3D parametric deformable models have been used to extract volumetric object boundaries and they generate smooth boundary surfaces as results. However, in some segmentation cases, such as cerebral cortex with complex folds and creases, and human lung with high curvature boundary, parametric deformable models often suffer from over-smoothing or decreased mesh quality during model deformation. To address this problem, we propose a 3D Laplacian-driven parametric deformable model with a new internal force. Derived from a Mesh Laplacian, the internal force exerted on each control vertex can be decomposed into two orthogonal vectors based on the vertex's tangential plane. We then introduce a weighting function to control the contributions of the two vectors based on the model mesh's geometry. Deforming the new model is solving a linear system, so the new model can converge very efficiently. To validate the model's performance, we tested our method on various segmentation cases and compared our model with Finite Element and Level Set deformable models.

In this paper, we introduce a novel method to solve shape alignment problems. We use gray-scale "images" to represent source shapes, and propose a novel two-component Gaussian Mixture (GM) distance map representation for target shapes. This asymmetric representation is a flexible image-based representation which is able to represent different kinds of shape data, including continuous contours, unstructured sparse point sets, edge maps, and even gray-scale gradient maps. Using this representation, a new energy function based on a novel two-component Gaussian Mixture distance model is proposed. The new energy function was empirically evaluated to be a more robust shape dissimilarity metric that can be computed efficiently. Such high efficiency is essential for global optimization methods. We adopt and modify one of them, the Particle Swarm Optimization (PSO), to effectively estimate the global optimum of the new energy function. Differently from the original PSO, several new strategies were employed to make the optimization more robust and prevent it from converging prematurely. The overall performance of the proposed framework as well as the properties of each algorithmic component were evaluated and compared with those of some state-of-the-art methods. Extensive experiments and comparison performed on generalized 2D and 3D shape data demonstrate the robustness and effectiveness of the method.

In this paper, we propose a novel predictive model, active volume model (AVM), for object boundary extraction. It is a dynamic "object" model whose manifestation includes a deformable curve or surface representing a shape, a volumetric interior carrying appearance statistics, and an embedded classifier that separates object from background based on current feature information. The model focuses on an accurate representation of the foreground object's attributes, and does not explicitly represent the background. As we will show, however, the model is capable of reasoning about the background statistics thus can detect when is change sufficient to invoke a boundary decision. When applied to object segmentation, the model alternates between two basic operations: 1) deforming according to current region of interest (ROI), which is a binary mask representing the object region predicted by the current model, and 2) predicting ROI according to current appearance statistics of the model. To further improve robustness and accuracy when segmenting multiple objects or an object with multiple parts, we also propose multiple-surface active volume model (MSAVM), which consists of several single-surface AVM models subject to high-level geometric spatial constraints. An AVM's deformation is derived from a linear system based on finite element method (FEM). To keep the model's surface triangulation optimized, surface remeshing is derived from another linear system based on Laplacian mesh optimization (LMO). Thus efficient optimization and fast convergence of the model are achieved by solving two linear systems. Segmentation, validation and comparison results are presented from experiments on a variety of 2-D and 3-D medical images.

We present a novel method for 3D brain tumor volume segmentation based on a parallel cellular automata framework. Our method incorporates prior label knowledge gathered from user seed information to influence the cellular automata decision rules. Our proposed method is able to segment brain tumor volumes quickly and accurately using any number of label classifications. Exploiting the inherent parallelism of our algorithm, we adopt this method to the Graphics Processing Unit (GPU). Additionally, we introduce the concept of individual label strength maps to visualize the improvements of our method. As we demonstrate in our quantitative and qualitative results, the key benefits of our system are accuracy, robustness to complex structures, and speed. We compute segmentations nearly 45× faster than conventional CPU methods, enabling user feedback at interactive rates.

In this paper, we introduce a novel algorithm to solve global shape registration problems. We use gray-scale “images” to represent source shapes, and propose a novel two-component Gaussian Mixtures (GM) distance map representation for target shapes. Based on this flexible asymmetric image-based representation, a new energy function is defined. It proves to be a more robust shape dissimilarity metric that can be computed efficiently. Such high efficiency is essential for global optimization methods. We adopt one of them, the Particle Swarm Optimization (PSO), to effectively estimate the global optimum of the new energy function. Experiments and comparison performed on generalized shape data including continuous shapes, unstructured sparse point sets, and gradient maps, demonstrate the robustness and effectiveness of the algorithm.

In this paper, we propose a novel predictive model for object boundary, which can integrate information from any sources. The model is a dynamic “object” model whose manifestation includes a deformable surface representing shape, a volumetric interior carrying appearance statistics, and an embedded classifier that separates object from background based on current feature information. Unlike Snakes, Level Set, Graph Cut, MRF and CRF approaches, the model is “self-contained” in that it does not model the background, but rather focuses on an accurate representation of the foreground object's attributes. As we will show, however, the model is capable of reasoning about the background statistics thus can detect when is change sufficient to invoke a boundary decision. The shape of the 3D model is considered as an elastic solid, with a simplex-mesh (i.e. finite element triangulation) surface made of thousands of vertices. Deformations of the model are derived from a linear system that encodes external forces from the boundary of a Region of Interest (ROI), which is a binary mask representing the object region predicted by the current model. Efficient optimization and fast convergence of the model are achieved using the Finite Element Method (FEM). Other advantages of the model include the ease of dealing with topology changes and its ability to incorporate human interactions. Segmentation and validation results are presented for experiments on noisy 3D medical images.

Abstract We propose a novel shape‐constrained flock animation system for interactively controlling flock navigation in virtual environments. This system is capable of making the spatial distribution of a flock meet static or deforming shape constraints while performing flock simulation. Such a capability can find many applications in the entertainment industry. Given a 3D constraining shape, our system first draws a set of uniform sample points through a 3D surface mosaicing process or a stratified point sampling strategy. Once correspondences between flock members and sample points have been established, points on the target shape are used as homing destinations to guide flock migration. Under a global path control scheme, an effective fuzzy control logic, which dynamically adjusts steering forces and control forces, has been developed to create visually pleasing shape‐constrained flock animations. Copyright © 2008 John Wiley & Sons, Ltd.