Post-hoc explanation methods of image recognition models often exhibit high variance or disagreement across explanations when the input data are perturbed, the underlying models are modified, or different explainability techniques are employed.To mitigate this issue, several approaches have been proposed, among which ensemble strategies that aggregate multiple explanations have attracted particular attention.Although some of these methods demonstrate good empirical performance, most existing works remain largely empirical, with limited theoretical justification or understanding of why ensemble strategies work and when they fail.In this paper, we analyze the factors that influence the success and failure of ensemble strategies that combines multiple explanations, using different datasets, convolutional neural network architectures, posthoc explanation techniques, and ensembling strategies to identify the most influential image patches.In particular, we compare various ensembling strategies based on distinct voting principles -namely, Borda Count, Kemeny-Young, Reciprocal Rank Fusion, and the Schulze method -and show that the performance of such ensemble methods depends on the degree of satisfaction of their underlying theoretical assumptions.

This article introduces the maximum coverage of shortest paths under limited cost (MCLC) problem, a novel optimization task focused on deploying nodes to cover the maximum number of shortest paths within a network under a strict budget. While crucial in many real-world scenarios, this problem is computationally challenging. We propose a novel hybrid greedy (HG) algorithm, which integrates two novel greedy operations—coverage-first and contribution-first—with new refinement techniques. We prove that the proposed HG algorithm achieves a worst case approximation ratio that doubles the state-of-the-art lower bound, a significant theoretical improvement for large-scale networks. To guide practical application, we analyze the tradeoff between coverage and cost-efficiency. We derive a new Pearson correlation-based criterion that accurately predicts when and why our proposed HG approach will outperform other methods, providing a valuable guideline for algorithm selection. Extensive experiments on both synthetic and real-world networks validate our theoretical findings and confirm the practical superiority of our approach.

It is challenging to deploy check-in nodes optimally in a complex network so as to perform specific check-in like services, e.g., fuel supplements etc., but crucial in many real-world applications. In this article, we propose and study the new optimization problem of placing check-in nodes with the minimum cost, i.e., the problem of finding the minimum-cost check-in nodes (MCCN), which is of great interests for real-world application situations, but even more difficult. We motivate the new algorithms through three typical worse cases by the often-used greedy-type algorithms, i.e., One-to-Many, Many-to-One, and Duplicate-Overrides. With this respect, the proposed novel optimization algorithms utilize a novel metric of contribution density for selecting check-in nodes iteratively, which successfully avoid the occurrence of the two worse cases of One-to-Many and Many-to-One. We also introduce an extra backward extraction step in one of new algorithms, which overcomes the crucial worse case of “duplicate overrides” and largely improves the algorithmic performance in solving the introduced optimization problem of MCCN. Meanwhile, we extend the new contribution density metric to a more general class of functions and study their effectiveness to eliminate the two worse cases of One-to-Many and Many-to-One; also, a detailed analysis on complexity and performance of the proposed algorithms is presented to show their numerical efficiency and accuracy. Extensive experiments over two classical artificial networks, i.e., BA network and ER network, and ten real-world networks, under two typical cost setups, show the proposed algorithms significantly outperform the four state-of-the-art algorithms. We also demonstrate that our proposed algorithms are much reliable and robust with different experiment settings of deployment cost and network-type and scale.

We propose a general variational framework of fair clustering, which integrates an original Kullback-Leibler (KL) fairness term with a large class of clustering objectives, including prototype or graph based. Fundamentally different from the existing combinatorial and spectral solutions, our variational multi-term approach enables to control the trade-off levels between the fairness and clustering objectives. We derive a general tight upper bound based on a concave-convex decomposition of our fairness term, its Lipschitz-gradient property and the Pinsker’s inequality. Our tight upper bound can be jointly optimized with various clustering objectives, while yielding a scalable solution, with convergence guarantee. Interestingly, at each iteration, it performs an independent update for each assignment variable. Therefore, it can be easily distributed for large-scale datasets. This scalability is important as it enables to explore different trade-off levels between the fairness and clustering objectives. Unlike spectral relaxation, our formulation does not require computing its eigenvalue decomposition. We report comprehensive evaluations and comparisons with state-of-the-art methods over various fair clustering benchmarks, which show that our variational formulation can yield highly competitive solutions in terms of fairness and clustering objectives.

