Energy Minimization Framework Research Articles

Abundance Estimation Using Discontinuity Preserving and Sparsity-Induced Priors

Abundance estimation is used to infer the proportions of endmembers with the given endmember signatures and reflectance value at each location. In this paper, we propose a two-phase iterative approach to estimate the abundances (fractions) of materials (endmembers) from the pixels of hyperspectral images (HSIs) by using the energy minimization framework. A linear mixture model is used to define the data term. We observe that abundance maps have homogeneous regions with limited discontinuity, and they exhibit spatial redundancy. Hence, we use inhomogeneous Gaussian Markov random field (IGMRF) and sparsity-induced priors as the regularization terms. While the IGMRF prior captures the smoothness and preserves discontinuities among abundance values, the sparsity-induced prior accounts for redundancy. We calculate the IGMRF parameters at every pixel location and learn a dictionary and the sparse representation for abundances using the initial estimate in phase 1, while the final abundance maps are estimated in phase 2. In order to learn the sparsity, we use the approach based on K-singular value decomposition. Both the IGMRF and sparseness parameters are initialized using an initial estimate of abundances and refined using the two-phase iterative approach. The experiments are conducted on synthetic hyperspectral HSIs with different noise levels, as well as on two real HSIs. The results are qualitatively and quantitatively compared with state-of-the-art approaches. Experimental results demonstrate the effectiveness of the proposed approach.

Medial axis segmentation of cranial nerves using shape statistics-aware discrete deformable models.

We propose a segmentation methodology for brainstem cranial nerves using statistical shape model (SSM)-based deformable 3D contours from T2 MR images. We create shape models for ten pairs of cranial nerves. High-resolution T2 MR images are segmented for nerve centerline using a 1-Simplex discrete deformable 3D contour model. These segmented centerlines comprise training datasets for the shape model. Point correspondence for the training dataset is performed using an entropy-based energy minimization framework applied to particles located on the centerline curve. The shape information is incorporated into the 1-Simplex model by introducing a shape-based internal force, making the deformation stable against low resolution and image artifacts. The proposed method is validated through extensive experiments using both synthetic and patient MRI data. The robustness and stability of the proposed method are experimented using synthetic datasets. SSMs are constructed independently for ten pairs (CNIII-CNXII) of brainstem cranial nerves using ten non-pathological image datasets of the brainstem. The constructed ten SSMs are assessed in terms of compactness, specificity and generality. In order to quantify the error distances between segmented results and ground truths, two metrics are used: mean absolute shape distance (MASD) and Hausdorff distance (HD). MASD error using the proposed shape model is 0.19 ± 0.13 (mean ± std. deviation) mm and HD is 0.21mm which are sub-voxel accuracy given the input image resolution. This paper described a probabilistic digital atlas of the ten brainstem-attached cranial nerve pairs by incorporating a statistical shape model with the 1-Simplex deformable contour. The integration of shape information as a priori knowledge results in robust and accurate centerline segmentations from even low-resolution MRI data, which is essential in neurosurgical planning and simulations for accurate and robust 3D patient-specific models of critical tissues including cranial nerves.

Level set model for water region segmentation in synthetic aperture radar images

A level set model is presented for water region segmentation in synthetic aperture radar (SAR) images. We formulate the segmentation problem within a global energy minimization framework. First, the background and foreground regions in SAR images are modeled as G0 distributions. They are then used to construct the energy functional for the desired regions. To avoid the local minimum problem, the energy functional is transferred into a strictly convex model that guarantees the existence of the global minimum. During the iterative process, a sinusoidal signed pressure force (SPF) function is applied to efficiently locate weak or blurred edges in the heterogeneous regions. Finally, a Gaussian convolution is used to equivalently substitute the Laplacian of the level set function in the evolution equation, which omits the reinitialization at each iteration. Since based on the stationary global minimum, the presented model can accurately detect inside edges, regardless of the position and shape of the initial contour. Furthermore, because the SPF function can enhance the acquisition ability to the target contour, the internal and external motions of the curve can be accelerated. Thus, the convergence speed of the curve can be improved significantly. The experimental results based on the simulated and real SAR data demonstrate the effectiveness of our method.

