Continuous Max-flow Research Articles

Automatic breast lesion segmentation in phase preserved DCE-MRIs

We offer a framework for automatically and accurately segmenting breast lesions from Dynamic Contrast Enhanced (DCE) MRI in this paper. The framework is built using max flow and min cut problems in the continuous domain over phase preserved denoised images. Three stages are required to complete the proposed approach. First, post-contrast and pre-contrast images are subtracted, followed by image registrations that benefit to enhancing lesion areas. Second, a phase preserved denoising and pixel-wise adaptive Wiener filtering technique is used, followed by max flow and min cut problems in a continuous domain. A denoising mechanism clears the noise in the images by preserving useful and detailed features such as edges. Then, lesion detection is performed using continuous max flow. Finally, a morphological operation is used as a post-processing step to further delineate the obtained results. A series of qualitative and quantitative trials employing nine performance metrics on 21 cases with two different MR image resolutions were used to verify the effectiveness of the proposed method. Performance results demonstrate the quality of segmentation obtained from the proposed method.

Fracture reduction planning and guidance in orthopaedic trauma surgery via multi-body image registration.

Surgical reduction of pelvic fracture is a challenging procedure, and accurate restoration of natural morphology is essential to obtaining positive functional outcome. The procedure often requires extensive preoperative planning, long fluoroscopic exposure time, and trial-and-error to achieve accurate reduction. We report a multi-body registration framework for reduction planning using preoperative CT and intraoperative guidance using routine 2D fluoroscopy that could help address such challenges. The framework starts with semi-automatic segmentation of fractured bone fragments in preoperative CT using continuous max-flow. For reduction planning, a multi-to-one registration is performed to register bone fragments to an adaptive template that adjusts to patient-specific bone shapes and poses. The framework further registers bone fragments to intraoperative fluoroscopy to provide 2D fluoroscopy guidance and/or 3D navigation relative to the reduction plan. The framework was investigated in three studies: (1) a simulation study of 40 CT images simulating three fracture categories (unilateral two-body, unilateral three-body, and bilateral two-body); (2) a proof-of-concept cadaver study to mimic clinical scenario; and (3) a retrospective clinical study investigating feasibility in three cases of increasing severity and accuracy requirement. Segmentation of simulated pelvic fracture demonstrated Dice coefficient of 0.92±0.06. Reduction planning using the adaptive template achieved 2-3 mm and 2-3° error for the three fracture categories, significantly better than planning based on mirroring of contralateral anatomy. 3D-2D registration yielded ~2 mm and 0.5° accuracy, providing accurate guidance with respect to the preoperative reduction plan. The cadaver study and retrospective clinical study demonstrated comparable accuracy: ~0.90 Dice coefficient in segmentation, ~3 mm accuracy in reduction planning, and ~2 mm accuracy in 3D-2D registration. The registration framework demonstrated planning and guidance accuracy within clinical requirements in both simulation and clinical feasibility studies for a broad range of fracture-dislocation patterns. Using routinely acquired preoperative CT and intraoperative fluoroscopy, the framework could improve the accuracy of pelvic fracture reduction, reduce radiation dose, and could integrate well with common clinical workflow without the need for additional navigation systems.

Segmentation of the Common Carotid Intima-Media Complex in Ultrasound Images Using 2-D Continuous Max-Flow and Stacked Sparse Auto-encoder

The intima-media thickness (IMT) of a common carotid artery in an ultrasound image is considered an important indicator of the onset of atherosclerosis. However, it is challenging to segment the intima-media complex (IMC) directly in ultrasound images. This study proposes a fully automatic method to segment the IMC on longitudinal B-mode ultrasound images. Our method consists of two stages: (i) extraction of the region of interest with a continuous max-flow algorithm and region-of-interest reconstruction using a stacked sparse auto-encoder model, and (ii) IMC segmentation using a trained random forest classifier. The proposed method has been tested on three databases from three different imaging centres, comprising a total of 228 ultrasound images of the common carotid artery. On the three databases, our method yields mean absolute errors of 0.028 ± 0.016 mm, 0.579 ± 0.288 pixel and 0.582 ± 0.341 pixel; polyline distance (PD) measures of 0.026 ± 0.017 mm, 0.657 ± 0.275 pixel and 0.731 ± 0:282 pixel; Hausdorff distance measures of 0.249 ± 0.101 mm, 4.760 ± 1.085 pixels and 5.825 ± 2.059 pixels; and correlation coefficients of 95.19%, 93.79%, and 98.96%, respectively. These results indicate that the proposed method performs well in segmentation of the IMC and measurement of the IMT.

Fast Segmentation Algorithm of 3D Lung Parenchyma Based on Continuous Max-Flow

Fast Segmentation Algorithm of 3D Lung Parenchyma Based on Continuous Max-Flow

A Voxel-Based Fully Convolution Network and Continuous Max-Flow for Carotid Vessel-Wall-Volume Segmentation From 3D Ultrasound Images.

