Multiscale Active Contours

We propose a new multiscale image segmentation model, based on the active contour/snake model and the Polyakov action. The concept of scale, general issue in physics and signal processing, is introduced in the active contour model, which is a well-known image segmentation model that consists of evolving a contour in images toward the boundaries of objects. The Polyakov action, introduced in image processing by Sochen-Kimmel-Malladi in Sochen et al. (1998), provides an efficient mathematical framework to define a multiscale segmentation model because it generalizes the concept of harmonic maps embedded in higher-dimensional Riemannian manifolds such as multiscale images. Our multiscale segmentation model, unlike classical multiscale segmentations which work scale by scale to speed up the segmentation process, uses all scales simultaneously, i.e. the whole scale space, to introduce the geometry of multiscale images in the segmentation process. The extracted multiscale structures will be useful to efficiently improve the robustness and the performance of standard shape analysis techniques such as shape recognition and shape registration. Another advantage of our method is to use not only the Gaussian scale space but also many other multiscale spaces such as the Perona-Malik scale space, the curvature scale space or the Beltrami scale space. Finally, this multiscale segmentation technique is coupled with a multiscale edge detecting function based on the gradient vector flow model, which is able to extract convex and concave object boundaries independent of the initial condition. We apply our multiscale segmentation model on a synthetic image and a medical imag

3D Image Based Structural Analysis of Leather for Macroscopic Structure- Property Simulation

Content: The intrinsic structure significantly influences the mechanical properties of leather. In consequence, knowledge of leather’s hierarchical structure is essential in order to find the most suited leather for specific application. Leather structure based parameters are of major importance for both manufacturing and leather processing industries. In this respect, intensive structure investigations have been subjected in continuous research work. Quantitative image analysis combined with stochastic micro-structure modelling and numerical simulation of macroscopic properties is a promising approach to gain a deeper understanding of complex relations between material’s micro-structure geometry and macroscopic properties. Key ingredient is a reliable geometric description provided by the quantitative analysis of 3D images of the material micro-structures. For leather, both imaging and image analysis are particularly challenging, due to the multi-scale nature of the leather’s micro-structure. Scales in leather are not well separated. Previously, high resolution computed tomography allowed 3D imaging of purely vegetable tanned leather samples at micro- and submicro- scale. Segmentation of leather structure as well as of typical structural elements in resulting image data is however hampered by a strong heterogeneity caused by lower scale structural information. The first method for automatic segmentation of typical structural elements at varying scales combined morphological smoothing with defining and iteratively coarsening regions using the waterfall algorithm on local orientations. It yields a hierarchical segmentation of the leather into coarse and fine structural elements that can be used to analyze and compare the structure of leather samples. Size and shape of the structural elements as well as their sub-structure yield information, e. g. on undulation, branching, thickness, cross-sectional shape, and preferred directions. In order to compare the micro-structure of leather samples from various body parts or even species, the segmentation has to be applicable without extensive pre-processing and parameter tuning. Robustness can be gained by applying smoothing methods that are adapted to the goal of defining image regions by similar local orientation. The challenge is that the space of fiber orientations in 3D is not equipped with an order. Motivated by a recent approach for nevertheless defining erosion and dilation on the sphere, we suggest new definitions for these morphological base transformations on the space of directions in 3D. We present segmentation results for 3D images of leather samples derived by these new morphological smoothing methods. Take-Away: The intrinsic structure significantly influences the mechanical properties of leather. Leather’s hierarchical structure can be analyzed by quantitative 3D image analysis combined with stochastic micro-structure modelling. Segmentation results for 3D images of leather samples derived by new morphological smoothing methods

Micro-computed tomography pore-scale study of flow in porous media: Effect of voxel resolution

A fundamental understanding of flow in porous media at the pore-scale is necessary to be able to upscale average displacement processes from core to reservoir scale. The study of fluid flow in porous media at the pore-scale consists of two key procedures: Imaging - reconstruction of three-dimensional (3D) pore space images; and modelling such as with single and two-phase flow simulations with Lattice-Boltzmann (LB) or Pore-Network (PN) Modelling. Here we analyse pore-scale results to predict petrophysical properties such as porosity, single-phase permeability and multi-phase properties at different length scales. The fundamental issue is to understand the image resolution dependency of transport properties, in order to up-scale the flow physics from pore to core scale. In this work, we use a high resolution micro-computed tomography (micro-CT) scanner to image and reconstruct three dimensional pore-scale images of five sandstones (Bentheimer, Berea, Clashach, Doddington and Stainton) and five complex carbonates (Ketton, Estaillades, Middle Eastern sample 3, Middle Eastern sample 5 and Indiana Limestone 1) at four different voxel resolutions (4.4 µm, 6.2 µm, 8.3 µm and 10.2 µm), scanning the same physical field of view. Implementing three phase segmentation (macro-pore phase, intermediate phase and grain phase) on pore-scale images helps to understand the importance of connected macro-porosity in the fluid flow for the samples studied. We then compute the petrophysical properties for all the samples using PN and LB simulations in order to study the influence of voxel resolution on petrophysical properties. We then introduce a numerical coarsening scheme which is used to coarsen a high voxel resolution image (4.4 µm) to lower resolutions (6.2 µm, 8.3 µm and 10.2 µm) and study the impact of coarsening data on macroscopic and multi-phase properties. Numerical coarsening of high resolution data is found to be superior to using a lower resolution scan because it avoids the problem of partial volume effects and reduces the scaling effect by preserving the pore-space properties influencing the transport properties. This is evidently compared in this study by predicting several pore network properties such as number of pores and throats, average pore and throat radius and coordination number for both scan based analysis and numerical coarsened data