As-planar-as-possible depth map estimation

We propose an approach to compute dense disparity maps that takes the characteristics of man-made environments into account. The key contribution is to generate a piecewise planar disparity map while preventing the oversimplification problem in non-planar regions. To achieve this, we decompose the stereo matching problem into three sequential subproblems: initial disparity map estimation, plane hypotheses generation, and global optimization with plane hypotheses. After finding an initial disparity map, we find local and global plane hypotheses from the disparity map through segmentation-based local plane fitting, agglomerative hierarchical clustering, and energy-based multi-model fitting techniques. We then estimate a disparity map that is a mixture of over-parameterized and scalar disparity values while identifying unreliable pixels in an energy minimization framework; disparity values in planar regions are parameterized as a plane, disparity values in non-planar regions are represented as scalar, and unreliable pixels are marked as outliers. As a post-processing step, we perturb assigned plane parameters as well as scalar disparity values. We experimentally verify the proposed method using publicly available benchmarks and various stereo matching algorithms.

Digital Foveation: An Energy-Aware Machine Vision Framework

In machine vision applications, imaging systems and analysis algorithms are generally interdependent and energy intensive. We describe a machine vision energy minimization framework in which imaging hardware and vision algorithms are co-designed and tightly integrated. Digital foveation is inspired by the human vision system, which uses a spatially varying sensing architecture to generate oculomotory feedback and capture a series of high-resolution images using the densely sampling fovea. A multiround process with bidirectional information flow between camera hardware and analysis software optimizes energy consumption while preserving accuracy. By using existing hardware mechanisms, namely, row / column skipping, random access via readout circuitry, and frame preservation, digital foveation adapts to the chosen analysis algorithm. It aims to transmit and process only the necessary parts of the scene under consideration. This framework is general across a wide range of embedded machine vision applications and enables large improvements in energy efficiency. When evaluated for an embedded license plate recognition vision application, it reduces system energy consumption by 81.3% with at most 0.65% reduction in accuracy.

Segmenting Oil Spills from Blurry Images Based on Alternating Direction Method of Multipliers

We exploit the alternating direction method of multipliers (ADMM) for developing an oil spill segmentation method, which effectively detects oil spill regions in blurry synthetic aperture radar (SAR) images. We commence by constructing energy functionals for SAR image deblurring and oil spill segmentation separately. We then integrate the two energy functionals into one overall energy functional subject to a linear mapping constraint that correlates the deblurred image and the segmentation indicator. The overall energy functional along with the linear constraint follows the form of ADMM and thus enables an effective augmented Lagrangian optimization. Furthermore, the iterative updates in the ADMM maintain information exchanges between the energy minimizations for SAR image deblurring and oil spill segmentation. Most existing blurry image segmentation strategies tend to consider deblurring and segmentation as two independent procedures with no interactions, and the operation of deblurring is thus not guided for obtaining an accurate segmentation. In contrast, we integrate deblurring and segmentation into one overall energy minimization framework with information exchanges between the two procedures. Therefore, the deblurring procedure is inclined to operate in favor of the more accurate oil spill segmentation. Experimental evaluations validate that our framework outperforms the separate deblurring and segmentation strategy for detecting oil spill regions in blurry SAR images.

Decision Fusion With Multiple Spatial Supports by Conditional Random Fields

Classification of remotely sensed images into land cover or land use is highly dependent on geographical information at least at two levels. First, land cover classes are observed in a spatially smooth domain separated by sharp region boundaries. Second, land classes and observation scale are also tightly intertwined: they tend to be consistent within areas of homogeneous appearance, or regions, in the sense that all pixels within a roof should be classified as roof, independently on the spatial support used for the classification. In this paper, we follow these two observations and encode them as priors in an energy minimization framework based on conditional random fields (CRFs), where classification results obtained at pixel and region levels are probabilistically fused. The aim is to enforce the final maps to be consistent not only in their own spatial supports (pixel and region) but also across supports, i.e., by getting the predictions on the pixel lattice and on the set of regions to agree. To this end, we define an energy function with three terms: 1) a data term for the individual elements in each support (support-specific nodes); 2) spatial regularization terms in a neighborhood for each of the supports (support-specific edges); and 3) a regularization term between individual pixels and the region containing each of them (intersupports edges). We utilize these priors in a unified energy minimization problem that can be optimized by standard solvers. The proposed 2LCRF model consists of a CRF defined over a bipartite graph, i.e., two interconnected layers within a single graph accounting for interlattice connections.

