3D Deformable Model Research Articles

Weakly Supervised 3D Face Reconstruction with Joint Spatial and Frequency Domain Information

3D face reconstruction is an important research direction in computer vision, and its goal is to recover a 3D face model from a single face picture. In the absence of real 3D face data, how to reconstruct a 3D face with a high degree of realism has become a hot research topic in recent years. Existing reconstruction algorithms usually rely on 3D labels generated from a large number of 2D face images as training data, however, inaccurate data will seriously affect the reconstruction quality. For this reason, the paper proposes a joint spatial-frequency domain decoupled weak supervision to achieve 3D face reconstruction, the main idea of which is to construct a multi-level loss function by using the weakly supervised information extracted from the spatial domain, and separating the frequency-domain information between the input and the rendered image in the frequency domain, and minimizing the difference between the two by difference computation. The method combines deep learning with 3D deformable models to reconstruct 3D models with high quality texture and shape from only a single face image. Quantitative experiments on the AFLW2000-3D and MICC Florence datasets show that the normalized average error in the small pose interval is as low as 2.42%, and the face reconstruction accuracy in the outdoor scene is 0.98 0.22 mm. Qualitative experiments on the MoFa-test, MICA datasets show that when faced with reconstruction with different poses, lighting, and expressions , our method outperforms other state-of-the-art reconstruction methods.

3D deformation analysis for earth dam monitoring based on terrestrial laser scanning (TLS) and the iterative closest point (ICP) algorithm

Introduction: The conventional 3-D point cloud-based deformation analysis methods, such as the shortest distance (SD), cloud-to-cloud (C2C), and multiscale model-to-model cloud comparison (M3C2), essentially regard the closest distance between two periods of point cloud data as the deformation, rather than the true position of the same point in 3-D space before and after deformation.Methods: This paper proposes a method based on the ICP algorithm to calculate the differences between the chunked multi-period point clouds to recognizes the 3-D deformations.Results and discussion: The results show that the obtained results are very close to the GNSS data but with a much larger spatial monitoring range. The accuracy is higher than that of the SD method. Moreover, we analyze the statistical relationship between the point cloud block size and the deformation vector error and determine the optimal block size. The aim of this article is to optimize the deformation analysis method and improve its accuracy to provide techniques and ideas for the wider surface deformation monitoring research field. For instance, combining this method with data from contact methods constructs a 3D overall deformation model of the mountain, enabling real-time monitoring and early warning of debris flows.

A proposed reconstruction method of a 3D animation scene based on a fuzzy long and short-term memory algorithm.

With the development of computer technology leading to a broad range of virtual technology implementations, the construction of virtual tasks has become highly demanded and has increased rapidly, especially in animation scenes. Constructing three-dimensional (3D) animation characters utilizing properties of actual characters could provide users with immersive experiences. However, a 3D face reconstruction (3DFR) utilizing a single image is a very demanding operation in computer graphics and vision. In addition, limited 3D face data sets reduce the performance improvement of the proposed approaches, causing a lack of robustness. When datasets are large, face recognition, transformation, and animation implementations are relatively practical. However, some reconstruction methods only consider the one-to-one processes without considering the correlations or differences in the input images, resulting in models lacking information related to face identity or being overly sensitive to face pose. A face model composed of a convolutional neural network (CNN) regresses 3D deformable model coefficients for 3DFR and alignment tasks. The manuscript proposes a reconstruction method for 3D animation scenes employing fuzzy LSMT-CNN (FLSMT-CNN). Multiple collected images are employed to reconstruct 3D animation characters. First, the serialized images are processed by the proposed method to extract the features of face parameters and then improve the conventional deformable face modeling (3DFDM). Afterward, the 3DFDM is utilized to reconstruct animation characters, and finally, high-precision reconstructions of 3D faces are achieved. The FLSMT-CNN has enhanced both the precision and strength of the reconstructed 3D animation characters, which provides more opportunities to be applied to other animation scenes.

A Lightweight Monocular 3D Face Reconstruction Method Based on Improved 3D Morphing Models.

