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Representing a 3D shape by a set of one-dimensional curves, that are locally symmetric with respect to its boundary (i.e., curve skeletons) is of importance in several applications such as object matching and retrieval, virtual endoscopy, character animation and morphing, medical image analysis of tubular structures, and collision detection. In this project, we propose a fast, automatic, and robust variational framework for computing continuous, sub-voxel accurate curve skeletons from volumetric objects that are represented by closed manifolds. Unlike the state-of-the-art techniques, the proposed framework is highly robust because it avoids locating and classifying the skeleton junction points, employs a new energy that does not form medial surfaces, and finally starts curve skeletons from those nodes that correspond to the most prominent parts of the shape, and hence less sensitive to noise. The accuracy and robustness of the proposed framework are validated both quantitatively and qualitatively against competing techniques as well as a database of 3D objects.

CVPR'05  -  ICCV'07 -  PAMI'08                                             » more

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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 project, 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.

CVPR'06  -  PAMI'07                                                                » more

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In this project, we propose a new PDE-based method for extracting the shape salient nodes that correspond to its prominent parts. The method is highly robust to boundary noise and works for both 2D and  3D. The key idea is to propagate inside the object a monotonic wave front, whose motion is governed by the Eikonal equation, such that it divides the object into a set of adjacent clusters that are normal to the shape curve skeletons or symmetry axis. These clusters are then converted into a graph, from which the shape prominent nodes are easily found.


CVPR'05                                                                                     » more

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In this project, we propose a new visualization technique, known as Virtual Fly-Over for virtual colonoscopy (VC). The proposed method splits the entire colon anatomy into exactly two halves. Then, it assigns a virtual camera to each half to perform fly-over 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 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, or at sharp corners, are less likely to be overlooked. Finally, because the orientation of the splitting surface is controllable, navigation can be repeated at a different split orientation, for the current colon segment, to overcome the problem of having a polyp that is divided between the two colon halves. We have quantitatively validated the effectiveness of the proposed method and have found that the average surface visibility coverage is 99.59±0.2%

MICCAI'06 - SPIE'06                                                                » more

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Large numbers of people suffer a major cerebrovascular event, usually a stroke, each year. Serious types of vascular diseases such as carotid stenosis, aneurysms, and arterio-venous malformations (AVM) may lead to brain stroke unless they are detected at early stages. This project proposes 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, while the high level process characterizes their statistical dependence among neighboring voxels. The low level process of the background signal is modeled by a finite mixture of one Rayleigh and two normal distributions, while the blood vessels are modeled by one normal distribution. The high level process is modeled as a 3D Markov random field (MRF). Experimental results on phantoms and clinical datasets have showed that the proposed model provides good quality of segmentation and is capable of delineating vessels down to 3 voxel diameters.

MICCAI'03  -  MEDIA'06                                                          » more

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Colorectal colon cancer (CCC) is the third most common form of cancer and the second leading cause of death among cancers in the western world. Colonoscopy is the current gold standard screening test, in which a thin flexible fiber optic endoscope is inserted into the patient’s rectum to inspect the entire colon for potential polyps. Although colonoscopy can detect more than 90% of CCC, it is invasive, uncomfortable, and inconvenient. On the contrary, virtual colonoscopy (VC) is a computer based alternative to real colonoscopy, in which a virtual camera with a specific field of view moves along a special planned path inside the colon to render its internal views. In this project, we propose a new centerline extraction technique for tubular structures that is highly centered, connected, and thin. Hence, it can be used reliably as a flight path for navigation.

IPMI'05  -  MICCAI'05                                                              » more

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In robotic navigation, path planning is aimed at getting the optimum collision-free path between a starting and target locations. The optimality criterion depends on the surrounding environment and the running conditions. In this project, we propose a general, robust, and fast path planning framework for robotic navigation using level set methods. A level set speed function is proposed such that the minimum cost path between the starting and target locations in the environment, is the optimum planned path. The speed function is controlled by one parameter, which takes one of three possible values to generate either the safest, the shortest, or the hybrid planned path. The hybrid path is much safer than the shortest path, but less shorter than the safest one. The framework supports both local and global planning for for both 2D and 3D environments. The robustness of the proposed framework is demonstrated by correctly extracting planned paths of complex maps.

This project is funded by NASA.

CRV'05  -  IMAVIS'07                                                               » more

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A hand-held surgical probe is an essential component of any image-guided neurosurgery system (IGNS). During the surgical procedure, the IGNS tracks the probe position and displays the anatomy beneath it as three orthogonal image slices on a workstation-based 3D imaging system. Existing IGNS systems use different tracking techniques including mechanical, optical, ultrasonic, and electromagnetic. This project presents a new computational vision-based probe tracking technique, which provides its position and orientation. Also, it proposes another new computational vision based technique to track the patient head and thus compensates for its movement during probing procedure. The proposed system is completely passive, works in real time, and has been validated using a skull phantom, rotating table driven by a stepper motor, and a hand made probe.

CARS'04                                                                                     » more

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