Iterative Graph Seeking for Object Tracking

To effectively solve the challenges in object tracking, such as large deformation and severe occlusion, many existing methods use graph-based models to capture target part relations, and adopt a sequential scheme of target part selection, part matching, and state estimation. However, such methods have two major drawbacks: 1) inaccurate part selection leads to performance deterioration of part matching and state estimation and 2) there are insufficient effective global constraints for local part selection and matching. In this paper, we propose a new object tracking method based on iterative graph seeking, which integrate target part selection, part matching, and state estimation using a unified energy minimization framework. Our method also incorporates structural information in local parts variations using the global constraint. We devise an alternative iteration scheme to minimize the energy function for searching the most plausible target geometric graph. Experimental results on several challenging benchmarks (i.e., VOT2015, OTB2013, and OTB2015) demonstrate improved performance and robustness in comparison with existing algorithms.

A PHASE FIELD METHOD TO SIMULATE CRACK NUCLEATION AND CRACK PROPAGATION IN ROCK-LIKE MATERIALS

In the phase field method, by defining a continuous distribution function to approximate discontinuous cracks, a variational-based energy minimization framework was established to obtain the governing equations of the physical field. As an outstanding feature, it allows describing crack nucleation and branching without any prescription of the shape, size and orientation of the cracks, thus providing a very robust numerical framework for crack propagation simulation. In this paper, rock specimens containing two parallel cracks with different rock bridge angles are simulated under uniaxial compression condition to investigate crack nucleation and propagation configuration with the phase field method. The simulation results are compared with the experimental data, showing that the phase field method, as a new numerical technique in rock mechanics community, works quite satisfactorily in simulating the cracks nucleation and propagation of rock-like materials under the considered loading paths. Meanwhile, perspectives would be envisaged that the phase field method has important engineering significance in stability and durability analysis of rock structures.

Superpixel-based optimal seamline detection in the gradient domain via graph cuts for orthoimage mosaicking

ABSTRACTThis paper presents an optimal seamline detection method for orthoimage mosaicking. To ensure that the detected optimal seamlines avoid crossing many obvious objects, we first design a simple but effective criterion in the gradient domain in lieu of the traditionally used intensity domain to measure the visibility of the seam. Thereafter, we fuse this new criterion into the graph cuts energy minimisation framework to globally find the last optimal seamlines. Instead of finding the optimal solutions of seamlines in overlap regions via graph cuts among the entire set of pixels, we first find them among superpixels created from input images and then refine them in the pixel level, which greatly improves the efficiency of the global graph cuts energy optimisation because the number of elements in graph cuts dramatically decreases. Experimental results on orthoimages show that our proposed method is capable of finding high-quality seamlines for orthoimage mosaicking, and outperforms state-of-the-art algorithms and software.

Geometric-constrained multi-view image matching method based on semi-global optimization

Targeting at a reliable image matching of multiple remote sensing images for the generation of digital surface models, this paper presents a geometric-constrained multi-view image matching method, based on an energy minimization framework. By employing a geometrical constraint, the cost value of the energy function was calculated from multiple images, and the cost value was aggregated in an image space using a semi-global optimization approach. A homography transform parameter calculation method is proposed for fast calculation of projection pixel on each image when calculating cost values. It is based on the known interior orientation parameters, exterior orientation parameters, and a given elevation value. For an efficient and reliable processing of multiple remote sensing images, the proposed matching method was performed via a coarse-to-fine strategy through image pyramid. Three sets of airborne remote sensing images were used to evaluate the performance of the proposed method. Results reveal that the multi-view image matching can improve matching reliability. Moreover, the experimental results show that the proposed method performs better than traditional methods.

Reading Nanomagnetic Energy Minimizing Coprocessor

Nanomagnetic coprocessor enacts an energy minimization framework to solve the quadratic optimization problem often arisen in a computer vision paradigm. Our approach relies on the fact that the Hamiltonian of a system of coupled nanomagnets is quadratic. Therefore, a wide class of quadratic energy minimization can be solved directly by the relaxation physics of a grid of nanomagnets. The solutions of such problems are obtained from reading the magnetic state of the cells, in other words, the resistance. This monograph explores the methods to detect the magnetic states, and also considers the dimensional variation of each cell of the coprocessor and inspects the resultant change in resistance. We measure at most ${\text{7.8}}$ % change in resistance due to the process imperfection of in-house fabrication processes. This requires a read circuitry that can handle the largest deviation. Unlike STT-MRAM, the circular magnets do not have shape anisotropy but, here we show that with an additional preamplifier circuit, we are able to improve sense margin by at least ${\text{73}}$ %.