In the past few years, 3D Morphing Model (3DMM)-based methods have achieved remarkable results in single-image 3D face reconstruction. However, high-fidelity 3D face texture generation has been successfully achieved with this method, which mostly uses the power of deep convolutional neural networks during the parameter fitting process, which leads to an increase in the number of network layers and computational burden of the network model and reduces the computational speed. Currently, existing methods increase computational speed by using lightweight networks for parameter fitting, but at the expense of reconstruction accuracy. In order to solve the above problems, we improved the 3D deformation model and proposed an efficient and lightweight network model: Mobile-FaceRNet. First, we combine depthwise separable convolution and multi-scale representation methods to fit the parameters of a 3D deformable model (3DMM); then, we introduce a residual attention module during network training to enhance the network's attention to important features, guaranteeing high-fidelity facial texture reconstruction quality; and, finally, a new perceptual loss function is designed to better address smoothness and image similarity for the smoothing constraints. Experimental results show that the method proposed in this paper can not only achieve high-precision reconstruction under the premise of lightweight, but it is also more robust to influences such as attitude and occlusion.

Semi-automatic 3D reconstruction of middle and inner ear structures using CBCT

ABSTRACT We present a semi-automatic reconstruction approach of middle and inner ear structures using generic 3D deformable surface models from Cone Beam CT (CBCT) examination. First, the user must position a set of control points in the CBCT volume for each of the 4 structures of the inner and middle ear. These points are used to position the deformable surface models and to customize them so that they are as close to the boundaries as possible. Finally, each mesh is refined iteratively segmenting the limits of the structure while taking into account neighbouring structures as boundary constraints. Our method is tested on left and right ears of 20 scans of patients analysed retrospectively. The results show the efficiency and reliability of this approach with an average Dice Similarity Coefficient of 91.8% for the inner ear model and 89.9% for the ossicular chain and a total reconstruction time of 5 minutes. The implementation of our method in a clinical setting could provide clinicians with distinct and accurate 3D models of the ear structures without requiring a tedious manual segmentation step, in order to give them a better understanding of the auditory system in vivo and help them in diagnosis and follow-up.

Measurements of Rayleigh wave ellipticity anisotropy and implications for distinct crustal deformation styles across the SE Tibet margin

Plateau growth of southeastern Tibet is often understood by applying the end-member conceptual models, such as ductile material flow in the deep crust, and lateral extrusion of coherently deforming or rigid blocks. Though recent studies suggest the local crustal flow and movements of rigid blocks may be compatible in a way, ambiguities still persist in the formation of the gently sloping margin of southeastern Tibet and interactions between the plateau and the outer forelands. Here we present a 3D crustal deformation model in southeastern Tibet and adjacent regions, by summarizing different types of seismic anisotropy measurements including a newly obtained continuous map of uppermost crustal anisotropy, which are derived from observations of the directionally dependent teleseismic Rayleigh wave ellipticity. Layered deformation is observed within the crust beneath the southeastern Tibet Plateau, while the outer foreland shows an overall coherently deforming mode. The conspicuous change of the crustal deformation styles across the southeastern Tibet margin is against the idea that the low topographic gradients of the plateau margin were produced by leakage of ductile deep crust beneath the plateau. We argue that both the crustal flow beneath the plateau interior and lateral extrusion of the outer foreland accommodate the intracontinental convergence at southeastern Tibet.

Preoperative Simulation of Ileal Pouch-Anal Anastomosis in Patients With Ulcerative Colitis Using a 3-Dimensional Printed Model.

During restorative proctocolectomy with ileal pouch-anal anastomosis for ulcerative colitis-associated colorectal cancer or dysplasia, ileal pouch-anal handsewn anastomosis (IAA) is preferred to avoid the risk of cancer development in the remaining rectal mucosa. However, there is a risk of the ileal pouch not reaching the anus with this procedure. Here, we created deformable 3-dimensional (3D) models for simulation. Six patients who underwent IAA without vessel ligation and 5 patients who underwent ileal pouch-anal canal double-stapled anastomosis (IACA) because the ileal pouch did not reach the anus were studied. A 3D printer was used to create deformable 3D models from the data obtained from computed tomography scans. The positional relationship among the mesenteric arteries, pubis, and coccyx were evaluated. The distance between the superior mesenteric artery root and the tip of the ileal artery was longer in the IAA group than that in the IACA group (IAA vs IACA: 26.2 ± 2.1 cm vs 20.9 ± 1.6cm). The distance from the tip of the ileal artery to the coccyx (IAA vs IACA: 6.7 ± 1.7 cm vs 12.1 ± 2.1 cm) and the distance from the tip of the ileal artery to the lower edge of the pubis (IAA vs IACA; 8.1 ± 1.3 cm vs 12.7 ± 2.4 cm) were longer in the IACA group than those in the IAA group. We established a method for creating 3D deformable models of patients with ileal pouch-anal anastomosis. These 3D models may be useful for preoperative simulation.