Vessel-wall-volume (VWV) is an important three-dimensional ultrasound (3DUS) metric used in the assessment of carotid plaque burden and monitoring changes in carotid atherosclerosis in response to medical treatment. To generate the VWV measurement, we proposed an approach that combined a voxel-based fully convolution network (Voxel-FCN) and a continuous max-flow module to automatically segment the carotid media-adventitia (MAB) and lumen-intima boundaries (LIB) from 3DUS images. Voxel-FCN includes an encoder consisting of a general 3D CNN and a 3D pyramid pooling module to extract spatial and contextual information, and a decoder using a concatenating module with an attention mechanism to fuse multi-level features extracted by the encoder. A continuous max-flow algorithm is used to improve the coarse segmentation provided by the Voxel-FCN. Using 1007 3DUS images, our approach yielded a Dice-similarity-coefficient (DSC) of 93.2±3.0% for the MAB in the common carotid artery (CCA), and 91.9±5.0% in the bifurcation by comparing algorithm and expert manual segmentations. We achieved a DSC of 89.5±6.7% and 89.3±6.8% for the LIB in the CCA and the bifurcation respectively. The mean errors between the algorithm-and manually-generated VWVs were 0.2±51.2 mm3 for the CCA and -4.0±98.2 mm3 for the bifurcation. The algorithm segmentation accuracy was comparable to intra-observer manual segmentation but our approach required less than 1s, which will not alter the clinical work-flow as 10s is required to image one side of the neck. Therefore, we believe that the proposed method could be used clinically for generating VWV to monitor progression and regression of carotid plaques.

Cyclic Continuous Max-Flow: A Third Paradigm in Generating Local Phase Shift Maps in MRI.

Sensitivity to phase deviations in MRI forms the basis of a variety of techniques, including magnetic susceptibility weighted imaging and chemical shift imaging. Current phase processing techniques fall into two families: those which process the complex image data with magnitude and phase coupled, and phase unwrapping-based techniques that first linearize the phase topology across the image. However, issues, such as low signal and the existence of phase poles, can lead both methods to experience error. Cyclic continuous max-flow (CCMF) phase processing uses primal-dual-variational optimization over a cylindrical manifold, which represent the inherent topology of phase images, increasing its robustness to these issues. CCMF represents a third distinct paradigm in phase processing, being the only technique equipped with the inherent topology of phase. CCMF is robust and efficient with at least comparable accuracy as the prior paradigms.

改进的连续型最大流算法脑肿瘤磁核共振成像三维分割

改进的连续型最大流算法脑肿瘤磁核共振成像三维分割

Three-dimensional continuous max flow optimization-based serous retinal detachment segmentation in SD-OCT for central serous chorioretinopathy.

Assessment of serous retinal detachment plays an important role in the diagnosis of central serous chorioretinopathy (CSC). In this paper, we propose an automatic, three-dimensional segmentation method to detect both neurosensory retinal detachment (NRD) and pigment epithelial detachment (PED) in spectral domain optical coherence tomography (SD-OCT) images. The proposed method involves constructing a probability map from training samples using random forest classification. The probability map is constructed from a linear combination of structural texture, intensity, and layer thickness information. Then, a continuous max flow optimization algorithm is applied to the probability map to segment the retinal detachment-associated fluid regions. Experimental results from 37 retinal SD-OCT volumes from cases of CSC demonstrate the proposed method can achieve a true positive volume fraction (TPVF), false positive volume fraction (FPVF), positive predicative value (PPV), and dice similarity coefficient (DSC) of 92.1%, 0.53%, 94.7%, and 93.3%, respectively, for NRD segmentation and 92.5%, 0.14%, 80.9%, and 84.6%, respectively, for PED segmentation. The proposed method can be an automatic tool to evaluate serous retinal detachment and has the potential to improve the clinical evaluation of CSC.

Shape complexes: the intersection of label orderings and star convexity constraints in continuous max-flow medical image segmentation

Optimization-based segmentation approaches deriving from discrete graph-cuts and continuous max-flow have become increasingly nuanced, allowing for topological and geometric constraints on the resulting segmentation while retaining global optimality. However, these two considerations, topological and geometric, have yet to be combined in a unified manner. The concept of "shape complexes," which combine geodesic star convexity with extendable continuous max-flow solvers, is presented. These shape complexes allow more complicated shapes to be created through the use of multiple labels and super-labels, with geodesic star convexity governed by a topological ordering. These problems can be optimized using extendable continuous max-flow solvers. Previous approaches required computationally expensive coordinate system warping, which are ill-defined and ambiguous in the general case. These shape complexes are demonstrated in a set of synthetic images as well as vessel segmentation in ultrasound, valve segmentation in ultrasound, and atrial wall segmentation from contrast-enhanced CT. Shape complexes represent an extendable tool alongside other continuous max-flow methods that may be suitable for a wide range of medical image segmentation problems.