Magnetoelasticity of gels

Magnetoelastic gel is an active material that is used widely these days. The behavior of these multifunctional gels is derived from a polymer matrix and magnetoresponsive inclusions. The polymer matrix provides structural integrity as well as load bearing capacity to the magnetoelastic gel. The magnetic behavior of the magnetoelastic gel is attributed to a large number of nano-to-micron-sized magnetic particles disbursed in the polymer matrix. The magnetoelastic gel is said to be diluted if the interparticle interactions are negligible/small or concentrated if there are strong interparticle interactions. We consider strong interparticle interactions in the magnetoelastic gel. When the magnetic field is applied to the magnetoelastic gel, the disbursed magnetic particles tend to translate and rotate to a new deformed configuration. Due to these translations and rotations of the many magnetoelastic particles, the polymer matrix around each particle deforms. These micro-deformations then coalesce and lead to the overall macroscopic deformation of the magnetoelastic gel. Both magnetization and mechanical strain characterize the magnetoelastic behavior of the magnetoelastic gel. In this article, an energy minimization approach is followed to find the equilibrium magnetization and strain. We formulate the total energy of the magnetoelastic gel on multiple-length scales and minimize it to obtain these equilibrium magnetization and mechanical strain. We also investigate the effect of particle size and polarization under the framework of energy minimization.

Boundary connectedness-based salient video object segmentation

One of the most challenging tasks in computer vision is to emulate human cognitive ability to extract the salient object in a scene. We tackle the task of unsupervised salient video object segmentation using boundary connectedness and space-time salient regions. First, boundary prior measure is used to separate salient regions detected in both space and time. Then, background-foreground regions connectedness is computed and combined with appearance model via an iterative energy minimization framework to segment the salient moving object. For temporal consistency, the segmentation result of the current frame is used in addition to the optical flow and the boundary prior to segmenting the next frame. The experiments show a good performance of our algorithm for salient video object segmentation on benchmark datasets even in the presence of different challenges.

Balancing the data term of graph-cuts algorithm to improve segmentation of hepatic vascular structures

PurposeThe accurate delineation of hepatic vessels is important to diagnosis and treatment planning. To improve the segmentation of these vessels and extract small structures, we adaptively calculate the data term in conventional graph-cuts algorithm. MethodTo assign higher costs to the data term in small vessel regions, we estimate the statistical parameters of the vessel adaptively. After preprocessing an input CT image, we model the liver and its vessels by two Gaussian distributions. The Maximum Intensity Projection (MIP) of the image is employed in the Expectation-Maximization algorithm to estimate the parameters of the model. These parameters are used together with a medial-axes enhancement algorithm to find the axes of the vessels. The skeleton of these vessels is considered to be the image voxels that are most similar to the hepatic vascular structures. To calculate the cost function of the graph-cuts algorithm, those axes that are nearby are employed to estimate the vessel parameters. The conventional minimum-cut/maximum-flow energy minimization framework finds the global minimum of the cost function and labels vessel voxels. ResultWe evaluated our method using synthetic data and clinical images. We compared our algorithm with state-of-the-art vessel segmentation methods. The mean Dice measure of our results was 95.51% (0.9% lower than the first rank method). Quantitatively, our method segmented small hepatic vessels that were not extracted by traditional techniques including conventional graph-cuts. ConclusionThe proposed method improved the segmentation of small vessels in the presence of noise.

Rapid conceptual design and analysis of spatial flexure mechanisms

Flexure mechanisms are the central part of precision instruments and devices for numerous science and engineering applications. Currently, design of flexure mechanisms often heavily relies on finite element analysis. However, the modeling complexity and low computational efficiency make it not suitable for the early design stage when many concepts need to be evaluated in a short period of time. To reduce the overhead in the conceptual design stage, we present a multi-segment energy minimization framework that integrates linear elastic theory for kinetostatic analysis of spatial flexure mechanisms. Compliance matrices for commonly used flexure elements are presented and their accuracy was studied and verified in detail. While deformation of each individual segment depends on the linear elastic theory, the multi-segment model allows accurate calculation of large deformations with high computational efficiency. To facilitate modeling of spatial flexure mechanisms, we have also implemented rich Graphical User Interfaces (GUI) in MATLAB environment. The proposed framework and software tool are tested with spatial mechanisms in which nonlinear kinematic constraints and combined loading are present. The examples showed that the proposed multi-segment framework can accurately capture large kinematic motion subjected to complex loading.