Coseismic Deformation Responses due to Geometrical Structure and Heterogeneity of the Accretionary Wedge: Study Case 2010 Mentawai Earthquake, West Sumatra, Indonesia

The assumption of a homogeneous elastic half-space model is widely used to model the earth’s deformation. However, the homogeneous assumption would not accurately reflect the complexity of the shallow crust. We performed a 3D coseismic deformation model using the finite element method and referred to the 2010 Mentawai earthquake. The 2010 tsunami earthquake was located at the Mentawai segment, which is a part of the accretionary wedge in the Sumatra subduction zone. This active accretionary wedge is identified as the most complicated structure on earth and lies along the Sumatra subduction zone, at which most destructive earthquakes happen in this region. We examined the impact of the accretionary wedge geometry and material properties by considering the wedge as a single different property separated from the continental plate. Various geometrical features, such as topography and wedge dimension, as well as physical properties, were simulated. Those features are then observed for their responses on the surface deformation. The topography affected the magnitude of the horizontal deformation up to 10% but only the pattern of the vertical deformation. The wedge dimension seems to have an insignificant influence on the surface deformation compared to the topography. Different physical properties of the accretionary wedge affect not only the magnitude of the horizontal deformation up to 40% but also the orientation. The direction of the lateral movement is seemingly affected by the material under the GPS station and by the source. On the other hand, the variations in the physical properties resulted in discrepancies of 0.5 meters in the vertical deformation near the source. These results indicated that regional physical property information and geometrical features are critical in estimating coseismic deformation, leading to more accurate slip inversion and earthquake and tsunami hazard prediction, particularly in regions with significant inhomogeneity.

Fault Displacement of the 2011 Mw 6.6 Fukushima-ken Hamadori Earthquake Based on a 3D Crustal Deformation Model Constructed Using Differential InSAR–Lidar

ABSTRACT 3D coseismic deformation detected by remote sensing yields essential information for estimating the geometry and slip distribution of the causative fault. However, it is often difficult to be obtained by a single observation method due to data acquisition constraints. This study constructs a 3D coseismic deformation model of the 2011 Fukushima-ken Hamadori earthquake by integrating Differential Interferometric Synthetic Aperture Radar (DInSAR), and differential light detection and ranging (Dlidar) analyses. Both horizontal and vertical movements observed are almost consistent with those of the theoretical dislocation model of normal faulting. The fault displacements measured within ±45 m of the rupture based on the 3D deformation model is also in good agreement with the possible maximum field displacements. Fault dips and lateral displacement components are also harmonious with the field survey measurements. Dlidar detects full 3D motion, whereas the DInSAR detects deformations too small for the light detection and ranging (lidar). Combining the two products is helpful to produce a more robust 3D displacement field than possible from the lidar alone.

Femoral strength can be predicted from 2D projections using a 3D statistical deformation and texture model with finite element analysis

Ultimate force of the proximal human femur can be predicted using Finite Element Analysis (FEA), but the models rely on 3D computed tomography images. Landmark-based statistical appearance models (SAM) and B-Spline transformation-based statistical deformation models (SDM) have been used to estimate 3D images from 2D projections, which facilitates model generation and reduces the radiation dose. However, there is no literature on the accuracy of SDM-based FEA models of bones with respect to experimental results. In this study, a methodology for an enhanced SDM with textural information is presented. The statistical deformation and texture models (SDTMs) are based on a set of 37 quantitative CT (QCT) images. They were used to estimate 3D images from two or one projections of the set in a leave-one-out setup. These estimations where then used to create FEA models. The ultimate force predicted by FEA models estimated from two or one projection using the SDTMs were compared to the experimental ultimate force from a previous study on the same femora and to the results of standard QCT-based FEA models. High correlations between predictions and experimental measurements were found for FEA models reconstructed from 2D projections with R2=0.835 when based on two projections and R2=0.724 when using one projection. The correlations were comparable to those reached with standard QCT-based FE-models with the experimental results (R2=0.795). This study shows the high potential of SDTM-based 3D image reconstruction and FEA modelling from 2D projections to predict femoral ultimate force.