Reliable volumetry of the cervical spinal cord in MS patient follow-up data with cord image analyzer (Cordial).

Spinal cord (SC) atrophy is an important contributor to the development of disability in many neurological disorders including multiple sclerosis (MS). To assess the spinal cord atrophy in clinical trials and clinical practice, largely automated methods are needed due to the sheer amount of data. Moreover, using these methods in longitudinal trials requires them to deliver highly reliable measurements, enabling comparisons of multiple data sets of the same subject over time. We present a method for SC volumetry using 3D MRI data providing volume measurements for SC sections of fixed length and location. The segmentation combines a continuous max flow approach with SC surface reconstruction that locates the SC boundary based on image voxel intensities. Two cutting planes perpendicular to the SC centerline are determined based on predefined distances to an anatomical landmark, and the cervical SC volume (CSCV) is then calculated in-between these boundaries. The development of the method focused on its application in MRI follow-up studies; the method provides a high scan-rescan reliability, which was tested on healthy subject data. Scan-rescan reliability coefficients of variation (COV) were below 1%, intra- and interrater COV were even lower (0.1-0.2%). To show the applicability in longitudinal trials, 3-year follow-up data of 48 patients with a progressive course of MS were assessed. In this cohort, CSCV loss was the only significant predictor of disability progression (p=0.02). We are, therefore, confident that our method provides a reliable tool for SC volumetry in longitudinal clinical trials.

Myocardial Infarct Segmentation From Magnetic Resonance Images for Personalized Modeling of Cardiac Electrophysiology.

Accurate representation of myocardial infarct geometry is crucial to patient-specific computational modeling of the heart in ischemic cardiomyopathy. We have developed a methodology for segmentation of left ventricular (LV) infarct from clinically acquired, two-dimensional (2D), late-gadolinium enhanced cardiac magnetic resonance (LGE-CMR) images, for personalized modeling of ventricular electrophysiology. The infarct segmentation was expressed as a continuous min-cut optimization problem, which was solved using its dual formulation, the continuous max-flow (CMF). The optimization objective comprised of a smoothness term, and a data term that quantified the similarity between image intensity histograms of segmented regions and those of a set of training images. A manual segmentation of the LV myocardium was used to initialize and constrain the developed method. The three-dimensional geometry of infarct was reconstructed from its segmentation using an implicit, shape-based interpolation method. The proposed methodology was extensively evaluated using metrics based on geometry, and outcomes of individualized electrophysiological simulations of cardiac dys(function). Several existing LV infarct segmentation approaches were implemented, and compared with the proposed method. Our results demonstrated that the CMF method was more accurate than the existing approaches in reproducing expert manual LV infarct segmentations, and in electrophysiological simulations. The infarct segmentation method we have developed and comprehensively evaluated in this study constitutes an important step in advancing clinical applications of personalized simulations of cardiac electrophysiology.

Joint segmentation of lumen and outer wall from femoral artery MR images: Towards 3D imaging measurements of peripheral arterial disease

Three-dimensional (3D) measurements of peripheral arterial disease (PAD) plaque burden extracted from fast black-blood magnetic resonance (MR) images have shown to be more predictive of clinical outcomes than PAD stenosis measurements. To this end, accurate segmentation of the femoral artery lumen and outer wall is required for generating volumetric measurements of PAD plaque burden. Here, we propose a semi-automated algorithm to jointly segment the femoral artery lumen and outer wall surfaces from 3D black-blood MR images, which are reoriented and reconstructed along the medial axis of the femoral artery to obtain improved spatial coherence between slices of the long, thin femoral artery and to reduce computation time. The developed segmentation algorithm enforces two priors in a global optimization manner: the spatial consistency between the adjacent 2D slices and the anatomical region order between the femoral artery lumen and outer wall surfaces. The formulated combinatorial optimization problem for segmentation is solved globally and exactly by means of convex relaxation using a coupled continuous max-flow (CCMF) model, which is a dual formulation to the convex relaxed optimization problem. In addition, the CCMF model directly derives an efficient duality-based algorithm based on the modern multiplier augmented optimization scheme, which has been implemented on a GPU for fast computation. The computed segmentations from the developed algorithm were compared to manual delineations from experts using 20 black-blood MR images. The developed algorithm yielded both high accuracy (Dice similarity coefficients ≥ 87% for both the lumen and outer wall surfaces) and high reproducibility (intra-class correlation coefficient of 0.95 for generating vessel wall area), while outperforming the state-of-the-art method in terms of computational time by a factor of ≈ 20.

