Coupled Geodesic Active Regions for Image Segmentation: A Level Set Approach

Disjunctive Normal Parametric Level Set With Application to Image Segmentation

Level set methods are widely used for image segmentation because of their convenient shape representation for numerical computations and capability to handle topological changes. However, in spite of the numerous works in the literature, the use of level set methods in image segmentation still has several drawbacks. These shortcomings include formation of irregularities of the signed distance function, sensitivity to initialization, lack of locality, and expensive computational cost, which increases dramatically as the number of objects to be simultaneously segmented grows. In this paper, we propose a novel parametric level set method called disjunctive normal level set (DNLS), and apply it to both two-phase (single object) and multiphase (multiobject) image segmentations. DNLS is a differentiable model formed by the union of polytopes, which themselves are created by intersections of half-spaces. We formulate the segmentation algorithm in a Bayesian framework and use a variational approach to minimize the energy with respect to the parameters of the model. The proposed DNLS can be considered as an open framework that allows the use of different appearance models and shape priors. Compared with the conventional level sets available in the literature, the proposed DNLS has the following major advantages: it requires significantly less computational time and memory, it naturally keeps the level set function regular during the evolution, it is more suitable for multiphase and local region-based image segmentations, and it is less sensitive to noise and initialization. The experimental results show the potential of the proposed method.

Energy minimization in medical image analysis: Methodologies and applications

Energy minimization is of particular interest in medical image analysis. In the past two decades, a variety of optimization schemes have been developed. In this paper, we present a comprehensive survey of the state-of-the-art optimization approaches. These algorithms are mainly classified into two categories: continuous method and discrete method. The former includes Newton-Raphson method, gradient descent method, conjugate gradient method, proximal gradient method, coordinate descent method, and genetic algorithm-based method, while the latter covers graph cuts method, belief propagation method, tree-reweighted message passing method, linear programming method, maximum margin learning method, simulated annealing method, and iterated conditional modes method. We also discuss the minimal surface method, primal-dual method, and the multi-objective optimization method. In addition, we review several comparative studies that evaluate the performance of different minimization techniques in terms of accuracy, efficiency, or complexity. These optimization techniques are widely used in many medical applications, for example, image segmentation, registration, reconstruction, motion tracking, and compressed sensing. We thus give an overview on those applications as well.

Partitioned edge-function-scaled region-based active contour (p-ESRAC): automated liver segmentation in multiphase contrast-enhanced MRI

PURPOSE

In multiphase contrast-enhanced magnetic resonance imaging (CE-MRI), liver segmentation is an important preprocessing step for the computer-aided evaluation of liver disease. However, because of the liver's irregular shape, proximity to surrounding organs, and large intensity variation, and peripheral contrast enhancement in the kidney, liver segmentation has been very challenging. This paper presents a novel hybrid active contour model and overall procedures that are specific to liver segmentation.

METHODS

The authors introduced an edge-function-scaled (weighted) region-based active contour model (ESRAC) and utilization of registered, multiphase sequences to address leakage-to-kidney and oversegmentation problems. The model incorporated weighted regional information with a compactly supported edge map, computed from a combination of images obtained during arterial and delayed phases, and it was coupled with a geodesic edge term. To cope with signal-inhomogeneity on MRI, all of the axial slices were partitioned into eight sectors with an angular span of 45°, centered on the inferior vena cava, each in the superior and inferior regions and the regional information regarding ESRAC was computed for each partition, henceforth the so-called partitioned ESRAC (p-ESRAC). Initialization of the active contour was performed by thresholding with a range of [200, +∞) and simple morphological operation during the delayed phase. At the end, to fill the holes in the segmented images caused by high gradients around the vasculature, noise, or outstanding texture features, iterative morphological operations were performed until convergence. The authors compared the segmentation accuracy of p-ESRAC to that with geodesic active contour, region-based active contour, geodesic active region, and localized region-based active contour using quantitative and visual assessments.

RESULTS

In three-dimensional experimental studies conducted on 30 subjects (14 normal or benign cases and 16 malignant cases), compared with other active contours, p-ESRAC achieved the highest dice similarity coefficients of 93.9 ± 1.6% (normal) and 91.6 ± 2.2% (malignant), respectively. In addition, p-ESRAC resulted in the lowest false positive rates of 4.5 ± 3.2% (normal) and 7.9 ± 3.0% (malignant), demonstrating it to be the most effective in reducing oversegmentation. The partition scheme improved segmentation accuracy by 5.4 ± 9.2% (normal) and 22.2 ± 27.6% (malignant) of the true segmentation that was missed by ESRAC. Visual assessment confirmed that p-ESRAC prevented leakage of the segmentation results of the liver into the kidney.

CONCLUSIONS

A novel active-contour model was developed, allowing for accurate liver segmentation on multiphase CE-MRI, with conditions that include signal inhomogeneity and weak boundary conditions. Such a technique could be useful for applications that involve computer-aided diagnosis of liver disease.

