Knowledge-Assisted Visualization
Knowledge-Assisted Visualization and Segmentation of Geologic Features Benjamin J. Kadlec and Henry M. Tufo ■ University of Colorado Geoffrey A. Dorn ■ TerraSpark Geosciences
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cientists have been using 3D seismic data to explore the Earth’s crust for over 30 years. Interpreting seismic data is an important component of oil and gas exploration that’s challenging owing to the data sets’ scale and complexity. In addition, few geoscientists have the expert skills necessary to interpret the increasing number of these data sets. In particular, segmenting the 3D bounding surface of many complex geologic features remains A 3D visualization difficult. The opportunity thus environment contains domain exists to harness the knowledge information about geologic of experts to facilitate easier segfeatures in seismic data and mentation of geologic features. lets users interactively steer Traditional interpretation apsegmentations on the basis of proaches generate attribute data visual sources of information sets that try to highlight specific geologic features to aid and knowledge. A user study identification. These approaches demonstrates this approach’s then segment the features using ability to transfer domain manual drawing tools along 2D knowledge to nonexperts. slices of the data sets while referencing these attributes. To reduce the need to acquire knowledge about seismic data and attributes, our technique uses steered surfaces that grow into the known shapes of geologic features. As surfaces evolve toward geologic features, our approach renders visual feedback on the surface to provide users with simple information they can use to generate knowledgeable modifications of the segmentation. The result is a knowledge-assisted visualization and segmentation system that lets nonexperts quickly segment 30
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geologic features in complex seismic data sets (see Figure 1).
Background Most published research in this area of segmentation has used explicit surfaces constructed from triangles. (For more information on other research, see the “Related Work” sidebar.) Deforming triangulated surfaces requires extreme care when discontinuous topological changes occur, and guaranteeing the surface’s smoothness is difficult. In addition, there’s no guarantee that the result of a deformed explicit surface will be physically realizable. Implicit surfaces are represented volumetrically using level-set methods. Compared to explicit surfaces, they allow easier computation of dynamic topological changes and geometric quantities. Level-set simulations produce physically realizable surface models, which are desirable when you’re trying to represent real-life geologic features. Dynamic implicit surfaces, which are implicit surfaces in motion, have shown great potential in the computational sciences for applications such as modeling, simulation, and segmentation. Levelset methods allow implicit handling of complex topologies deformed by operations where large changes can occur, without destroying the levelset representation. The challenge remains in devising level-set methods to represent unique geologic shapes and to devise a surface evolution that follows features imaged by seismic data attributes. Unfortunately, fully automated surface evolution can’t take into account the variability of real-
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Related Work in Level-Set Segmentation and Seismic Interpretation
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ecause of the main article’s interdisciplinary nature, previous related research falls into two general categories: interactive level-set segmentation and seismic interpretation. Although no one has attempted to conduct seismic interpretation using guided surfaces and knowledge visualization, some previous researchers have made contributions that motivate our research. Regarding level-set segmentation, Aaron Lefohn and his colleagues describe a GPU-based technique for interactively visualizing level-set evolutions for segmenting tumors.1 They use real-time volume rendering to visualize the level-set surface as it deforms, and they expose controls to allow interactive modification of parameters. Regarding seismic interpretation, researchers have developed techniques for extracting geologic features such as channels and geobodies2 and faults3 (for more on these features, see the “Geologic Features in Seismic Data Sets” sidebar). Randolph Pepper and Gaston Bejarano present an extensive review of automatic fault extraction techniques.4 Daniel Patel and his colleagues developed the Seismic Analyzer, a toolbox for interpreting and illustrating 2D seismic data sets. 5 To support the visualization of geology, the toolbox uses horizon structures to improve searching for features and provides multiattribute visualizations for annotating geologic structures. Patel and his colleagues’ techniques add knowledge to the visualization of seismic data sets and reduce the need for seismic illustrators and interpreters to generate this same information. Commercial software used
Seismic data
in oil companies includes Petrel and VoxelGeo. Previously, we presented a technique for segmenting faults using level sets.6 However, unlike the approach we describe in the main article, that research didn’t use domain knowledge for visualization, steering, or interaction during segmentation.