It is of great importance for proper radiological interpretations to register multiphase liver scans, but much challenging due to different breathing-holding levels and physiological motions while imaging. In this paper, we propose a novel nonlinear registration method for multiphase liver scans upon iterative reweighted local cross correlation (IRLCC) measure, which employs the metric of local cross correlation (LCC) to evaluate image similarity. In addition, the introduced method explores a new volume-preserving prior of liver to boost registration accuracy. A multilevel iterative fixed-point optimization algorithm is proposed to compute pixel-wise displacement efficiently with a moderate numerical load. We validate our approach over a LSHCC dataset acquired from the radiology department in hospital and a LSPIG public dataset. The results over LSHCC demonstrate that the volume-preserving prior well improved the registration accuracy. The results over LSPIG reveal that our method outperforms several state-of-the-art methods while keeping efficiency in time.

Recently, dense connections have attracted substantial attention in computer vision because they facilitate gradient flow and implicit deep supervision during training. Particularly, DenseNet that connects each layer to every other layer in a feed-forward fashion and has shown impressive performances in natural image classification tasks. We propose HyperDenseNet, a 3-D fully convolutional neural network that extends the definition of dense connectivity to multi-modal segmentation problems. Each imaging modality has a path, and dense connections occur not only between the pairs of layers within the same path but also between those across different paths. This contrasts with the existing multi-modal CNN approaches, in which modeling several modalities relies entirely on a single joint layer (or level of abstraction) for fusion, typically either at the input or at the output of the network. Therefore, the proposed network has total freedom to learn more complex combinations between the modalities, within and in-between all the levels of abstraction, which increases significantly the learning representation. We report extensive evaluations over two different and highly competitive multi-modal brain tissue segmentation challenges, iSEG 2017 and MRBrainS 2013, with the former focusing on six month infant data and the latter on adult images. HyperDenseNet yielded significant improvements over many state-of-the-art segmentation networks, ranking at the top on both benchmarks. We further provide a comprehensive experimental analysis of features re-use, which confirms the importance of hyper-dense connections in multi-modal representation learning. Our code is publicly available.

Preterm neonates with a very low birth weight of less than 1,500 grams are at increased risk for developing intraventricular hemorrhage (IVH), which is a major cause of brain injury in preterm neonates. Quantitative measurements of ventricular dilatation or shrinkage play an important role in monitoring patients and evaluating treatment options. 3D ultrasound (US) has been developed to monitor ventricle volume as a biomarker for ventricular changes. However, ventricle volume as a global indicator does not allow for precise analysis of local ventricular changes, which could be linked to specific neurological problems often seen in the patient population later in life. In this work, a 3D+t spatial-temporal deformable registration approachis proposed, which is applied to the analysis of the detailed local changes of preterm IVH neonatal ventricles from 3D US images. In particular, a novel sequential convex/dual optimization algorithm is introduced to extract the optimal 3D+t spatial-temporal deformable field, which simultaneously optimizes the sequence of 3D deformation fieldswhile enjoying both efficiencyand simplicity in numerics. The developed registration technique was evaluated by comparing two manually extracted ventricle surfaces from the baseline and the registered follow-up images using the metrics of Dice similarity coefficient (DSC), mean absolute surface distance (MAD), and maximum absolute surface distance (MAXD). The performed experiments using 14 patients with 5 time-point images per patient show that the proposed 3D+t registration approach accurately recovered the longitudinal deformation of ventricle surfaces from 3D US images. The proposed approach may be potentially used to analyse the change pattern of cerebral ventricles of IVH patients, their response to different treatment options, and to elucidate the deficiencies that a patient could have later in life. To the best of our knowledge, this paper reports the first study on the longitudinalanalysis of neonatal ventricular system from 3D US images.

