On the (parameterized) complexity of recognizing well-covered (r,l)-graphs.

An (r,ℓ)(r,ℓ)-partition of a graph G is a partition of its vertex set into r independent sets and ℓℓ cliques. A graph is (r,ℓ)(r,ℓ) if it admits an (r,ℓ)(r,ℓ)-partition. A graph is well-covered if every maximal independent set is also maximum. A graph is (r,ℓ)(r,ℓ)-well-covered if it is both (r,ℓ)(r,ℓ) and well-covered. In this paper we consider two different decision problems. In the (r,ℓ)(r,ℓ)-Well-Covered Graph problem ((r,ℓ)(r,ℓ) wcg for short), we are given a graph G, and the question is whether G is an (r,ℓ)(r,ℓ)-well-covered graph. In the Well-Covered (r,ℓ)(r,ℓ)-Graph problem (wc (r,ℓ)(r,ℓ) g for short), we are given an (r,ℓ)(r,ℓ)-graph G together with an (r,ℓ)(r,ℓ)-partition of V(G) into r independent sets and ℓℓ cliques, and the question is whether G is well-covered. We classify most of these problems into P, coNP-complete, NP-complete, NP-hard, or coNP-hard. Only the cases wc(r, 0)g for r≥3r≥3 remain open. In addition, we consider the parameterized complexity of these problems for several choices of parameters, such as the size αα of a maximum independent set of the input graph, its neighborhood diversity, or the number ℓℓ of cliques in an (r,ℓ)(r,ℓ)-partition. In particular, we show that the parameterized problem of deciding whether a general graph is well-covered parameterized by αα can be reduced to the wc (0,ℓ)(0,ℓ) g problem parameterized by ℓℓ, and we prove that this latter problem is in XP but does not admit polynomial kernels unless coNP⊆NP/polycoNP⊆NP/poly

Fast Shape from Shading for Phong-Type Surfaces

Abstract. Shape from Shading (SfS) is one of the oldest problems in image analysis that is modelled by partial differential equations (PDEs). The goal of SfS is to compute from a single 2-D image a reconstruction of the depicted 3-D scene. To this end, the brightness variation in the image and the knowledge of illumination conditions are used. While the quality of models has reached maturity, there is still the need for efficient nu-merical methods that enable to compute sophisticated SfS processes for large images in reasonable time. In this paper we address this problem. We consider a so-called Fast Marching (FM) scheme,which is one of the most efficient numerical approaches available. However, the FM scheme is not trivial to use for modern non-linear SfS models. We show how this is done for a recent SfS model incorporating the non-Lambertian reflectance model of Phong. Numerical experiments demonstrate that – without compromising quality – our FM scheme is two orders of magni-tude faster than standard methods.

Modeling in vitro osteoarthritis phenotypes in a vascularized bone model based on a bone-marrow derived mesenchymal cell line and endothelial cells

The subchondral bone and its associated vasculature play an important role in the onset of osteoarthritis (OA). Integration of different aspects of the OA environment into multi-cellular and complex human, in vitro models is therefore needed to properly represent the pathology. In this study, we exploited a mesenchymal stromal cell line/endothelial cell co-culture to produce an in vitro human model of vascularized osteogenic tissue. A cocktail of inflammatory cytokines, or conditioned medium from mechanically-induced OA engineered microcartilage, was administered to this vascularized bone model to mimic the inflamed OA environment, hypothesizing that these treatments could induce the onset of specific pathological traits. Exposure to the inflammatory factors led to increased network formation by endothelial cells, reminiscent of the abnormal angiogenesis found in OA subchondral bone, demineralization of the constructs, and increased collagen production, signs of OA related bone sclerosis. Furthermore, inflammation led to augmented expression of osteogenic (alkaline phosphatase (ALP) and osteocalcin (OCN)) and angiogenic (vascular endothelial growth factor (VEGF)) genes. The treatment, with a conditioned medium from the mechanically-induced OA engineered microcartilage, also caused increased demineralization and expression of ALP, OCN, ADAMTS5, and VEGF; however, changes in network formation by endothelial cells were not observed in this second case, suggesting a possible different mechanism of action in inducing OA-like phenotypes. We propose that this vascularized bone model could represent a first step for the in vitro study of bone changes under OA mimicking conditions and possibly serve as a tool in testing anti-OA drugs

Efficient Focusing and Face Detection

We present an algorithm for shape detection and apply it to frontal views of faces in still grey level images with arbitrary backgrounds. Detection is done in two stages: (i) "focusing," during which a relatively small number of regions-of-interest are identified, minimizing computation and false negatives at the (temporary) expense of false positives; and (ii) "intensive classification," during which a selected region-of-interest is labeled face or background based on multiple decision trees and normalized data. In contrast to most detection algorithms, the processing is then very highly concentrated in the regions near faces and near false positives. Focusing is based on spatial arrangements of edge fragments. We first define an enormous family of these, all invariant over a wide range of photometric and geometric transformations. Then, using only examples of faces, we select particular arrangements which are more common in faces than in general backgrounds. The second phase is textu..

Perspective Photometric Stereo with Shadows ⋆

Abstract. High resolution reconstruction of 3D surfaces from images remains an active area of research since most of the methods in use are based on practical assumptions that limit their applicability. Furthermore, an additional complication in all active illumination 3D reconstruction methods is the presence of shadows, whose presence cause loss of information in the image data. We present an approach for the reconstruction of surfaces via Photometric Stereo, based on the perspective formulation of the Shape from Shading problem, solved via partial differential equations. Unlike many photometric stereo solvers that use computationally costly variational methods or a two-step approach, we use a novel, well-posed, differential formulation of the problem that enables us to solve a first order partial differential equation directly via an alternating directions raster scanning scheme. The resulting formulation enables surface computation for very large images and allows reconstruction in the presence of shadows