Quantitative textural analysis of sedimentary grains and basin subsidence modelling

Part 1: Quantitative textural analysis Shape analysis can provide important information regarding the origin, transport and deposition history of grains. Particle shape measurement has been an active area of research for sedimentologists since the 20th century. However, there is a lack of standardised methodology for quantitative characterisation of grain shapes. The main objective of this work is to develop methodologies that can be used by sedimentologists for quantitative textural analysis of grains such that the results obtained are comparable. A modular suite of code written in the Mathematica environment for the quantitative characterisation of sedimentary grains in 2- dimensions is presented. This image analysis package can be used to analyse consolidated as well as loose sediment samples. Using newly implemented image analysis methods, 20 loose sediment samples from four known depositional environments (beach, aeolian, glacial and fluvial) were analysed. This research aims to identify the most useful shape parameters for textural characterisation of populations of grains and determine the relative importance of the parameters. A key aspect of this study is to determine whether, in a particular sedimentary environment, textural maturity of the samples can be ranked based on their grain shape data. Furthermore, discrimination of sedimentary depositional environments is explored on the basis of grain shape. The available shape parameters suffer from a common shortcoming that particles, which are visually distinct, are not differentiated. To address this issue, the Inverse Radius of Curvature (IRC) plot which can be used to identify corners and measure their sharpness is introduced. Using the IRC plot, four shape parameters are proposed: number of corners, cumulative angularity, sharpest corner and straight fraction. This methodology is applied to a 4000 sand grain dataset. The textural analysis software package developed here allow users to quantitatively characterise large set of grains with a fast, cheap and robust methodology. This study indicate that textural maturity is readily categorised using automated grain shape parameter analysis. However, it is not possible to absolutely discriminate between different depositional environments on the basis of shape parameters alone. The four new shape parameters proposed here based on the IRC plot can be collectively used to quantitatively describe grains shape which correlates closely with visual perceptions. This work opens up the possibility of using detailed quantitative textural dataset of sediment grains along with other standard analyses (mineralogy, bulk composition, isotopic analysis, etc) for diverse sedimentary studies. Part 2: Basin modelling Subsidence modelling is an important part of basin analysis to better understand the tectonic evolution of sedimentary basins. The McKenzie model has been widely applied for subsidence modelling and stretching factor estimation for sedimentary basins formed in an extensional tectonic environment. In this contribution, a numerical model is presented that takes into account the effect of sedimentary cover on stretching factor estimation. Subsidence modelling requires values of physical parameters (crustal thickness, lithospheric thickness, stretching factor, etc.) which may not be always available. With a given subsidence history of a basin estimated using a stratigraphic backstripping method, these parameters can be estimated by quantitatively comparing the known subsidence curve with modelled subsidence curves. In this contribution, a method to compare known and modelled subsidence curves is presented aiming to constrain valid combinations of stretching factor, crustal thickness and lithospheric thickness of a basin. The parameter fitting method presented here is first applied to synthetically generated subsidence curves. Next, a case study using a known subsidence curve from the Campos Basin, offshore Brazil is considered. The range of stretching factors estimated for the Campos basin from this study is in accordance with previous work, with an additional estimate of corresponding lithospheric thickness. This study provides insights into the dependence of subsidence modelling methods on assumptions about input parameters as well as allowing for the estimation of valid combinations of physical lithospheric parameters, where the subsidence history is known

Interactive Brain Tumor Segmentation with Inclusion Constraints

This thesis proposes an improved interactive brain tumor segmentation method based on graph cuts, which is an efficient global optimization framework for image segmentation, and star shape, which is a general segmentation shape prior with minimal user assistance. Our improvements lie in volume ballooning, compactness measure and inclusion constraints. Volume ballooning is incorporated to help to balloon segmentation for situations where the foreground and background have similar appearance models and changing relative weight between appearance model and smoothness term cannot help to achieve an accurate segmentation. We search different ballooning parameters for different slices since an appropriate ballooning force may vary between slices. As the evaluation for goodness of segmentation in parameter searching, two new compactness measures are introduced, ellipse fitting and convexity deviation. Ellipse fitting is a measure of compactness based on the deviation from an ellipse of best fit, which prefers segmentation with an ellipse shape. And convexity deviation is a more strict measure for preferring convex segmentation. It uses the number of convexity violation pixels as the measure for compactness. Inclusion constraints is added between slices to avoid side slice segmentation larger than the middle slice problem. The inclusion constraints consist of mask inclusion, which is implemented by an unary term in graph cuts, and pairwise inclusion, which is implemented by a pairwise term. Margin is allowed in inclusion so that the inclusion region is enlarged. With all these improvements, the final result is promising. The best performance for our dataset is 88% compared to the previous system that achieved 87%

A graph theoretic approach to scene matching

The ability to match two scenes is a fundamental requirement in a variety of computer vision tasks. A graph theoretic approach to inexact scene matching is presented which is useful in dealing with problems due to imperfect image segmentation. A scene is described by a set of graphs, with nodes representing objects and arcs representing relationships between objects. Each node has a set of values representing the relations between pairs of objects, such as angle, adjacency, or distance. With this method of scene representation, the task in scene matching is to match two sets of graphs. Because of segmentation errors, variations in camera angle, illumination, and other conditions, an exact match between the sets of observed and stored graphs is usually not possible. In the developed approach, the problem is represented as an association graph, in which each node represents a possible mapping of an observed region to a stored object, and each arc represents the compatibility of two mappings. Nodes and arcs have weights indicating the merit or a region-object mapping and the degree of compatibility between two mappings. A match between the two graphs corresponds to a clique, or fully connected subgraph, in the association graph. The task is to find the clique that represents the best match. Fuzzy relaxation is used to update the node weights using the contextual information contained in the arcs and neighboring nodes. This simplifies the evaluation of cliques. A method of handling oversegmentation and undersegmentation problems is also presented. The approach is tested with a set of realistic images which exhibit many types of sementation errors