In magnetic resonance (MR)-targeted, 3-D transrectal ultrasound (TRUS)-guided biopsy, prostate motion during the procedure increases the needle targeting error and limits the ability to accurately sample MR-suspicious tumor volumes. The robustness of the 2-D-3-D registration methods for prostate motion compensation is impacted by local optima in the search space. In this paper, we analyzed the prostate motion characteristics and investigated methods to incorporate such knowledge into the registration optimization framework to improve robustness against local optima. Rigid motion of the prostate was analyzed adopting a mixture-of-Gaussian (MoG) model using 3-D TRUS images acquired at bilateral sextant probe positions with a mechanically assisted biopsy system. The learned motion characteristics were incorporated into Powell's direction set method by devising multiple initial search positions and initial search directions. Experiments were performed on data sets acquired during clinical biopsy procedures, and registration error was evaluated using target registration error (TRE) and converged image similarity metric values after optimization. After incorporating the learned initialization positions and directions in Powell's method, 2-D-3-D registration to compensate for motion during prostate biopsy was performed with rms ± std TRE of 2.33 ± 1.09 mm with ~3 s mean execution time per registration. This was an improvement over 3.12 ± 1.70 mm observed in Powell's standard approach. For the data acquired under clinical protocols, the converged image similarity metric value improved in ≥8% of the registrations whereas it degraded only ≤1% of the registrations. The reported improvements in optimization indicate useful advancements in robustness to ensure smooth clinical integration of a registration solution for motion compensation that facilitates accurate sampling of the smallest clinically significant tumors.

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.

In this study, we proposed an efficient nonrigid magnetic resonance (MR) to transrectal ultrasound (TRUS) deformable registration method in order to improve the accuracy of targeting suspicious regions during a three dimensional (3-D) TRUS guided prostate biopsy. The proposed deformable registration approach employs the multi-channel modality independent neighborhood descriptor (MIND) as the local similarity feature across the two modalities of MR and TRUS, and a novel and efficient duality-based convex optimization-based algorithmic scheme was introduced to extract the deformations and align the two MIND descriptors. The registration accuracy was evaluated using 20 patient images by calculating the TRE using manually identified corresponding intrinsic fiducials in the whole gland and peripheral zone. Additional performance metrics [Dice similarity coefficient (DSC), mean absolute surface distance (MAD), and maximum absolute surface distance (MAXD)] were also calculated by comparing the MR and TRUS manually segmented prostate surfaces in the registered images. Experimental results showed that the proposed method yielded an overall median TRE of 1.76 mm. The results obtained in terms of DSC showed an average of 80.8±7.8% for the apex of the prostate, 92.0±3.4% for the mid-gland, 81.7±6.4% for the base and 85.7±4.7% for the whole gland. The surface distance calculations showed an overall average of 1.84±0.52 mm for MAD and 6.90±2.07 mm for MAXD.

This paper investigates a convex-relaxed kernel mapping formulation of image segmentation. We optimize, under some partition constraints, a functional containing two characteristic terms: 1) a data term, which maps the observation space to a higher (possibly infinite) dimensional feature space via a kernel function, thereby evaluating nonlinear distances between the observations and segments parameters and 2) a total-variation term, which favors smooth segment surfaces (or boundaries). The algorithm iterates two steps: 1) a convex-relaxation optimization with respect to the segments by solving an equivalent constrained problem via the augmented Lagrange multiplier method and 2) a convergent fixed-point optimization with respect to the segments parameters. The proposed algorithm can bear with a variety of image types without the need for complex and application-specific statistical modeling, while having the computational benefits of convex relaxation. Our solution is amenable to parallelized implementations on graphics processing units (GPUs) and extends easily to high dimensions. We evaluated the proposed algorithm with several sets of comprehensive experiments and comparisons, including: 1) computational evaluations over 3D medical-imaging examples and high-resolution large-size color photographs, which demonstrate that a parallelized implementation of the proposed method run on a GPU can bring a significant speed-up and 2) accuracy evaluations against five state-of-the-art methods over the Berkeley color-image database and a multimodel synthetic data set, which demonstrates competitive performances of the algorithm.

