Representing a 3D shape by a set of 1D curves that are locally symmetric with respect to its boundary (i.e., curve skeletons) is of importance in several machine intelligence tasks. This paper presents a fast, automatic, and robust variational framework for computing continuous, subvoxel accurate curve skeletons from volumetric objects. A reference point inside the object is considered a point source that transmits two wave fronts of different energies. The first front (beta-front) converts the object into a graph, from which the object salient topological nodes are determined. Curve skeletons are tracked from these nodes along the cost field constructed by the second front (alpha-front) until the point source is reached. The accuracy and robustness of the proposed work are validated against competing techniques as well as a database of 3D objects. Unlike other state-of-the-art techniques, the proposed framework is highly robust because it avoids locating and classifying skeletal junction nodes, employs a new energy that does not form medial surfaces, and finally extracts curve skeletons that correspond to the most prominent parts of the shape and hence are less sensitive to noise.

In this paper, we propose a new variational framework for computing continuous curve skeletons from discrete objects that are suitable for structural shape representation. We have derived a new energy function, which is proportional to some medialness function, such that the minimum cost path between any two medial voxels in the shape is a curve skeleton. We have employed two different medialness functions; the Euclidean distance field and a variant of the magnitude of the gradient vector flow (GVF), resulting in two different energy functions. The first energy controls the identification of the shape topological nodes from which curve skeletons start, while the second one controls the extraction of curve skeletons. The accuracy and robustness of the proposed framework are validated both quantitatively and qualitatively against competing techniques as well as several 3D shapes of different complexity.

Curvature-based geometric features have been proven to be important for colonic polyp detection. In this paper, we present an automatic detection framework and color coding scheme to highlight the detected polyps. The key idea is to place the detected polyps at the same locations in a newly created polygonal dataset with the same topology and geometry properties as the triangulated mesh surface of real colon dataset, and assign different colors to the two separated datasets to highlight the polyps. Finally, we validate the proposed framework by computer simulated and real colon datasets. For fifteen synthetic polyps with different shapes and different sizes, the sensitivity is 100%, and false positive is 0. For four real colon datasets, the proposed algorithm has achieved the sensitivity of 75%.

A wide range of computer vision applications require an accurate solution of a particular Hamilton- Jacobi (HJ) equation, known as the Eikonal equation. In this paper, we propose an improved version of the fast marching method (FMM) that is highly accurate for both 2D and 3D Cartesian domains. The new method is called multi-stencils fast marching (MSFM), which computes the solution at each grid point by solving the Eikonal equation along several stencils and then picks the solution that satisfies the upwind condition. The stencils are centered at each grid point and cover its entire nearest neighbors. In 2D space, 2 stencils cover the 8-neighbors of the point, while in 3D space, 6 stencils cover its 26-neighbors. For those stencils that are not aligned with the natural coordinate system, the Eikonal equation is derived using directional derivatives and then solved using higher order finite difference schemes. The accuracy of the proposed method over the state-of-the-art FMM-based techniques has been demonstrated through comprehensive numerical experiments.

A wide range of computer vision applications such as distance field computation, shape from shading, and shape representation require an accurate solution of a particular Hamilton-Jacobi (HJ) equation, known as the Eikonal equation. Although the fast marching method (FMM) is the most stable and consistent method among existing techniques for solving such equation, it suffers from large numerical error along diagonal directions as well as its computational complexity is not optimal. In this paper, we propose an improved version of the FMMthat is both highly accurate and computationally efficient for Cartesian domains. The new method is called the multi-stencils fast marching (MSFM), which computes the solution at each grid point by solving the Eikonal equation along several stencils and then picks the solution that satisfies the fast marching causality relationship. The stencils are centered at each grid point x and cover its entire nearest neighbors. In 2D space, 2 stencils cover the 8-neighbors of x, while in 3D space, 6 stencils cover its 26-neighbors. For those stencils that are not aligned with the natural coordinate system, the Eikonal equation is derived using directional derivatives and then solved using a higher order finite difference scheme.

In this paper, we present a novel framework for computing centerlines for both 2D and 3D shape analysis. The framework works as follows: an object centerline point is selected automatically as the point of global maximum Euclidean distance from the boundary, and is considered a point source (Ps) that transmits a wave front that evolves over time and traverses the object domain. The front propagates at each object point with a speed that is proportional to its Euclidean distance from the boundary. The motion of the front is governed by a nonlinear partial differential equation whose solution is computed efficiently using level set methods. Initially, the P/sub S/ transmits a moderate speed wave to explore the object domain and extract its topological information such as merging and extreme points. Then, it transmits a new front that is much faster at centerline points than non central ones. As a consequence, centerlines intersect the propagating fronts at those points of maximum positive curvature. Centerlines are computed by tracking them, starting from each topological point until the Ps is reached, by solving an ordinary differential equation using an efficient numerical scheme. The proposed method is computationally inexpensive, handles efficiently objects with complex topology, and computes centerlines that are centered, connected, one point thick, and less sensitive to boundary noise. In addition, the extracted paths form a tree graph without additional cost. We have extensively validated the robustness of the proposed method both quantitatively and qualitatively against several 2D and 3D shapes.

In this paper, we propose a general and robust robotic path planning framework for both planar and terrain environments using level set methods. The framework is general in the sense that it can be used for both 2D and 3D environments. It generates a collision-free optimum paths for the entire or a portion of the configuration space. The optimum planned path can be controlled to follow the safest, shortest, or hybrid path. We have demonstrated the robustness of the proposed framework by correctly extracting all planned paths of complex maps with several obstacles.

In this paper, we present an automatic statistical approach for extracting 3D blood vessels from time-of-flight (TOF) magnetic resonance angiography (MRA) data. The voxels of the dataset are classified as either blood vessels or background noise. The observed volume data is modeled by two stochastic processes. The low level process characterizes the intensity distribution of the data across the volume, while the high level process characterizes the statistical dependence among neighboring voxels. 3D Markov random field (MRF) has been employed to model the high level process, whose parameters are estimated using the maximum pseudo likelihood estimator (MPLE). Our proposed model exhibits a good fit to the clinical data and is extensively tested on different synthetic vessel phantoms and several TOF datasets. Experimental results showed that the proposed model is capable of delineating vessels down to 3 voxel diameters.

We have recently developed a level set based-framework for computing medial curves or curve skeletons CS for arbitrary 2D shapes as well as tubular and articulated 3D objects. The proposed framework is robust, fully automatic, computationally efficient, and produces curve skeletons that are connected, centered, thin, and less sensitive to boundary noise. In this paper, we introduce two improvements to the framework in order to enhance its performance in terms of stability and topology preserving.