Crystal image analysis using 2D2D synchrosqueezed transforms

We propose efficient algorithms based on a band-limited version of 2D synchrosqueezed transforms to extract mesoscopic and microscopic information from atomic crystal images. The methods analyze atomic crystal images as an assemblage of non-overlapping segments of 2D general intrinsic mode type functions, which are superpositions of non-linear wave-like components. In particular, crystal defects are interpreted as the irregularity of local energy; crystal rotations are described as the angle deviation of local wave vectors from their references; the gradient of a crystal elastic deformation can be obtained by a linear system generated by local wave vectors. Several numerical examples of synthetic and real crystal images are provided to illustrate the efficiency, robustness, and reliability of our methods.Comment: 27 pages, 17 figure

Combining 2D2D synchrosqueezed wave packet transform with optimization for crystal image analysis

We develop a variational optimization method for crystal analysis in atomic resolution images, which uses information from a 2D synchrosqueezed transform (SST) as input. The synchrosqueezed transform is applied to extract initial information from atomic crystal images: crystal defects, rotations and the gradient of elastic deformation. The deformation gradient estimate is then improved outside the identified defect region via a variational approach, to obtain more robust results agreeing better with the physical constraints. The variational model is optimized by a nonlinear projected conjugate gradient method. Both examples of images from computer simulations and imaging experiments are analyzed, with results demonstrating the effectiveness of the proposed method

Joint methods in imaging based on diffuse image representations

This thesis deals with the application and the analysis of different variants of the Mumford-Shah model in the context of image processing. In this kind of models, a given function is approximated in a piecewise smooth or piecewise constant manner. Especially the numerical treatment of the discontinuities requires additional models that are also outlined in this work. The main part of this thesis is concerned with four different topics. Simultaneous edge detection and registration of two images: The image edges are detected with the Ambrosio-Tortorelli model, an approximation of the Mumford-Shah model that approximates the discontinuity set with a phase field, and the registration is based on these edges. The registration obtained by this model is fully symmetric in the sense that the same matching is obtained if the roles of the two input images are swapped. Detection of grain boundaries from atomic scale images of metals or metal alloys: This is an image processing problem from materials science where atomic scale images are obtained either experimentally for instance by transmission electron microscopy or by numerical simulation tools. Grains are homogenous material regions whose atomic lattice orientation differs from their surroundings. Based on a Mumford-Shah type functional, the grain boundaries are modeled as the discontinuity set of the lattice orientation. In addition to the grain boundaries, the model incorporates the extraction of a global elastic deformation of the atomic lattice. Numerically, the discontinuity set is modeled by a level set function following the approach by Chan and Vese. Joint motion estimation and restoration of motion-blurred video: A variational model for joint object detection, motion estimation and deblurring of consecutive video frames is proposed. For this purpose, a new motion blur model is developed that accurately describes the blur also close to the boundary of a moving object. Here, the video is assumed to consist of an object moving in front of a static background. The segmentation into object and background is handled by a Mumford-Shah type aspect of the proposed model. Convexification of the binary Mumford-Shah segmentation model: After considering the application of Mumford-Shah type models to tackle specific image processing problems in the previous topics, the Mumford-Shah model itself is studied more closely. Inspired by the work of Nikolova, Esedoglu and Chan, a method is developed that allows global minimization of the binary Mumford-Shah segmentation model by solving a convex, unconstrained optimization problem. In an outlook, segmentation of flowfields into piecewise affine regions using this convexification method is briefly discussed

INFLUENCE OF PORE GEOMETRY, PRESSURE AND PARTIAL WATER SATURATION TO ELECTRICAL PROPERTIES OF RESERVOIR ROCK: MODEL AND LABORATORY INVESTIGATION

Pressure and saturation are of two important parameters to be considered to evaluate the electrical properties of reservoir rock. As confining pressure can cause pore space of the rock to collapse and rock properties to change, it is necessary to examine in details how much the pressure and saturation changes affect the electrical properties. Investigations of electrical properties of sandstones and carbonates are the main focus in this work. The effects of pore geometries, confining pressure, and partial water saturation on electrical properties are investigated. The new electrical dispersion models from 0.1 Hz until 0.2 MHz for shaly sandstone are also developed. Petrographic image analysis is carried out to asses pore geometry of the media. Circularity, pore aspect ratio, pore size distribution and pore angle distribution are calculated to evaluate their effect on electrical dispersion. Confining pressure and water saturation observation are then evaluated to obtain their impact on pore structure and complex resistivity. The result of this work shows that surface conductivity plays as a dominant factor particularly in shaly media and it is indicated by electrical resistivity dispersion in low water saturation. When evaluating surface conductivity, the pore geometry has to be considered because large structure is easier to saturate rather than small structure. Moreover, the high water salinity can significantly reduce diffusive layer thickness and if the pore radii are very small, the diffusive layer thickness will touch each other and block the anion movement. In addition to these results, it is found that pore radius distribution provides more contribution to the electrical resistivity dispersion and becomes a basis to extract porosity from resistivity. Confining pressure only contributes small changes in pore geometry of media and the use of imaginary resistivity gives a better detection on it