Large-Amplitude Vibrations of Spider Web Structures

Spider silk, as a natural material, shows exceptional performance in its properties. The combination of the superior properties of spider silk and the geometry of spider structures make the spider web very resilient. A spider web structure can be considered as a cable-like structure with inappreciable torsional, bending and shear rigidities. An investigation emphasising on natural frequencies and corresponding mode shapes with and without the consideration of geometric nonlinearity is presented in this paper. This study is the world’s first discovery of large amplitude free vibration behaviours of spider web structures. Large deformable finite element 3D models of spider web structures have been developed and validated. By using the energy method, the variational model of the spider web structures have been established to further extend the finite element model, consisting of the strain energy due to axial deformation, kinetic energy due to the spider web movement and the virtual work caused by the self-weight per unit unstretched length. The emphasis of this study is placed on the linear and geometric nonlinear behaviour of the spider web structures considering different structural patterns and material properties. To determine the large-amplitude free vibrational behaviours, a series of pretension load is applied to the first step in Abaqus to initiate the nonlinear strain-displacement relationships enabling a precursor to free vibrations. The parametric studies stemming from structural patterns (the number of radial and capture threads), elastic modulus, density, and inertia moment have been highlighted. The insight will help engineers and scientists to adapt the concept of spider webs, their geometric properties, and damage patterns for the design of any structural membranes, preventing any failure from dynamic resonances and nonlinear phenomena.

3-Dimensional personalized planning for transcatheter pulmonary valve implantation in a dysfunctional right ventricular outflow tract

BackgroundIdentification of adequate landing zone for transcatheter pulmonary valve implantation (TPVI) is crucial to successfully treat an aneurysmatic native right ventricle outflow tract (RVOT); three-dimensional (3D) patient-tailored digital and physical printed models are available but their actual strengths and weaknesses still not well documented. The aim of the study was to tackle TPVI planning in the dysfunctional and borderline RVOT exploiting both digital and physical printed 3D patient-specific models. MethodsElectrocardiographically gated computed tomography (CT) angiography was segmented and anatomical RVOT geometrical changes dynamically tracked throughout the cardiac cycle using in-house processing. A compliant 3D-printed model was manufactured from the diastolic rest phase to test in vitro the catheter-based procedure feasibility; results were compared against CT-derived in vivo measurements and the actual catheterization outcome. ResultsCT-gated analysis successfully quantified in vivo RVOT dynamic changes corroborating the feasibility of non-conventional pulmonary jailing percutaneous intervention. Clinicians used the 3D-printed model to test the steps of the jailing procedure; yet, the deformable 3D model printed at diastole underestimated the final implant dimensions obtained during cardiac catheterization by the same operators. ConclusionsMultidisciplinary synergy between CT-gated analysis and pre-procedural tests on 3D-printed phantoms can help the interventional team to tackle complex TPVI procedures. To fully exploit 3D-printed models, adequate selection of the still frame to print and tuning of printing material properties is crucial and can be aided by 3D dynamic virtual models.

A study on 3D virtual body formation and deformation by body shape analysis

Purpose The purpose of this paper is to use body shape analysis and develop a 3D virtual body formation and deformation model that can accurately express size and shape. Design/methodology/approach In this paper, 1,882 sets of direct measurement data of Korean women in their 20s (19–29 years) were analyzed. These data sets were sourced from the sixth and seventh “Size Korea” anthropometric survey data. Through body shape analysis, the authors classified them into seven body types and selected their representative bodies. A 2D image based on the height, breadth, depth and length was first formed, and the representative virtual body was modeled using the polygon technique. The authors calculated the grading ratios for each body type according to the clothing sizing system, and modified the virtual body size type by morphing technique. Findings In order to accurately evaluate the fit in a virtual fitting system, it is necessary to study the body size and shape of the target age; this makes it possible to form virtual body reflecting the size and shape. Originality/value In this paper, the authors propose a new 3D virtual body formation method that is more accurate in shape and size compared to the present system. Through this, it will be possible to grasp the accurate simulation state in the virtual fitting system, and thereby evaluate the accurate fit.

