Robust curvature extrema detection based on new numerical derivation

International audienceExtrema of curvature are useful key points for different image analysis tasks. Indeed, polygonal approximation or arc decomposition methods used often these points to initialize or to improve their algorithms. Several shape-based image retrieval methods focus also their descriptors on key points. This paper is focused on the detection of extrema of curvature points for a raster-to-vector-conversion framework. We propose an original adaptation of an approach used into nonlinear control for fault-diagnosis and fault-tolerant control based on algebraic derivation and which is robust to noise. The experimental results are promising and show the robustness of the approach when the contours are bathed into a high level speckled noise

Localization of transversal cracks in sandwich beams and evaluation of their severity

An algorithm to assess transversal cracks in composite structures based on natural frequency changes due to damage is proposed. The damage assessment is performed in two steps; first the crack location is found, and afterwards an evaluation of its severity is performed. The technique is based on a mathematical relation that provides the exact solution for the frequency changes of bending vibration modes, considering two terms. The first term is related to the strain energy stored in the beam, while the second term considers the increase of flexibility due to damage. Thus, it is possible to separate the problems of localization and severity assessment, which makes the localization process independent of the beams cross-section shape and boundary conditions. In fact, the process consists of comparing vectors representing the measured frequency shifts with patterns constructed using the mode shape curvatures of the undamaged beam. Once the damage is localized, the evaluation of its severity is made taking into account the global rigidity reduction. The damage identification algorithm was validated by experiments performed on numerous sandwich panel specimens

Perceptual Color Image Smoothing via a New Region-Based PDE Scheme

In this paper, we present a new color image regularization method using a rotating smoothing filter. This approach combines a pixel classification method, which roughly determines if a pixel belongs to a homogenous region or an edge with an anisotropic perceptual edge detector capable of computing two precise diffusion directions. Using a now classical formulation, image regularization is here treated as a variational model, where successive iterations of associated PDE (Partial Differential Equation) are equivalent to a diffusion process. Our model uses two kinds of diffusion: isotropic and anisotropic diffusion. Anisotropic diffusion is accurately controlled near edges and corners, while isotropic diffusion is applied to smooth regions either homogeneous or corrupted by noise. A comparison of our approach with other regularization methods applied on real images demonstrate that our model is able to efficiently restore images as well as handle diffusion, and at the same time preserve edges and corners well

The three dimensional skeleton: tracing the filamentary structure of the universe

The skeleton formalism aims at extracting and quantifying the filamentary structure of the universe is generalized to 3D density fields; a numerical method for computating a local approximation of the skeleton is presented and validated here on Gaussian random fields. This method manages to trace well the filamentary structure in 3D fields such as given by numerical simulations of the dark matter distribution on large scales and is insensitive to monotonic biasing. Two of its characteristics, namely its length and differential length, are analyzed for Gaussian random fields. Its differential length per unit normalized density contrast scales like the PDF of the underlying density contrast times the total length times a quadratic Edgeworth correction involving the square of the spectral parameter. The total length scales like the inverse square smoothing length, with a scaling factor given by 0.21 (5.28+ n) where n is the power index of the underlying field. This dependency implies that the total length can be used to constrain the shape of the underlying power spectrum, hence the cosmology. Possible applications of the skeleton to galaxy formation and cosmology are discussed. As an illustration, the orientation of the spin of dark halos and the orientation of the flow near the skeleton is computed for dark matter simulations. The flow is laminar along the filaments, while spins of dark halos within 500 kpc of the skeleton are preferentially orthogonal to the direction of the flow at a level of 25%.Comment: 17 pages, 11 figures, submitted to MNRA