Initial condition for efficient mapping of level set algorithms on many-core architectures

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.

SummaryThe parametric level set approach is an extension of the conventional level set methods for topology optimization. By parameterizing the level set function, level set methods can be directly coupled with mathematical programming to achieve better numerical robustness and computational efficiency. Moreover, the parametric level set scheme can not only inherit the primary advantages of the conventional level set methods, such as clear boundary representation and the flexibility in handling topological changes, but also alleviate some undesired features from the conventional level set methods, such as the need for reinitialization. However, in the existing radial basis function–based parametric level set method, it is difficult to identify the range of the design variables. Besides, the parametric level set evolution often struggles with large fluctuations during the optimization process. Those issues cause difficulties both in numerical stability and in material property mapping. In this paper, a cardinal basis function is constructed based on the radial basis function partition of unity collocation method to parameterize the level set function. The benefit of using cardinal basis function is that the range of the design variables can now be clearly specified as the value of the level set function. A distance regularization energy functional is also introduced, aiming to maintain the desired signed distance property during the level set evolution. With this desired feature, the level set evolution is stabilized against large fluctuations. In addition, the material properties mapped from the level set function to the finite element model can be more accurate.

ABSTRACTThis letter presents a novel method for unsupervised change detection (CD) from remote sensing images using level set evolution with local uncertainty constraints (LSELUC). Uncertainty analysis of pixel labels was implemented as prior information to guide the evolution of level curves. Then, local uncertainty and gradient information of level curves were incorporated into the level set energy function to construct local energy constraints. The proposed method can reduce noise, while preserving details in change regions. Furthermore, an advanced regularization strategy of the level set function was adopted to improve the computational efficiency. The performance of the proposed method was validated on two remote sensing data sets. Experimental results show that the proposed method can produce satisfactory CD results.

Level set evolution with locally linear classification for image segmentation

4D MR phase and magnitude segmentations with GPU parallel computing

In this paper, we propose a hybrid multi-cell tracking approach to accurately and jointly estimate the state and its contour of each cell. Our approach consists of level set evolution and ant colony optimization, representing, respectively, the deterministic and stochastic methods for cell tracking. Firstly, birth ants are directly distributed into the regions depicted by raw curves achieved by the traditional level set evolution. Then, the ants move towards potential regions based on the pheromone deposited by ants and the gradient information of current image. Finally, the resulting pheromone field is embedded in the variational level set to drive the evolution of cell curve to yield an accurate one and correspond cell position estimate. The experiment results show that our method could automatically track multi-cell and achieve an accurate contour estimation of each cell.

Segmentation of hippocampus in the brain is one of a major challenge in medical image segmentation due to its’ imaging characteristics, with almost similar intensity between another adjacent gray matter structure, such as amygdala. The intensity similarity has causes the hippocampus to have weak or fuzzy boundaries. With this main challenge being demonstrated by hippocampus, a segmentation method that relies on image information alone may not produce accurate segmentation results. Therefore, it is needed an assimilation of prior information such as shape and spatial information into existing segmentation method to produce the expected segmentation. Previous studies has widely integrated prior information into segmentation methods. However, the prior information has been utilized through a global manner integration, and this does not reflect the real scenario during clinical delineation. Therefore, in this paper, a locally integrated prior information into a level set model is presented. This work utilizes a mean shape model to provide automatic initialization for level set evolution, and has been integrated as prior information into the level set model. The local integration of edge based information and prior information has been implemented through an edge weighting map that decides at voxel level which information need to be observed during a level set evolution. The edge weighting map shows which corresponding voxels having sufficient edge information. Experiments shows that the proposed integration of prior information locally into a conventional edge-based level set model, known as geodesic active contour has shown improvement of 9% in averaged Dice coefficient.

To solve the problem that many image segmentation methods cannot be applied to forward looking sonar image accurately, an improved level set segmentation method was proposed in this paper. Firstly, the level set evolution without re-initialization was introduced. Secondly the different characteristics of forward looking sonar image from the optical image were analyzed, and we got the factors affecting segmentation. Then, to overcome these negative effects, this paper did preprocessing by morphological top-hat and bottom-hat transformation, and carried on level set method without re-initialization to construct an improved level set sonar image segmentation system. Finally, our method was compared with the traditional level set method in computer experiments. Simulation results show that it is more adapted to forward looking sonar image segmentation.

Image segmentation plays an important role in computer vision and image processing. Level set model is a classical image segmentation method. During level set evolution, almost all the level set energy minimization of image segmentation are based on the gradient descent method and the finite difference scheme. The speed of evolution is slow and easy to fall into local minima. In this paper, we propose a fast sweeping optimization algorithm to minimize global cosine fitting (GCF) model. When moving a pixel from the one side region to the another side region of evolving contour, the sweeping algorithm calculates the energy change directly and checks whether the cosine fitting energy is decreased. With this, we can avoid solving the Euler-Lagrange equation and the partial differential equation, which usually take a lot of time. Moreover, our proposal is robust to initial level set contour and it automatically handles the topological variety, algorithm automatic termination and no longer requires the reinitialization step, parameter adjustment and the distance regularization term. The experiments on real noise and synthetic images show the effectiveness of the sweeping algorithm.