References 1. A. Lefohn et al., “Interactive Deformation and Visualization of Level Set Surfaces Using Graphics Hardware,” Proc. 2003 IEEE Visualization Conf. (VIS 03), IEEE Press, 2003, pp. 75–82. 2. J. Carlson, “Surface Wrapping: A Deformable Mesh Approach to Semi-automatic 3D Volume Segmentation,” PhD thesis, Univ. of Colorado at Boulder, 2009. 3. W.K. Jeong, R. Whitaker, and M. Dobin, “Interactive 3D Seismic Fault Detection on the Graphics Hardware,” Proc. 2006 Eurographics/IEEE VGTC Workshop Volume Graphics (VG 06), Eurographics Assoc., 2006. 4. R. Pepper and G. Bejarano, “Advances in Seismic Fault Inter pretation Automation,” Search and Discovery Article 40170, 2005; www.searchanddiscovery.net/documents/2005/pepper/ index.htm. 5. D. Patel et al., “The Seismic Analyzer: Interpreting and Illustrating 2D Seismic Data,” IEEE Trans. Visualization and Computer Graphics, vol. 14, no. 6, 2008, pp. 1571–1578. 6. B.J. Kadlec et al., “Interactive 3-D Computation of Fault Surfaces Using Level Sets,” Visual Geosciences, vol. 13, no. 1, 2008, pp. 133–138.
Information-guided surface growth
Information visualization
∂φ/∂t φ
Knowledge-assisted visualization
Final segmentation
φ
Domain knowledge User knowledge Figure 1. Knowledge-assisted visualization and segmentation for geologic features in 3D seismic data. The system uses domain information about geologic features to transfer knowledge to users in an interactive environment.
world geologic features, which requires a trained eye and the subjective analysis of experts. Similar problems occur in other imaging fields when an evolving surface segmentation requires human knowledge, possibly owing to poor imaging or a highly complex feature. To account for unknowns in data, it’s necessary to employ domain knowledge to provide visual monitoring and user control of the segmentation.
So, an opportunity exists to incorporate knowledge of seismic attributes with level-set surface evolution into an interactive environment for 3D segmentation. This article presents a unified approach in the form of an interactive technique designed to efficiently segment geologic features with high accuracy. The interactive environment unifies seismic attributes and implicit-surface modeling as a surface-driven solution that provides users with IEEE Computer Graphics and Applications
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Geologic Features in Seismic Data Sets
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he fundamentals of seismic interpretation are based on interpreting changes in the amplitude signal of seismic traces. Because large impedance contrasts at geologic boundaries will generally have higher amplitudes in a seismic trace, changes in seismic amplitudes coincide with changes in geology.1 To visualize seismic data, scientists first used wiggle traces, and then color-mapped amplitude slices (see Figure A). Traditionally, for color-mapped amplitude data, negative amplitudes are in the blue spectrum, positive amplitudes are in the red spectrum, and zero amplitude is white. Geobodies are sets of connected voxels in seismic data that have the same impedance characteristics and therefore similar amplitudes.
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amplitude data. Strata appear as consistent positive (red) or negative (blue) amplitudes that can be connected horizontally across the data.
Seismic-Interpretation Knowledge Research and commercial systems have implemented a variety of seismic-interpretation techniques. Although fully automated techniques exist, their results aren’t accurate enough to use directly for many interpretation tasks. So, most geoscientists still rely on some level of manual segmentation to generate their interpretations. To do this, they typically enhance geologic features from a seismic-amplitude data set using various mathematical algorithms to generate attribute volumes highlighting specific features. To conduct manual segmentation, they visualize the original seismic-amplitude data alongside the attribute data and manually draw or track feature boundaries. Visualization of the final segmentation is usually available only as a postprocessing step, creating a January/February 2010
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Figure A. Wiggle traces overlain on standard color-mapped seismic-
visualizations of expert knowledge for the segmentation of geologic features in 3D seismic data.
