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.

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.

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The high increase in the number of companies competing in mature markets makes customer retention an important factor for any company to survive. Thus, many methodologies (e.g., data mining and statistics) have been proposed to analyse and study customer retention. The validity of such methods is not yet proved though. This paper tries to fill this gap by empirically comparing two techniques: Customer churn -decision tree and logistic regression models. The paper proves the superiority of decision tree technique and stresses the needs for more advanced methods to churn modelling.

In this paper, we propose a new visualization technique for virtual colonoscopy (VC). The proposed method is called Virtual FlyOver , which splits the entire colon anatomy into exactly two halves. Then, it assigns a virtual camera to each half to perform flyover navigation, which has several advantages over both traditional fly-through and related methods. First, by controlling the elevation of the camera, there is no restriction on its field of view (FOV) angle (e.g., > 90 o) to maximize visualized surface areas, and hence no perspective distortion. Second, the camera viewing volume is perpendicular to each colon half, so potential polyps that are hidden behind haustral folds are easily found. Finally, because the orientation of the splitting surface is controllable, the navigation can be repeated at a different split orientation to overcome the problem of having a polyp that is divided between the two halves of the colon. Quantitative experimental results on 15 clinical datasets have shown that the average surface visibility coverage is 99.59±0.2%.

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In this paper, we propose a new variational framework based on distance transform and gradient vector flow, to compute flight paths through tubular and non-tubular structures, for virtual endoscopy. The proposed framework propagates two wave fronts of different speeds from a point source voxel, which belongs to the medial curves of the anatomical structure. The first wave traverses the 3D structure with a moderate speed that is a function of the distance field to extract its topology, while the second wave propagates with a higher speed that is a function of the magnitude of the gradient vector flow to extract the flight paths. The motion of the fronts are governed by a nonlinear partial equation, whose solution is computed efficiently using the higher accuracy fast marching level set method (HAFMM). The framework is robust, fully automatic, and computes flight paths that are centered, connected, thin, and less sensitive to boundary noise. We have validated the robustness of the proposed method both quantitatively and qualitatively against synthetic and clinical datasets.