As an attempt to introduce interactive, content‐dependent adaptive (ICDA) image processing, a simple but powerful active image sensing and two image enhancement methods are introduced via adaptive CNN‐UM sensor‐computers. Thus, the method ICDA can be used for adaptive control of image sensing and for subsequent on‐line or off‐line image enhancement as well. The algorithms use both intensity and contrast content. The image sensing technology can be realized with the current CNN‐UM chip. Our first image enhancement method is also executable on this chip, but it is more suitable for the adaptive cellular neural network universal machine (ACNN‐UM) architecture. Some results of simulator and chip experiments and an adaptive extended cell are presented. Our second, dynamical image enhancement method is planned to be executable on a multi‐layer, complex cell CNN architecture. In (Proceedings of the 6th IEEE International Workshop on Cellular Neural Networks and their Applications(CNNA‐2000) Catania, 2000; 213–217) 3‐layer architecture is described which is capable of realizing the main part of the second enhancement method.The main issues of our paper are as follows: the novel outlook of the ICDA framework, three new methods for two key application areas of CNN‐UM, the notion of ‘regional’ adaptive computing, the novelty of application of equilibrium‐computing in the third method. However, the key novelty of our work is not just a new method and a new realization: by combining sensing and computing, dynamically and pixelwise, a new quality becomes practical. Copyright © 2002 John Wiley & Sons, Ltd.

We address image estimation from sparse Fourier samples. The problem is formulated as joint estimation of the supports of unknown sparse objects in the image, and pixel values on these supports. The domain and the pixel values are alternately estimated using the level-set method and the conjugate gradient method, respectively. Our level-set evolution shows a unique switching behavior, which stabilizes the level-set evolution and removes the re-initialization steps in conventional level set approaches.

Level set evolution is an essential method for image segmentation. However, the region-based level set is sensitive to contour initialization, and it is difficult to obtain good results in images with intensity inhomogeneity. We propose an improved level set method based on local entropy and enhanced Laplacian of Gaussian (LoG) operator for image segmentation. Specifically, the local entropy reflects the local intensity variations, which improves the method's ability to handle inhomogeneity. Then, the enhanced LoG operator smoothes the heterogeneous regions to reduce the influence of the regions on the curve. Experimental results show that the method can effectively segment inhomogeneous images and has good adaptability to contour initialization and noise.

In order to improve the accuracy of image segmentation, an improved adaptive level set method is proposed based on level set evolution without re-initialization method and adaptive distance preserving level set evolution method. A new definition of weight coefficient in evolution equations is the main innovation of this paper. The improved method can detect certain object boundaries, interior and exterior contours of an object, edges of multi-objects and weak boundaries of an object by synthetic and real images numerical experiments. Numerical results show that the improved adaptive level set method has faster segmentation speed and higher segmentation accuracy compared with the previous two methods, especially in weak boundaries and edges of multi-objects segmentation problems.

Glaucoma is a leading cause of blindness. The measurement of vertical cup-to-disc ratio combined with other clinical features is one of the methods used to screen glaucoma. In this paper, we propose a deep level set method to implement the segmentation of optic cup (OC) and optic disc (OD). We present a multi-scale convolutional neural network as the prediction network to generate level set initial contour and evolution parameters. The initial contour will be further refined based on the evolution parameters. The network is integrated with augmented prior knowledge and supervised by active contour loss, which makes the level set evolution yield more accurate shape and boundary details. The experimental results on the REFUGE dataset show that the IoU of the OC and OD are 93.61% and 96.69%, respectively. To evaluate the robustness of the proposed method, we further test the model on the Drishthi-GS1 dataset. The segmentation results show that the proposed method outperforms the state-of-the-art methods.

In this paper, considering the local variance of intensity inhomogeneity, we propose a novel local regional level set model based on a so-called Three-Layer structure to segment images with intensity inhomogeneity. The local region intensity mean idea is used to construct region descriptor. Especially, three descriptors separately based on ‘large’, ‘median’ and ‘small’ scales of local regions are utilized to derive the Three-Layer structure. Compared to the traditional methods based on fixed scale for all local regions, the Three-Layer structure is more reliable for capturing local intensity information. Then, the Three-Layer structure is incorporated into the level set energy functional construction. As a result, more effective local intensity information is incorporated into the level set evolution. Finally, the experimental results demonstrate that the proposed method yields results comparative to and even better than the existing popular models for segmenting images with intensity inhomogeneity.Keywordslocal informationlevel setintensity inhomogeneitythree-Layer structure