Development of a finite element musculoskeletal model with the ability to predict contractions of three-dimensional muscles

Representation of realistic muscle geometries is needed for systematic biomechanical simulation of musculoskeletal systems. Most of the previous musculoskeletal models are based on multibody dynamics simulation with muscles simplified as one-dimensional (1D) line-segments without accounting for the large muscle attachment areas, spatial fibre alignment within muscles and contact and wrapping between muscles and surrounding tissues. In previous musculoskeletal models with three-dimensional (3D) muscles, contractions of muscles were among the inputs rather than calculated, which hampers the predictive capability of these models. To address these issues, a finite element musculoskeletal model with the ability to predict contractions of 3D muscles was developed. Muscles with realistic 3D geometry, spatial muscle fibre alignment and muscle-muscle and muscle-bone interactions were accounted for. Active contractile stresses of the 3D muscles were determined through an efficient optimization approach based on the measured kinematics of the lower extremity and ground force during gait. This model also provided stresses and strains of muscles and contact mechanics of the muscle-muscle and muscle-bone interactions. The total contact force of the knee predicted by the model corresponded well to the in vivo measurement. Contact and wrapping between muscles and surrounding tissues were evident, demonstrating the need to consider 3D contact models of muscles. This modelling framework serves as the methodological basis for developing musculoskeletal modelling systems in finite element method incorporating 3D deformable contact models of muscles, joints, ligaments and bones.

Adaptive representation of dynamic 3D meshes for low-latency applications

Recently, 3D visual representations of highly deformable 3D models, such as dynamic 3D meshes, are becoming popular due to their capability to represent realistically the motion of real-world objects/humans, paving the road for new and more advanced immersive virtual, augmented and mixed reality experiences. However, the real-time streaming of such models introduces increasing challenges related to low cost, low-latency and scalable coding of the acquired information. In view of this, this article proposes an efficient scalable coding mechanism, that decomposes a mesh sequence into spatial and temporal layers that remove a single vertex at each layer. The removed vertices are predicted by performing Laplacian interpolation of the motion vectors. The artifacts that are introduced in low-resolution representations are mitigated using a subspace based normal-vector denoising procedure, that is optimized to support low-latency streaming scenarios using incremental SVD. A novel initialization strategy offers robustness to outliers generated due to local deformations. An extensive evaluation study using several synthetic and scanned dynamic 3D meshes highlights the benefits of the proposed approach in terms of both execution time and reconstruction quality even in very low throughput scenarios of bit-per-vertex-per-frame (bpvf).

Automatic liver tumour segmentation in CT combining FCN and NMF-based deformable model

ABSTRACT Automatic liver tumour segmentation is an important step towards digital medical research, clinical diagnosis and therapy planning. However, the existence of noise, low contrast and heterogeneity make the automatic liver tumour segmentation remaining an open challenge. In this work, we focus on a novel automatic method to segment liver tumour in abdomen images from CT scans using fully convolutional networks (FCN) and non-negative matrix factorization (NMF) based deformable model. We train the FCN for semantic liver and tumour segmentation using preprocessed training data by BM3D. The segmented liver and tumour regions of FCN are used as ROI and initialization for the NMF-based tumour refinement, respectively. We refine the surfaces of tumours using a 3D deformable model which derived from NMF and driven by local cumulative spectral histograms (LCSH). The refinement is designed to obtain a smoother, more accurate and natural liver tumour surface. Experiments on 11 clinical datasets demonstrated that the proposed segmentation method achieves satisfactory results.

Patch-based facial texture super-resolution by fitting 3D face models

Incorporating 3D models for face hallucination (FH) is an ill-posed problem in light of the low-resolution (LR) conditions. To deal with the challenges, a specific 3D shape modeling approach targeting LR face images is first proposed. Based on a few automatically detected 2D facial feature points, an adaptive fitting scheme to relax the fixed correspondence assumption on the facial contour is devised, allowing for pose-invariant shape recovery. In order to exploit the obtained 3D shape and pose for FH, a resolution-aware approach for registering the training 3D faces with the LR input is designed to avoid warping the LR face. Finally, the LR image formation process is reformulated to facilitate super-resolution (SR) of the 3D facial texture. Using this interpretation, the Lucas–Kanade algorithm is extended for 3D deformable models to rectify the imperfect landmark-based fitting on LR images in a posterior fashion. In this way, the final patch-wise SR stage is able to produce realistic facial textures and synthesize self-occluded regions for non-frontal poses. All in all, our main contribution is a novel and pragmatic “2D landmarks $$\rightarrow $$ 3D dense shape $$\rightarrow $$ LR fitting refinement $$\rightarrow $$ 3D FH” pipeline dedicated for the LR scenario. To justify its advantages, extensive evaluation is conducted on several publicly available datasets, revealing superior accuracy over state-of-the-art methods in 3D fitting and high-quality SR results for in-the-wild faces with an interocular distance of as few as five pixels. Moreover, the frontalized high-resolution texture is also verified to help boost the performance of cross-pose face recognition.