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Structural Features The most common structural features interpreted in seismic data are faults. A fault is a fracture in the Earth’s crust along which displacement has occurred. This displacement can have vertical and horizontal components. Faults are important for interpreting seismic data because they provide clues to the relative location of depositional layers in a survey and act as traps for oil and gas reservoirs. In particular, faults can be sealing and block fluid flow through rocks, or they can provide a path for fluid to flow. So, geoscientists spend considerable time mapping out faults, which can number in the thousands for a moderate-sized survey. Figure B shows a vertical slice with multiple faults, which appear as linear discontinuous features moving vertically through the data. Viewing multiple slices at once can reveal how the faults extend in 3D. However, it’s a challenge to identify and segment these fault discontinuities and to determine the 3D envelope around a fault plane
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two-stage process in which the scientists typically can’t observe a feature’s 3D extents during manual interpretation. This disconnect prevents geoscientists from fully using their geologic insight because they must focus on localized 2D regions of the data set rather than a global view of the entire 3D feature. In general, previous research has also offered little realtime interaction or live editing capabilities, such as we present here. Attributes store information about seismic data, such as edges, orientations, textures, and shapes. The proper application of attributes to interpreting specific features in seismic data requires geologic knowledge. So, we can accomplish knowledgeassisted visualization of seismic data by visualizing these attributes to provide insight about a data set’s geology. The “Geologic Features in Seismic Data Sets” sidebar describes how geologic faults, channels, and geobodies are imaged in seismic-
(1)
(2)
Figure C. Channels. (1) Vertical cross-sections of three typical layering structures that form channels and (2) a horizontal slice of a 3D volume, with red arrows pointing to channel features. The geoscientist’s task is to segment the 3D bounding surface of these structures. Figure B. A vertical slice of a 3D seismic data set, with black arrows pointing to many crossing faults. The geoscientist’s task is to segment a 3D envelope around the fault plane.
that coincides with the thickness of the damage zone near the fault.
Stratigraphic Features Stratigraphy studies the ancient layering or deposition of rock layers on top of each other. Features in seismic data sets represented in this way are called stratigraphic features. Channels are stratigraphic features having a sedimentary structure often formed by flowing water; they have a distinctive morphology or shape. Figure C1 shows a vertical cross-section of the three most
amplitude data sets. Figure 2 illustrates the attributes we use to identify these features. In the case of faults (see Figure 2a), we align a vertical structuring element to the local strata and compute horizontal differences, which produces a strong response at the location of faults. For channels (see Figure 2b), we align a horizontal structuring element with the local strata to compute a measure of curvature associated with the existence of channels. Geobodies are regions with similar seismic amplitude characteristics; the attribute to identify them uses the stratigraphic orientation to highlight connected amplitude regions (see Figure 2c). To create these attributes, seismic-processing experts have tuned a number of data-dependent parameters from combinations of algorithms that highlight one geologic feature in a data set. Ideally, an attribute describes a particular type of feature for a given survey; that attribute is stored as a par
common types of layering that form channels. Although channels might form under other situations, channel structure always displays some curvature. This layering is reflected in the channel feature’s structure in a 3D data volume. You can most easily recognize these features by looking at a stratal slice that approximates a depositional surface at some time in the past (see Figure C2). Stratigraphic segmentation aims to extract the bounding surfaces of channels or other stratigraphic features (for example, sand bars) with similar characteristics.
Reference 1. A. Brown, Interpretation of Three-Dimensional Seismic Data, Soc. of Exploration Geophysicists, 1999.
allel volume of the input data set. If the seismicprocessing expert gleans new information about the survey, such as from the drilling of a well or feedback from other experts, he or she can feed it back into an updated attribute calculation. The result of these volumetric attributes is a value that gives a particular geologic feature’s likelihood at a given voxel. So, an attribute with a high value is likely to contain a feature, and an attribute with a low value is unlikely to contain one. Using these predefined attributes, the challenge remains to effectively transfer this geologic knowledge to first-time users tasked with segmenting complex features.
