M. Han, T.M. Athawale, D. Pugmire, C.R. Johnson. Accelerated Probabilistic Marching Cubes by Deep Learning for Time-Varying Scalar Ensembles, In 2022 IEEE Visualization and Visual Analytics (VIS), IEEE, pp. 155-159. 2022.
Visualizing the uncertainty of ensemble simulations is challenging due to the large size and multivariate and temporal features of en-semble data sets. One popular approach to studying the uncertainty of ensembles is analyzing the positional uncertainty of the level sets. Probabilistic marching cubes is a technique that performs Monte Carlo sampling of multivariate Gaussian noise distributions for positional uncertainty visualization of level sets. However, the technique suffers from high computational time, making interactive visualization and analysis impossible to achieve. This paper introduces a deep-learning-based approach to learning the level-set uncertainty for two-dimensional ensemble data with a multivariate Gaussian noise assumption. We train the model using the first few time steps from time-varying ensemble data in our workflow. We demonstrate that our trained model accurately infers uncertainty in level sets for new time steps and is up to 170X faster than that of the original probabilistic model with serial computation and 10X faster than that of the original parallel computation.
T. M. Athawale, S. Sane, C. R. Johnson. Uncertainty Visualization of the Marching Squares and Marching Cubes Topology Cases, Subtitled arXiv:2108.03066, 2021.
Marching squares (MS) and marching cubes (MC) are widely used algorithms for level-set visualization of scientific data. In this paper, we address the challenge of uncertainty visualization of the topology cases of the MS and MC algorithms for uncertain scalar field data sampled on a uniform grid. The visualization of the MS and MC topology cases for uncertain data is challenging due to their exponential nature and the possibility of multiple topology cases per cell of a grid. We propose the topology case count and entropy-based techniques for quantifying uncertainty in the topology cases of the MS and MC algorithms when noise in data is modeled with probability distributions. We demonstrate the applicability of our techniques for independent and correlated uncertainty assumptions. We visualize the quantified topological uncertainty via color mapping proportional to uncertainty, as well as with interactive probability queries in the MS case and entropy isosurfaces in the MC case. We demonstrate the utility of our uncertainty quantification framework in identifying the isovalues exhibiting relatively high topological uncertainty. We illustrate the effectiveness of our techniques via results on synthetic, simulation, and hixel datasets.
T. Athawale, C. R. Johnson. Probabilistic Asymptotic Decider for Topological Ambiguity Resolution in Level-Set Extraction for Uncertain 2D Data, In IEEE Transactions on Visualization and Computer Graphics, Vol. 25, No. 1, IEEE, pp. 1163-1172. Jan, 2019.
We present a framework for the analysis of uncertainty in isocontour extraction. The marching squares (MS) algorithm for isocontour reconstruction generates a linear topology that is consistent with hyperbolic curves of a piecewise bilinear interpolation. The saddle points of the bilinear interpolant cause topological ambiguity in isocontour extraction. The midpoint decider and the asymptotic decider are well-known mathematical techniques for resolving topological ambiguities. The latter technique investigates the data values at the cell saddle points for ambiguity resolution. The uncertainty in data, however, leads to uncertainty in underlying bilinear interpolation functions for the MS algorithm, and hence, their saddle points. In our work, we study the behavior of the asymptotic decider when data at grid vertices is uncertain. First, we derive closed-form distributions characterizing variations in the saddle point values for uncertain bilinear interpolants. The derivation assumes uniform and nonparametric noise models, and it exploits the concept of ratio distribution for analytic formulations. Next, the probabilistic asymptotic decider is devised for ambiguity resolution in uncertain data using distributions of the saddle point values derived in the first step. Finally, the confidence in probabilistic topological decisions is visualized using a colormapping technique. We demonstrate the higher accuracy and stability of the probabilistic asymptotic decider in uncertain data with regard to existing decision frameworks, such as deciders in the mean field and the probabilistic midpoint decider, through the isocontour visualization of synthetic and real datasets.
Image segmentation using disjunctive normal Bayesian shape, appearance models. F. Mesadi, E. Erdil, M. Cetin, T. Tasdizen, In IEEE Transactions on Medical Imaging, Vol. 37, No. 1, IEEE, pp. 293--305. Jan, 2018.
The use of appearance and shape priors in image segmentation is known to improve accuracy; however, existing techniques have several drawbacks. For instance, most active shape and appearance models require landmark points and assume unimodal shape and appearance distributions, and the level set representation does not support construction of local priors. In this paper, we present novel appearance and shape models for image segmentation based on a differentiable implicit parametric shape representation called a disjunctive normal shape model (DNSM). The DNSM is formed by the disjunction of polytopes, which themselves are formed by the conjunctions of half-spaces. The DNSM's parametric nature allows the use of powerful local prior statistics, and its implicit nature removes the need to use landmarks and easily handles topological changes. In a Bayesian inference framework, we model arbitrary shape and appearance distributions using nonparametric density estimations, at any local scale. The proposed local shape prior results in accurate segmentation even when very few training shapes are available, because the method generates a rich set of shape variations by locally combining training samples. We demonstrate the performance of the framework by applying it to both 2-D and 3-D data sets with emphasis on biomedical image segmentation applications.
F. Mesadi, M. Cetin, T. Tasdizen. Disjunctive normal level set: An efficient parametric implicit method, In 2016 IEEE International Conference on Image Processing (ICIP), IEEE, September, 2016.
