of Dynamic Programming Schemes for RNA Folding with Pseudoknots

Despite being a textbook application of dynamic programming (DP) and routine task in RNA structure analysis, RNA secondary structure prediction remains challenging whenever pseudoknots come into play. To circumvent the NP-hardness of energy minimization in realistic energy models, specialized algorithms have been proposed for restricted conformation classes that capture the most frequently observed configurations. While these methods rely on hand-crafted DP schemes, we generalize and fully automatize the design of DP pseudoknot prediction algorithms. We formalize the problem of designing DP algorithms for an (infinite) class of conformations, modeled by (a finite number of) fatgraphs, and automatically build DP schemes minimizing their algorithmic complexity. We propose an algorithm for the problem, based on the tree-decomposition of a well-chosen representative structure, which we simplify and reinterpret as a DP scheme. The algorithm is fixed-parameter tractable for the tree-width tw of the fatgraph, and its output represents a ?(n^{tw+1}) algorithm for predicting the MFE folding of an RNA of length n. Our general framework supports general energy models, partition function computations, recursive substructures and partial folding, and could pave the way for algebraic dynamic programming beyond the context-free case

Supervisory Control of Infinite Symbolic Systems using Abstract Interpretation

International audienceIn this paper, we investigate the control of infinite systems, modeled by symbolic transition system for safety properties. We first redefine the concept of controllability by applying it to the guards of symbolic transitions, instead of to the events. We then define synthesis algorithms based on symbolic transformations and abstract interpretation techniques so that we can ensure finiteness of the computations