Fully automated brain tumour segmentation system in 3D‐MRI using symmetry analysis of brain and level sets

This study presents a new fully automated, fast, and accurate brain tumour segmentation method which automatically detects and extracts whole tumours from 3D-MRI. The proposed method is based on a hybrid approach that relies on a brain symmetry analysis method and a combining region-based and boundary-based segmentation methods. The segmentation process consists of three main stages. In the first one, image pre-processing is applied to remove any noise, and to extract the brain from the head image. In the second stage, automated tumour detection is performed. It is based essentially on FBB method using brain symmetry. The obtained result constitutes the automatic initialisation of a deformable model, thus removing the need of selecting the initial region of interest by the user. Finally, the third stage focuses on the application of region growing combined with 3D deformable model based on geodesic level-set to detect the tumour boundaries containing the initial region, computed previously, regardless of its shape and size. The proposed segmentation system has been tested and evaluated on 3D-MRIs of 285 subjects with different tumour types and shapes obtained from BraTS'2017 dataset. The obtained results turn out to be promising and objective as well as close to ground truth data.

Structural variation within the Himalayan fold and thrust belt: A case study from the Kohat-Potwar Fold Thrust Belt of Pakistan

The Kohat and Potwar fold thrust belts (KP-FTB) in Pakistan exhibit structural variations over 250 km along strike within the Himalayan fold and thrust system. Our 3D deformation model shows that Kohat surface structures evolved above an active roof thrust in Eocene evaporites. The ramp-forming duplexes in the Kohat were stacked and passively transported toward the foreland above new ramps, resulting in up to 5 km of thickening between the two decollements. Ramps from the Kohat extend into the Potwar as thrust tips of fault propagation folds. The basement slope changes from flat (β < 1°) below the northern part to north-dipping (β > 1°) below the southern part, corresponding to the change in structural style and complexity of the KP-FTB. The Kalabagh Fault Zone, linking the two belts, is interpreted as a zone of complex dextral strike-slip rotational faulting. Salt expulsed from the hanging walls of normal faults and under synclines in the Kalabagh Fault Zone moved toward the footwall of normal faults, accumulated in the cores of anticlines, and formed lobe structures at the deformation front. The fundamental reasons for the variable structural styles are changes in decollement strength, basement slope, preexisting normal faulting, presence of a secondary decollement and spatially-variable salt mobility and accumulation.

3D kidney segmentation from abdominal diffusion MRI using an appearance-guided deformable boundary.

A new technique for more accurate automatic segmentation of the kidney from its surrounding abdominal structures in diffusion-weighted magnetic resonance imaging (DW-MRI) is presented. This approach combines a new 3D probabilistic shape model of the kidney with a first-order appearance model and fourth-order spatial model of the diffusion-weighted signal intensity to guide the evolution of a 3D geometric deformable model. The probabilistic shape model was built from labeled training datasets to produce a spatially variant, independent random field of region labels. A Markov-Gibbs random field spatial model with up to fourth-order interactions was adequate to capture the inhomogeneity of renal tissues in the DW-MRI signal. A new analytical approach estimated the Gibbs potentials directly from the DW-MRI data to be segmented, in order that the segmentation procedure would be fully automatic. Finally, to better distinguish the kidney object from the surrounding tissues, marginal gray level distributions inside and outside of the deformable boundary were modeled with adaptive linear combinations of discrete Gaussians (first-order appearance model). The approach was tested on a cohort of 64 DW-MRI datasets with b-values ranging from 50 to 1000 s/mm2. The performance of the presented approach was evaluated using leave-one-subject-out cross validation and compared against three other well-known segmentation methods applied to the same DW-MRI data using the following evaluation metrics: 1) the Dice similarity coefficient (DSC); 2) the 95-percentile modified Hausdorff distance (MHD); and 3) the percentage kidney volume difference (PKVD). High performance of the new approach was confirmed by the high DSC (0.95±0.01), low MHD (3.9±0.76) mm, and low PKVD (9.5±2.2)% relative to manual segmentation by an MR expert (a board certified radiologist).