We propose a novel global optimization-based approach to segmentation of 3-D prostate transrectal ultrasound (TRUS) and T2 weighted magnetic resonance (MR) images, enforcing inherent axial symmetry of prostate shapes to simultaneously adjust a series of 2-D slice-wise segmentations in a "global" 3-D sense. We show that the introduced challenging combinatorial optimization problem can be solved globally and exactly by means of convex relaxation. In this regard, we propose a novel coherent continuous max-flow model (CCMFM), which derives a new and efficient duality-based algorithm, leading to a GPU-based implementation to achieve high computational speeds. Experiments with 25 3-D TRUS images and 30 3-D T2w MR images from our dataset, and 50 3-D T2w MR images from a public dataset, demonstrate that the proposed approach can segment a 3-D prostate TRUS/MR image within 5-6 s including 4-5 s for initialization, yielding a mean Dice similarity coefficient of 93.2%±2.0% for 3-D TRUS images and 88.5%±3.5% for 3-D MR images. The proposed method also yields relatively low intra- and inter-observer variability introduced by user manual initialization, suggesting a high reproducibility, independent of observers.

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.

Segmenting 3D end firing transrectal ultrasound (TRUS) prostate images efficiently and accurately is of utmost importance for the planning and guiding 3D TRUS guided prostate biopsy. Poor image quality and imaging artifacts of 3D TRUS images often introduce a challenging task in computation to directly extract the 3D prostate surface. In this work, we propose a novel global optimization approach to delineate 3D prostate boundaries using its rotational resliced images around a specified axis, which properly enforces the inherent rotational symmetry of prostate shapes to jointly adjust a series of 2D slice wise segmentations in the global 3D sense. We show that the introduced challenging combinatorial optimization problem can be solved globally and exactly by means of convex relaxation. In this regard, we propose a novel coupled continuous max-flow model, which not only provides a powerful mathematical tool to analyze the proposed optimization problem but also amounts to a new and efficient duality-based algorithm. Extensive experiments demonstrate that the proposed method significantly outperforms the state-of-art methods in terms of efficiency, accuracy, reliability and less user-interactions, and reduces the execution time by a factor of 100.

In this paper, we propose a novel global optimization based 3-D multi-region segmentation algorithm for T1-weighted black-blood carotid magnetic resonance (MR) images. The proposed algorithm partitions a 3-D carotid MR image into three regions: wall, lumen, and background. The algorithm performs such partitioning by simultaneously evolving two coupled 3-D surfaces of carotid artery adventitia boundary (AB) and lumen-intima boundary (LIB) while preserving their anatomical inter-surface consistency such that the LIB is always located within the AB. In particular, we show that the proposed algorithm results in a fully time implicit scheme that propagates the two linearly ordered surfaces of the AB and LIB to their globally optimal positions during each discrete time frame by convex relaxation. In this regard, we introduce the continuous max-flow model and prove its duality/equivalence to the convex relaxed optimization problem with respect to each evolution step. We then propose a fully parallelized continuous max-flow-based algorithm, which can be readily implemented on a GPU to achieve high computational efficiency. Extensive experiments, with four users using 12 3T MR and 26 1.5T MR images, demonstrate that the proposed algorithm yields high accuracy and low operator variability in computing vessel wall volume. In addition, we show the algorithm outperforms previous methods in terms of high computational efficiency and robustness with fewer user interactions.

