Geometrically Induced Force Interaction for Three-Dimensional Deformable Models

This work introduces a novel 3D deformable model that is based on a geometrically induced external force field, which can be conveniently generalised to arbitrary dimensions. This external force field is based on hypothesised interactions between the relative geometries of the deformable model and the object boundary. The relative geometrical configurations contribute to a dynamic vector force field that changes accordingly as the deformable model evolves. In addition, we show that by enhancing the geometrical interaction field with a nonlocal edge preserving algorithm, the new model can effectively overcome image noise. We provide a comprehensive comparative study and show that the proposed method achieves significant improvements against existing techniques

Active Contouring Based on Gradient Vector Interaction and Constrained Level Set Diffusion

This paper addresses an important issue in deformable modeling: initialisation dependency for edge-based models. To the best of our knowledge, this is the first edge-based deformable method that can achieve practical initialisation invariance. It can handle more sophisticated topological changes than splitting and merging. It provides new potentials for edge-based active contour methods, particularly when detecting and localising objects with unknown location, geometry, and topology

The Potential of Active Contour Models in Extracting Road Edges from Mobile Laser Scanning Data

Active contour models present a robust segmentation approach, which makes efficient use of specific information about objects in the input data rather than processing all of the data. They have been widely-used in many applications, including image segmentation, object boundary localisation, motion tracking, shape modelling, stereo matching and object reconstruction. In this paper, we investigate the potential of active contour models in extracting road edges from Mobile Laser Scanning (MLS) data. The categorisation of active contours based on their mathematical representation and implementation is discussed in detail. We discuss an integrated version in which active contour models are combined to overcome their limitations. We review various active contour-based methodologies, which have been developed to extract road features from LiDAR and digital imaging datasets. We present a case study in which an integrated version of active contour models is applied to extract road edges from MLS dataset. An accurate extraction of left and right edges from the tested road section validates the use of active contour models. The present study provides valuable insight into the potential of active contours for extracting roads from 3D LiDAR point cloud data

Implicit deformable models for biomedical image segmentation.

In this thesis, new methods for the efficient segmentation of images are presented. The proposed methods are based on the deformable model approach, and can be used efficiently in the segmentation of complex geometries from various imaging modalities. A novel deformable model that is based on a geometrically induced external force field which can be conveniently generalized to arbitrary dimensions is presented. This external force field is based on hypothesized interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient. The evolution of the deformable model is solved using the level set method so that topological changes are handled automatically. The relative geometrical configurations between the deformable model and the object boundaries contributes to a dynamic vector force field that changes accordingly as the deformable model evolves. The geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries, and give the deformable model a high invariance in initialization configurations. The voxel interactions across the whole image domain provides a global view of the object boundary representation, giving the external force a long attraction range. The bidirectionality of the external force held allows the new deformable model to deal with arbitrary cross-boundary initializations, and facilitates the handling of weak edges and broken boundaries. In addition, it is shown that by enhancing the geometrical interaction field with a nonlocal edge-preserving algorithm, the new deformable model can effectively overcome image noise. A comparative study on the segmentation of various geometries with different topologies from both synthetic and real images is provided, and the proposed method is shown to achieve significant improvements against several existing techniques. A robust framework for the segmentation of vascular geometries is described. In particular, the framework consists of image denoising, optimal object edge representation, and segmentation using implicit deformable model. The image denoising is based on vessel enhancing diffusion which can be used to smooth out image noise and enhance the vessel structures. The image object boundaries are derived using an edge detection technique which can produce object edges of single pixel width. The image edge information is then used to derive the geometric interaction field for optimal object edge representation. The vascular geometries are segmented using an implict deformable model. A region constraint is added to the deformable model which allows it to easily get around calcified regions and propagate across the vessels to segment the structures efficiently. The presented framework is ai)plied in the accurate segmentation of carotid geometries from medical images. A new segmentation model with statistical shape prior using a variational approach is also presented in this thesis. The proposed model consists of an image attraction force that propagates contours towards image object boundaries, and a global shape force that attracts the model towards similar shapes in the statistical shape distribution. The image attraction force is derived from gradient vector interactions across the whole image domain, which makes the model more robust to image noise, weak edges and initializations. The statistical shape information is incorporated using kernel density estimation, which allows the shape prior model to handle arbitrary shape variations. It is shown that the proposed model with shape prior can be used to segment object shapes from images efficiently

Discrete Element Modeling of the Grading- and Shape-Dependent Behavior of Granular Materials

Granular materials, such as sand, biomass particles, and pharmaceutical pills, are widespread in nature, industrial systems, and our daily life. Fundamentally, the bulk mechanical behavior of such materials is governed by the physical and morphological features of and the interactions among constituent particles at the microscopic scale. From a modeling standpoint, the particle-based discrete element method (DEM) has emerged as the most prevalent numerical tool to model and study the behavior of granular materials and the systems they form. A critical step towards an accurate and predictive DEM model is to incorporate those physical and morphological features (e.g., particle size, shape, and deformability) pertaining to the constituent particles. The main objective of this dissertation is to approach an accurate characterization and modeling of the grading- and shape-dependent behavior of granular materials by developing DEM models that incorporate realistic physical and morphological features of granular particles. Revolving around this objective, three studies are presented: image-based particle reconstruction and morphology characterization, grading and shape-dependent shearing behavior of rigid-particle systems, and granular flow of deformable irregular particles. The first study presents a machine learning and level-set based framework to re- construct granular particles and to characterize particle morphology from X-ray computed tomography (X-ray CT) imaging of realistic granular materials. Images containing detailed microstructure information of a granular material are obtained using the X-ray CT tech- nique. Approaches such as the watershed method in two dimensions (2D) and the combined machine learning and level set method in three dimensions (3D) are then utilized and implemented to segment X-ray CT images and to numerically reconstruct individual particles in the granular material. Based on the realistic particle shapes, particle morphology is characterized by descriptors including aspect ratio, roundness, circularity (2D) or sphericity (3D). The particle shapes or morphology provide important constraints to develop DEM models with particle physical and morphological features conforming to the specific granular material of interest. In the second study, DEM models incorporated with realistic particle sizes and shapes are developed and applied to study the shearing behavior of sandy soils. The particle sizes and shapes are obtained from realistic samples of JSC-1A Martian regolith simulant. Irregular-shape particles are represented by rigid clumps based on the domain overlapping filling method. The effects of particle shape irregularity on the shearing behavior of granular materials are investigated through direct shear tests, along with the comparisons from spherical particles with or without rolling resistance. The micro-mechanisms of shape irregularity contributing to the shear resistance are identified. The last study investigates the effects of particle deformability (e.g., compression, deflection or torsion), together with particle sizes and shapes, on the granular flow of flexible granular materials. A bonded-sphere DEM model is implemented with the capability of embodying various particle sizes and irregular shapes, as well as capturing particle deformability. This approach is then applied to simulate and study the behavior of flexible granular materials in cyclic compression and hopper flow tests. The effects of particle size, shape and deformability on the bulk mechanical behavior are investigated on the basis of the DEM simulation results. The importance of particle deformability to the DEM simulations of flexible granular materials is demonstrated