Retina layer segmentation using kernel graph cuts and continuous max-flow.

Circular scan Spectral-Domain Optic Coherence Tomography imaging (SD-OCT) is one of the best tools for diagnosis of retinal diseases. This technique provides more comprehensive detail of the retinal morphology and layers around the optic disc nerve head (ONH). Since manual labelling of the retinal layers can be tedious and time consuming, accurate and robust automated segmentation methods are needed to provide the thickness evaluation of these layers in retinal disorder assessments such as glaucoma. The proposed method serves this purpose by performing the segmentation of retinal layers boundaries in circular SD-OCT scans acquired around the ONH. The layers are detected by adapting a graph cut segmentation technique that includes a kernel-induced space and a continuous multiplier based max-flow algorithm. Results from scan images acquired with Spectralis (Heidelberg Engineering, Germany) prove that the proposed method is robust and efficient in detecting the retinal layers boundaries in images. With a mean root-mean-square error (RMSE) of 0.0835 ± 0.0495 and an average Dice coefficient of 0.9468 ± 0.0705 pixels for the retinal nerve fibre layer thickness, the proposed method demonstrated effective agreement with manual annotations.

Myocardial infarct segmentation and reconstruction from 2D late-gadolinium enhanced magnetic resonance images.

In this paper, we propose a convex optimization-based algorithm for segmenting myocardial infarct from clinical 2D late-gadolinium enhanced magnetic resonance (LGE-MR) images. Previously segmented left ventricular (LV) myocardium was used to define a region of interest for the infarct segmentation. The infarct segmentation problem was formulated as a continuous min-cut problem, which was solved using its dual formulation, the continuous max-flow (CMF). Bhattacharyya intensity distribution matching was used as the data term, where the prior intensity distributions were computed based on a training data set LGE-MR images from seven patients. The algorithm was parallelized and implemented in a graphics processing unit for reduced computation time. Three-dimensional (3D) volumes of the infarcts were then reconstructed using an interpolation technique we developed based on logarithm of odds. The algorithm was validated using LGE-MR images from 47 patients (309 slices) by comparing computed 2D segmentations and 3D reconstructions to manually generated ones. In addition, the developed algorithm was compared to several previously reported segmentation techniques. The CMF algorithm outperformed the previously reported methods in terms of Dice similarity coefficient.

Interactive Hierarchical-Flow Segmentation of Scar Tissue From Late-Enhancement Cardiac MR Images

We propose a novel multi-region image segmentation approach to extract myocardial scar tissue from 3-D whole-heart cardiac late-enhancement magnetic resonance images in an interactive manner. For this purpose, we developed a graphical user interface to initialize a fast max-flow-based segmentation algorithm and segment scar accurately with progressive interaction. We propose a partially-ordered Potts (POP) model to multi-region segmentation to properly encode the known spatial consistency of cardiac regions. Its generalization introduces a custom label/region order constraint to Potts model to multi-region segmentation. The combinatorial optimization problem associated with the proposed POP model is solved by means of convex relaxation, for which a novel multi-level continuous max-flow formulation, i.e., the hierarchical continuous max-flow (HMF) model, is proposed and studied. We demonstrate that the proposed HMF model is dual or equivalent to the convex relaxed POP model and introduces a new and efficient hierarchical continuous max-flow based algorithm by modern convex optimization theory. In practice, the introduced hierarchical continuous max-flow based algorithm can be implemented on the parallel GPU to achieve significant acceleration in numerics. Experiments are performed in 50 whole heart 3-D LE datasets, 35 with left-ventricular and 15 with right-ventricular scar. The experimental results are compared to full-width-at-half-maximum and Signal-threshold to reference-mean methods using manual expert myocardial segmentations and operator variabilities and the effect of user interaction are assessed. The results indicate a substantial reduction in image processing time with robust accuracy for detection of myocardial scar. This is achieved without the need for additional region constraints and using a single optimization procedure, substantially reducing the potential for error.

A spatially continuous max-flow and min-cut framework for binary labeling problems

We propose and investigate novel max-flow models in the spatially continuous setting, with or without i priori defined supervised constraints, under a comparative study of graph based max-flow/min-cut. We show that the continuous max-flow models correspond to their respective continuous min-cut models as primal and dual problems. In this respect, basic conceptions and terminologies from discrete max-flow/min-cut are revisited under a new variational perspective. We prove that the associated nonconvex partitioning problems, unsupervised or supervised, can be solved globally and exactly via the proposed convex continuous max-flow and min-cut models. Moreover, we derive novel fast max-flow based algorithms whose convergence can be guaranteed by standard optimization theories. Experiments on image segmentation, both unsupervised and supervised, show that our continuous max-flow based algorithms outperform previous approaches in terms of efficiency and accuracy.