This study proposes a novel multiregion image segmentation method using convex relaxation optimization and kernel mapping of the image data. The image data is transformed by a kernel function in order to support various image models while avoiding complex modeling. This is embedded implicitly in an objective function which is optimized by iterating a two-step strategy. First, a fixed point sequence is used to evaluate the regions parameters. Second, the image partition is updated by an efficient multiplier-based algorithm which uses the standard augmented Lagrangian method. A thorough experimental study is carried out over a multi-model synthetic dataset, the Berkeley database, as well as cardiac 3D data to show the effectiveness of the proposed method.

This study investigates a convex relaxation approach to figure-ground separation with a global distribution matching prior evaluated by the Bhattacharyya measure. The problem amounts to finding a region that most closely matches a known model distribution. It has been previously addressed by curve evolution, which leads to suboptimal and computationally intensive algorithms, or by graph cuts, which result in metrication errors. Solving a sequence of convex subproblems, the proposed relaxation is based on a novel bound of the Bhattacharyya measure which yields an algorithm robust to initial conditions. Furthermore, we propose a novel flow configuration that accounts for labeling-function variations, unlike existing configurations. This leads to a new max-flow formulation which is dual to the convex relaxed subproblems we obtained. We further prove that such a formulation yields exact and global solutions to the original, nonconvex subproblems. A comprehensive experimental evaluation on the Microsoft GrabCut database demonstrates that our approach yields improvements in optimality and accuracy over related recent methods.

This paper is devoted to the optimization problem of continuous multi-partitioning, or multi-labeling, which is based on a convex relaxation of the continuous Potts model. In contrast to previous efforts, which are tackling the optimal labeling problem in a direct manner, we first propose a novel dual model and then build up a corresponding duality-based approach. By analyzing the dual formulation, sufficient conditions are derived which show that the relaxation is often exact, i.e. there exists optimal solutions that are also globally optimal to the original nonconvex Potts model. In order to deal with the nonsmooth dual problem, we develop a smoothing method based on the log-sum exponential function and indicate that such a smoothing approach leads to a novel smoothed primal-dual model and suggests labelings with maximum entropy. Such a smoothing method for the dual model also yields a new thresholding scheme to obtain approximate solutions. An expectation maximization like algorithm is proposed based on the smoothed formulation which is shown to be superior in efficiency compared to earlier approaches from continuous optimization. Numerical experiments also show that our method outperforms several competitive approaches in various aspects, such as lower energies and better visual quality.

This paper studies image segmentation based on the minimum description length (MDL) functional combining spatial regularization with a penality for the number of distinct segments, a.k.a. label cost prior. Continuous MDL-based segmentation functionals were introduced in [39]. We propose a convex relaxation approach for optimizing MDL criterion that leads to a globally optimal solution. As common in recent continuous convex formulations [30, 31], we use the totalvariation functional to encode spatial regularity of segmentation bondaries. To the best of our knowledge, we are the first to demostrate that the label cost prior can be also addressed within a continuous convex framework. The second-order cone programming algorithm is applied to tackle such nonsmooth convex energy functional. The experiments validate the proposed approach and theoretical results.

We propose and study novel max-flow models in the continuous setting, which directly map the discrete graph-based max-flow problem to its continuous optimization formulation. We show such a continuous max-flow model leads to an equivalent min-cut problem in a natural way, as the corresponding dual model. In this regard, we revisit basic conceptions used in discrete max-flow / min-cut models and give their new explanations from a variational perspective. We also propose corresponding continuous max-flow and min-cut models constrained by priori supervised information and apply them to interactive image segmentation/labeling problems. We prove that the proposed continuous max-flow and min-cut models, with or without supervised constraints, give rise to a series of global binary solutions λ*(x) ϵ {0,1}, which globally solves the original nonconvex image partitioning problems. In addition, we propose novel and reliable multiplier-based max-flow algorithms. Their convergence is guaranteed by classical optimization theories. Experiments on image segmentation, unsupervised and supervised, validate the effectiveness of the discussed continuous max-flow and min-cut models and suggested max-flow based algorithms.