A Multiple Object Geometric Deformable Model for Image Segmentation

Deformable models are widely used for image segmentation, most commonly to find single objects within an image. Although several methods have been proposed to segment multiple objects using deformable models, substantial limitations in their utility remain. This paper presents a multiple object segmentation method using a novel and efficient object representation for both two and three dimensions. The new framework guarantees object relationships and topology, prevents overlaps and gaps, enables boundary-specific speeds, and has a computationally efficient evolution scheme that is largely independent of the number of objects. Maintaining object relationships and straightforward use of object-specific and boundary-specific smoothing and advection forces enables the segmentation of objects with multiple compartments, a critical capability in the parcellation of organs in medical imaging. Comparing the new framework with previous approaches shows its superior performance and scalability.

Multi-object geodesic active contours (MOGAC)

An emerging topic is to build image segmentation systems that can segment hundreds to thousands of objects (i.e. cell segmentation\tracking, full brain parcellation, full body segmentation, etc.). Multi-object Level Set Methods (MLSM) perform this task with the benefit of sub-pixel precision. However, current implementations of MLSM are not as computationally or memory efficient as their region growing and graph cut counterparts which lack sub-pixel precision. To address this performance gap, we present a novel parallel implementation of MLSM that leverages the sparse properties of the algorithm to minimize its memory footprint for multiple objects. The new method, Multi-Object Geodesic Active Contours (MOGAC), can represent N objects with just two functions: a label mask image and unsigned distance field. The time complexity of the algorithm is shown to be O((M (power)d)/P) for M (power)d pixels and P processing units in dimension d = {2,3}, independent of the number of objects. Results are presented for 2D and 3D image segmentation problems.

Atlas-based segmentation of 3D cerebral structures with competitive level sets and fuzzy control

We propose a novel approach for the simultaneous segmentation of multiple structures with competitive level sets driven by fuzzy control. To this end, several contours evolve simultaneously toward previously defined anatomical targets. A fuzzy decision system combines the a priori knowledge provided by an anatomical atlas with the intensity distribution of the image and the relative position of the contours. This combination automatically determines the directional term of the evolution equation of each level set. This leads to a local expansion or contraction of the contours, in order to match the boundaries of their respective targets. Two applications are presented: the segmentation of the brain hemispheres and the cerebellum, and the segmentation of deep internal structures. Experimental results on real magnetic resonance (MR) images are presented, quantitatively assessed and discussed.

Fast and Robust Clinical Triple-Region Image Segmentation Using One Level Set Function

This paper proposes a novel method for clinical triple-region image segmentation using a single level set function. Triple-region image segmentation finds wide application in the computer aided X-ray, CT, MRI and ultrasound image analysis and diagnosis. Usually multiple level set functions are used consecutively or simultaneously to segment triple-region medical images. These approaches are either time consuming or suffer from the convergence problems. With the new proposed triple-regions level set energy modelling, the triple-region segmentation is handled within the two region level set framework where only one single level set function needed. Since only a single level set function is used, the segmentation is much faster and more robust than using multiple level set functions. Adapted to the clinical setting, individual principal component analysis and a support vector machine classifier based clinical acceleration scheme are used to accelerate the segmentation. The clinical acceleration scheme takes the strengths of both machine learning and the level set method while limiting their weaknesses to achieve automatic and fast clinical segmentation. Both synthesized and practical images are used to test the proposed method. These results show that the proposed method is able to successfully segment the triple-region using a single level set function. Also this segmentation is very robust to the placement of initial contour. While still quickly converging to the final image, with the clinical acceleration scheme, our proposed method can be used during pre-processing for automatic computer aided diagnosis and surgery.

Coupled Shape Distribution-Based Segmentation of Multiple Objects

In this paper we develop a multi-object prior shape model for use in curve evolution-based image segmentation. Our prior shape model is constructed from a family of shape distributions (cumulative distribution functions) of features related to the shape. Shape distribution-based object representations possess several desired properties, such as robustness, invariance, and good discriminative and generalizing properties. Further, our prior can capture information about the interaction between multiple objects. We incorporate this prior in a curve evolution formulation for shape estimation. We apply this methodology to problems in medical image segmentation.

Geodesic Active Contours with Adaptive Neighboring Influence

While geometric deformable models have brought tremendous impacts on shape representation and analysis in medical image analysis, some of the remaining problems include the handling of boundary leakage and the lack of global understanding of boundaries. We present a modification to the geodesic active contour framework such that influence from local neighbors of a front point is explicitly incorporated, and it is thus capable of robustly dealing with the boundary leakage problem. The fundamental power of this strategy rests with the local integration of evolution forces for each front point within its local influence domain, which is adaptively determined by the local level set geometry and image/prior information. Due to the combined effects of internal and external constraints on a point and the interactions with those of its neighbors, our method allows stable boundary detection when the edge information is noisy and possibly discontinuous (e.g. gaps in the boundaries) while maintaining the abilities to handle topological changes, thanks to the level set implementation. The algorithm has been implemented using the meshfree particle domain representation, and experimental results on synthetic and real images demonstrate its superior performance.