Level set methods are widely used for image segmentation because of their capability to handle topological changes. In this paper, we propose a novel parametric level set method called Disjunctive Normal Level Set (DNLS), and apply it to both two phase (single object) and multiphase (multi-object) image segmentations. The DNLS is formed by union of polytopes which themselves are formed by intersections of half-spaces. The proposed level set framework has the following major advantages compared to other level set methods available in the literature. First, segmentation using DNLS converges much faster. Second, the DNLS level set function remains regular throughout its evolution. Third, the proposed multiphase version of the DNLS is less sensitive to initialization, and its computational cost and memory requirement remains almost constant as the number of objects to be simultaneously segmented grows. The experimental results show the potential of the proposed method.
F. Mesadi, M. Cetin, T. Tasdizen. Disjunctive Normal Shape and Appearance Priors with Applications to Image Segmentation, In Lecture Notes in Computer Science, Springer International Publishing, pp. 703--710. 2015.
The use of appearance and shape priors in image segmentation is known to improve accuracy; however, existing techniques have several drawbacks. Active shape and appearance models require landmark points and assume unimodal shape and appearance distributions. Level set based shape priors are limited to global shape similarity. In this paper, we present a novel shape and appearance priors for image segmentation based on an implicit parametric shape representation called disjunctive normal shape model (DNSM). DNSM is formed by disjunction of conjunctions of half-spaces defined by discriminants. We learn shape and appearance statistics at varying spatial scales using nonparametric density estimation. Our method can generate a rich set of shape variations by locally combining training shapes. Additionally, by studying the intensity and texture statistics around each discriminant of our shape model, we construct a local appearance probability map. Experiments carried out on both medical and natural image datasets show the potential of the proposed method.
F. Chen, H. Obermaier, H. Hagen, B. Hamann, J. Tierny, V. Pascucci. Topology analysis of time-dependent multi-fluid data using the Reeb graph, In Computer Aided Geometric Design, Vol. 30, No. 6, pp. 557--566. 2013.
Keywords: Multi-phase fluid, Level set, Topology method, Point-based multi-fluid simulation
S. Kurugol, E. Bas, D. Erdogmus, J.G. Dy, G.C. Sharp, D.H. Brooks. Centerline extraction with principal curve tracing to improve 3D level set esophagus segmentation in CT images, In Proceedings of IEEE International Conference of the Engineering in Medicine and Biology Society (EMBS), pp. 3403--3406. 2011.
PubMed ID: 2225507
PubMed Central ID: PMC3349355
S. Kurugol, N. Ozay, J.G. Dy, G.C. Sharp, D.H. Brooks. Locally Deformable Shape Model to Improve 3D Level Set based Esophagus Segmentation, In Proceedings of the IAPR International Conference on Pattern Recognition, pp. 3955--3958. August, 2010.
PubMed ID: 21731883
PubMed Central ID: PMC3127393
In this paper we propose a supervised 3D segmentation algorithm to locate the esophagus in thoracic CT scans using a variational framework. To address challenges due to low contrast, several priors are learned from a training set of segmented images. Our algorithm first estimates the centerline based on a spatial model learned at a few manually marked anatomical reference points. Then an implicit shape model is learned by subtracting the centerline and applying PCA to these shapes. To allow local variations in the shapes, we propose to use nonlinear smooth local deformations. Finally, the esophageal wall is located within a 3D level set framework by optimizing a cost function including terms for appearance, the shape model, smoothness constraints and an air/contrast model.
J. Cates, A. Lefohn, R.T. Whitaker. GIST: an Interactive, GPU-Based Level Set Segmentation Tool for 3D Medical Images, No. UUCS-04-007, University of Utah School of Computing, 2004.
J. Cates, A. Lefohn, R.T. Whitaker. GIST: An Interactive, GPU-Based Level Set Segmentation Tool for 3D Medical Images, In Medical Image Analysis, Vol. 8, No. 3, pp. 217--231. September, 2004.
A.E. Lefohn, J.M. Kniss, C.D. Hansen, R.T. Whitaker. A Streaming Narrow-Band Algorithm: Interactive Deformation and Visualization of Level Sets, In IEEE Trans. Vis & Comp. Graph., pp. 422--433. 2004.
J.M. Kniss, S. Premoze, M. Ikits, A.E. Lefohn, C.D. Hansen. Closed Form Solution to the Volume Rendering Integral with Gaussian Transfer Functions, Technical Report, No. UUCS-03-013, University of Utah School of Computing, 2003.
A.E. Lefohn, J.M. Kniss, C.D. Hansen, R.T. Whitaker. Interactive Deformation and Visualization of Level Set Surfaces Using Graphics Hardware, In IEEE Visualization 2003, Seattle, Wa., pp. 75--82. October, 2003.
A.E. Lefohn, J. Cates, R.T. Whitaker. Interactive, GPU-Based Level Sets for 3D Brain Tumor Segmentation, Technical Report, No. UUCS-03-004, University of Utah School of Computing, 2003.
A.E. Lefohn, J.M. Kniss, C.D. Hansen, R.T. Whitaker. Interactive Deformation and Visualization of Level Set Surfaces Using Graphics Hardware, Technical Report, No. UUCS-03-005, University of Utah School of Computing, 2003.
A.E. Lefohn, J. Cates, R.T. Whitaker. Interactive, GPU-Based Level Sets for 3D Segmentation, In Medical Image Computing and Computer Assisted Intervention (MICCAI), pp. 564--572. 2003.
T. Tasdizen, R.T. Whitaker. Feature preserving variational smoothing of terrain data, In IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision, October, 2003.
A.E. Lefohn, R.T. Whitaker. A GPU-Based, Three-Dimensional Level Set Solver with Curvature Flow, Technical Report, No. UUCS-02-017, University of Utah School of Computing, 2002.
D. Breen, R.T. Whitaker. A Level-Set Approach for the Metamorphosis of Solid Models, In IEEE Trans. Vis & Comp. Graph., Vol. 7, No. 2, pp. 173--192. 2001.