Semi-automatic 3D construction of liver using single view CT images
16 Mar 2012-pp 157-158
TL;DR: This work segment the liver from CT images using the distance regularized edge based level set method and demonstrates the application of the developed algorithm in performing 3D construction of liver using only the axial slices from the abdominal CT scan.
Abstract: Liver is the largest and most important organ within the human body. It is important to detect if any abnormality lies in the liver and aid surgeons in their planning before performing the surgery. In our work, we segment the liver from CT images using the distance regularized edge based level set method and demonstrate the application of the developed algorithm in performing 3D construction of liver using only the axial slices from the abdominal CT scan. The 3D construction of liver is achieved by stacking the evolved contours of individual slices over one another. The initialization is done by evolving the initial input contour to the liver boundaries. The above resulting contour then behaves as the initial contour for the adjacent slices, thereby making this process a semi-automatic one. By controlling certain parameters such as the number of iterations, standard deviation and window size of the Gaussian blurring kernel an optimal segmentation result can be generated and no interfacing with third party toolkit is required.
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TL;DR: In this article, the authors proposed a shape model based on the Hamilton-Jacobi approach to shape modeling, which retains some of the attractive features of existing methods and overcomes some of their limitations.
Abstract: Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods and overcomes some of their limitations. The authors' techniques can be applied to model arbitrarily complex shapes, which include shapes with significant protrusions, and to situations where no a priori assumption about the object's topology is made. A single instance of the authors' model, when presented with an image having more than one object of interest, has the ability to split freely to represent each object. This method is based on the ideas developed by Osher and Sethian (1988) to model propagating solid/liquid interfaces with curvature-dependent speeds. The interface (front) is a closed, nonintersecting, hypersurface flowing along its gradient field with constant speed or a speed that depends on the curvature. It is moved by solving a "Hamilton-Jacobi" type equation written for a function in which the interface is a particular level set. A speed term synthesized from the image is used to stop the interface in the vicinity of object boundaries. The resulting equation of motion is solved by employing entropy-satisfying upwind finite difference schemes. The authors present a variety of ways of computing the evolving front, including narrow bands, reinitializations, and different stopping criteria. The efficacy of the scheme is demonstrated with numerical experiments on some synthesized images and some low contrast medical images. >
3,039 citations
TL;DR: A new variational level set formulation in which the regularity of the level set function is intrinsically maintained during thelevel set evolution called distance regularized level set evolution (DRLSE), which eliminates the need for reinitialization and thereby avoids its induced numerical errors.
Abstract: Level set methods have been widely used in image processing and computer vision. In conventional level set formulations, the level set function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore, a numerical remedy, called reinitialization, is typically applied to periodically replace the degraded level set function with a signed distance function. However, the practice of reinitialization not only raises serious problems as when and how it should be performed, but also affects numerical accuracy in an undesirable way. This paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution. The level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations. The distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level set function, particularly a signed distance profile near the zero level set. This yields a new type of level set evolution called distance regularized level set evolution (DRLSE). The distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors. In contrast to complicated implementations of conventional level set formulations, a simpler and more efficient finite difference scheme can be used to implement the DRLSE formulation. DRLSE also allows the use of more general and efficient initialization of the level set function. In its numerical implementation, relatively large time steps can be used in the finite difference scheme to reduce the number of iterations, while ensuring sufficient numerical accuracy. To demonstrate the effectiveness of the DRLSE formulation, we apply it to an edge-based active contour model for image segmentation, and provide a simple narrowband implementation to greatly reduce computational cost.
1,947 citations
"Semi-automatic 3D construction of l..." refers background or methods in this paper
...The level set contour evolves on the basis of minimizing an energy function that is defined as [3]: ( ) ( ) ( ) ( ) f D f L f A f ε μ λ α = + + where 0 μ > is a constant, ( ) D f is the distance regularization term, 0 λ > is the co-efficient of the line integral ( ) L f and α is the co-efficient of the area integral ( ) A f By including the distance regularization, edge indicator, dirac delta and heaviside function in the energy minimization equation (2), we arrive at the following equation [3]: ( ) ( ) ( ) | | ( ) f p f dX e f f dX eH f dX ε ε μ λ δ α Ω Ω Ω = ∇ + ∇ + − ∫ ∫ ∫ where p is a double well potential function, ∇ is the gradient of the zero level set Γ and e is the edge indicator function defined as [1]: e = 2 1 1 | * | G I + ∇ G is the Gaussian kernel with a standard deviation σ , I is the image and (*) is the convolution operator....
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...) div is the divergence operator and p d is a function given by [3]:...
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...The solution to this energy minimization function is obtained by solving the gradient flow given below [3]....
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...The initial user defined contour 0 f is a step function defined as [3]:...
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