Gradient-enhanced model and its micromorphic regularization for simulation of Lüders-like bands in shape memory alloys

Shape memory alloys, notably NiTi, often exhibit softening pseudoelastic response that results in formation and propagation of Lüders-like bands upon loading, for instance, in uniaxial tension. A common approach to modelling softening and strain localization is to resort to gradient-enhanced formulations that are capable of restoring well-posedness of the boundary-value problem. This approach is also followed in the present paper by introducing a gradient-enhancement into a simple one-dimensional model of pseudoelasticity. In order to facilitate computational treatment, a micromorphic-type regularization of the gradient-enhanced model is subsequently performed. The formulation employs the incremental energy minimization framework that is combined with the augmented Lagrangian treatment of the resulting non-smooth minimization problem. A thermomechanically coupled model is also formulated and implemented in a finite-element code. The effect of the loading rate on the localization pattern in a NiTi wire under tension is studied, and the features predicted by the model show a good agreement with the experimental observations. Additionally, an analytical solution is provided for a propagating interface (macroscopic transformation front) both for the gradient-enhanced model and for its micromorphic version.

Structure-preserving image completion with multi-level dynamic patches

In this paper, we present a novel structure-preserving image completion approach equipped with dynamic patches. We formulate the image completion problem into an energy minimization framework that accounts for coherence within the hole and global coherence simultaneously. The completion of the hole is achieved through iterative optimizations combined with a multi-scale solution. In order to avoid abnormal structure and disordered texture, we utilize a dynamic patch system to achieve efficient structure restoration. Our dynamic patch system functions in both horizontal and vertical directions of the image pyramid. In the horizontal direction, we conduct a parallel search for multi-size patches in each pyramid level and design a competitive mechanism to select the most suitable patch. In the vertical direction, we use large patches in higher pyramid level to maximize the structure restoration and use small patches in lower pyramid level to reduce computational workload. We test our approach on massive images with complex structure and texture. The results are visually pleasing and preserve nice structure. Apart from effective structure preservation, our approach outperforms previous state-of-the-art methods in time consumption.

P.3.b.043 - Two-year follow-up of patients with a first psychotic episode: comparison between affective and non-affective psychoses and predictors of functioning

Dense registration of different impressions of the same finger is beneficial to various fingerprint matching methods. This is a challenging problem due to elastic distortion of finger skin and sparsity of distinctive features (namely minutiae) in fingerprints. Most existing fingerprint registration algorithms produce only correspondences between minutiae, which are not sufficient for dense registration of fingerprints. In this paper, we proposed a novel dense fingerprint registration algorithm, which consists of a composite initial registration step and a dual-resolution block-based registration step. The dual-resolution block-based registration is approached in an energy minimization framework which consists of local search, energy function construction and global optimization. In local search step, a candidate set of transformations of every input image block are found using image correlation w.r.t. the corresponding reference image block. In energy function construction, two factors are considered: (1) the similarity between the transformed input block and the corresponding reference block, and (2) the compatibility between transformations of neighboring input blocks. In global optimization, a region growing style algorithm is proposed to minimize the energy function. Experimental results on three databases containing many distorted fingerprints, namely FVC2004 DB1, Tsinghua Distorted Fingerprint database and NIST SD27 latent fingerprint database, show that the proposed algorithm not only produces more accurate registration results but also improves the matching performance by fusion of minutiae matching and image correlation.

Optimal seamline detection in dynamic scenes via graph cuts for image mosaicking

In this paper, we present a novel method for creating a seamless mosaic from a set of geometrically aligned images captured from the scene with dynamic objects at different times. The artifacts caused by dynamic objects and geometric misalignments can be effectively concealed in our proposed seamline detection algorithm. In addition, we simultaneously compensate the image regions of dynamic objects based on the optimal seamline detection in the graph cuts energy minimization framework and create the mosaic with a relatively clean background. To ensure the high quality of the optimal seamline, the energy functions adopted in graph cuts combine the pixel-level similarities of image characteristics, including intensity and gradient, and the texture complexity. To successfully compensate the image regions covered by dynamic objects for creating a mosaic with a relatively clean background, we initially detect them in overlap regions between images based on pixel-level and region-level similarities, then refine them based on segments, and determine their image source in probability based on contour matching. We finally integrate all of these into the energy minimization framework to detect optimal seamlines. Experimental results on different dynamic scenes demonstrate that our proposed method is capable of generating high-quality mosaics with relatively clean backgrounds based on the detected optimal seamlines.