Disjunctive Normal Parametric Level Set With Application to Image Segmentation

Research on improved level set image segmentation method

Aiming at the shortcomings of the traditional level set model which only has good robustness to the weak boundary and strong noise of the original target image, this paper proposes an improved algorithm based on the no-weight initialization level set model, introducing bilateral filters and using implicit surface level sets to extract and segment the original target image object more accurately, clearly and intuitively in the evolution process. The experimental simulation results show that, compared with the traditional non-reinitialized level set model segmentation method, the improved method can more accurately extract the edge contours of the target image object, and has better edge contour extraction effect, and the original target noise reduction effect of the improved model is better than that of the model before the improvement. The original target image object edge contour takes less time to extract than the conventional non-reinitialized level set model before the improvement.

AW-SDRLSE: Adaptive Weighting and Scalable Distance Regularized Level Set Evolution for Lymphoma Segmentation on PET Images

Accurate lymphoma segmentation on Positron Emission Tomography (PET) images is of great importance for medical diagnoses, such as for distinguishing benign and malignant. To this end, this paper proposes an adaptive weighting and scalable distance regularized level set evolution (AW-SDRLSE) method for delineating lymphoma boundaries on 2D PET slices. There are three important characteristics with respect to AW-SDRLSE: 1) A scalable distance regularization term is proposed and a parameter q can control the contour's convergence rate and precision in theory. 2) A novel dynamic annular mask is proposed to calculate mean intensities of local interior and exterior regions and further define the region energy term. 3) As the level set method is sensitive to parameters, we thus propose an adaptive weighting strategy for the length and area energy terms using local region intensity and boundary direction information. AW-SDRLSE is evaluated on 90 cases of real PET data with a mean Dice coefficient of 0.8796. Comparative results demonstrate the accuracy and robustness of AW-SDRLSE as well as its performance advantages as compared with related level set methods. In addition, experimental results indicate that AW-SDRLSE can be a fine segmentation method for improving the lymphoma segmentation results obtained by deep learning (DL) methods significantly.

Pseudo-Marginal MCMC Sampling for Image Segmentation Using Nonparametric Shape Priors

Segmenting images of low quality or with missing data is a challenging problem. In such scenarios, exploiting statistical prior information about the shapes to be segmented can improve the segmentation results significantly. Incorporating prior density of shapes into a Bayesian framework leads to the posterior density of segmenting shapes given the observed data. Most segmentation algorithms that exploit shape priors optimize a cost function based on the posterior density and find a point estimate (e.g., using maximum a posteriori estimation). However, especially when the prior shape density is multimodal leading to a multimodal posterior density, a point estimate does not provide a measure of the degree of confidence in that result, neither does it provide a picture of other probable solutions based on the observed data and the shape priors. With a statistical view, addressing these issues would involve the problem of characterizing the posterior distributions of the shapes of the objects to be segmented. An analytic computation of such posterior distributions is intractable; however, characterization is still possible through their samples. In this paper, we propose an efficient pseudo-marginal Markov chain Monte Carlo (MCMC) sampling approach to draw samples from posterior shape distributions for image segmentation. The computation time of the proposed approach is independent from the training set size. Therefore, it scales well for very large data sets. In addition to better characterization of the statistical structure of the problem, such an approach has the potential to address issues with getting stuck at local optima, suffered by existing shape-based segmentation methods. Our approach is able to characterize the posterior probability density in the space of shapes through its samples, and to return multiple solutions, potentially from different modes of a multimodal probability density, which would be encountered, e.g., in segmenting objects from multiple shape classes. We present promising results on a variety of synthetic and real data sets.

RESLS: Region and Edge Synergetic Level Set Framework for Image Segmentation

The active contour models with level set evolution have been visited with a vast number of methods for image segmentation. They can be mainly classified into region-based and edge-based models, and it has been validated that the hybrid variants combining both region and edge information can improve the segmentation performance. However, to the best of our knowledge, the theoretical foundation of collaboration mechanism between the region and the edge information is limited. Specifically, most existing hybrid models are just combining all the energy terms together, resulting in great challenges of choosing an appropriate weight coefficient for each term and accommodating different modalities of imaging. To overcome these difficulties, this paper proposes a region and edge synergetic level set framework named RESLS. It provides an approach to construct new hybrid level set models using a normalized intensity indicator function that allows the region information easily embedding into the edge-based model. In this case, the energy weights of region and edge terms can be constrained by the global optimization condition deduced from the framework. Some representative as well as state-of-the-art models are taken as examples to demonstrate the generality of our method. The experiments validate that under the guidance of the optimization condition, the weighting parameter of each term can be reliably chosen. Meanwhile, the segmentation accuracy, robustness, and computational efficiency of RESLS can be improved compared with its component models.

Image Segmentation Using Disjunctive Normal Bayesian Shape and Appearance Models

The use of appearance and shape priors in image segmentation is known to improve accuracy; however, existing techniques have several drawbacks. For instance, most active shape and appearance models require landmark points and assume unimodal shape and appearance distributions, and the level set representation does not support construction of local priors. In this paper, we present novel appearance and shape models for image segmentation based on a differentiable implicit parametric shape representation called a disjunctive normal shape model (DNSM). The DNSM is formed by the disjunction of polytopes, which themselves are formed by the conjunctions of half-spaces. The DNSM's parametric nature allows the use of powerful local prior statistics, and its implicit nature removes the need to use landmarks and easily handles topological changes. In a Bayesian inference framework, we model arbitrary shape and appearance distributions using nonparametric density estimations, at any local scale. The proposed local shape prior results in accurate segmentation even when very few training shapes are available, because the method generates a rich set of shape variations by locally combining training samples. We demonstrate the performance of the framework by applying it to both 2-D and 3-D data sets with emphasis on biomedical image segmentation applications.

Nonparametric Joint Shape and Feature Priors for Image Segmentation

In many image segmentation problems involving limited and low-quality data, employing statistical prior information about the shapes of the objects to be segmented can significantly improve the segmentation result. However, defining probability densities in the space of shapes is an open and challenging problem, especially if the object to be segmented comes from a shape density involving multiple modes (classes). Existing techniques in the literature estimate the underlying shape distribution by extending Parzen density estimator to the space of shapes. In these methods, the evolving curve may converge to a shape from a wrong mode of the posterior density when the observed intensities provide very little information about the object boundaries. In such scenarios, employing both shape- and class-dependent discriminative feature priors can aid the segmentation process. Such features may involve, e.g., intensity-based, textural, or geometric information about the objects to be segmented. In this paper, we propose a segmentation algorithm that uses nonparametric joint shape and feature priors constructed by Parzen density estimation. We incorporate the learned joint shape and feature prior distribution into a maximum a posteriori estimation framework for segmentation. The resulting optimization problem is solved using active contours. We present experimental results on a variety of synthetic and real data sets from several fields involving multimodal shape densities. Experimental results demonstrate the potential of the proposed method.