Attribute-Guided Level-Set Segmentation An implicit representation of a surface consists of all points S = {i | f(i) = 0}, where f: R3 ⇒ R. Level sets relate the motion on the surface S to a partial differential equation on the image as IEEE Computer Graphics and Applications
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Knowledge-Assisted Visualization
Equation 1 is sometimes called the level-set equation, the name with which Stanley Osher and James Sethian introduced it.1 For segmenting geologic features using our technique, the velocity equation consists of two data-dependent terms and a mean-curvature term. So, we define the level-set evolution on a 3D image I as the combination of three terms: f = t
f fD ( I ) + f
×
÷ f÷ ÷ ÷ ÷+ f( A ( I ) × f) . ÷ ÷ ÷ f÷÷
(2)
(a)
(b)
(c) Figure 2. Previous research has developed a number of attributes for imaging the structure of geologic features such as (a) faults, (b) channels, and (c) geobodies. Attributes enhance features by using structuring elements aligned to the 3D shape of these features.
f = V × f, t
(1)
where V describes the surface’s motion in space and time. This framework lets us implement a variety of deformations by defining an appropriate V. We can combine the velocity (or speed) term with several other terms such as geometric terms (for example, mean curvature) and image-dependent terms. 34
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D is a propagation-speed term defined by an attribute’s intensity in the surface normal’s direction. The term ×( f f) is the surface’s mean curvature. The final term, A × f, is the dot product of the gradient vector of the advecting force, defined by a feature edge, with the surface normal. Each term’s influence is set by the scalar values a, b, and g. Figure 3 illustrates their contributions. The propagation term for level-set surface evolution is given by the likelihood value in the attribute volume for each respective geologic feature. This lets the surface evolve into regions with a high likelihood of a feature and shrink from regions with low feature likelihood. An expert predefines the initial threshold that determines whether an attribute value causes growth or shrinkage, although users can adjust the threshold during runtime to account for data variability. The mean-curvature term helps keep the surface smooth during evolution and prevents it from leaking into noisy regions. The advection force is given by magnitude changes in the attribute volume; it prevents the evolving surface from crossing edges that separate features. Domain knowledge about geologic features describes the existence of a preferred orientation for faults, channels, and geobodies, which can serve as additional knowledge to assist visualization and segmentation. For instance, stratigraphic features such as channels and geobodies extend further horizontally than vertically through a volume. The opposite is true for faults, which have a much more extensive vertical orientation. We use this knowledge to restrain the growth of features to their preferred orientation by applying a global advection force to the surface evolution. This additional restraint helps users visualize and segment complex features by leveraging geologic expertise to further guide surfaces. Figure 4 illustrates how a surface evolves according to speed values given by a seismic-data attribute. Figure 5 shows the approach for segmenting three geologic features by first placing seed points,
Intensity propagation flow
Mean curvature flow
Edge advection flow
Combined result
Figure 3. The contribution of level-set terms in Equation 2 for a surface (or contour) that evolves toward a bright intensity feature. Propagation flow moves the surface in the normal direction toward the feature attribute. Mean curvature flow maintains a smooth surface and prevents leaking into nonfeatures. Advection flow moves the surface toward an edge attribute but prevents it from crossing. The combination of flows causes an initial surface to evolve into the geologic feature of interest.
then letting those seeds evolve into geologic features. During the surface’s growth, users can adjust parameters and rotate the 3D visualization on the fly.
Knowledge-Assisted Visualization Min Chen and his colleagues define knowledge in the computational space as “data that represents the transcripts of some knowledge acquired by human beings.”2 This best describes how human knowledge enters our visualization process. To help obtain satisfactory results, we want to utilize knowledge captured both from domain experts and from the user’s visualization of an interactive segmentation process. Our process begins with the user exploring the space of a seismic data set by using 2D slices to interactively search the 3D volume for possible features of interest. After locating them, the user places seed points inside the features. The user then decides what type of feature (fault, channel, or geobody) he or she is trying to find. Next, the surface evolves into the geologic feature of interest, using the appropriate level-set terms and attributes representing expert knowledge. As the surface evolves, our approach renders the attribute values onto the surface to provide visual feedback to users about the segmentation’s quality (see Figure 6). If the visual feedback’s color indicates that the surface is leaking into a nonfeature, the user can adjust the level set’s threshold values to steer the surface back toward the feature of interest. If the attribute guiding the evolution has an inaccuracy that causes the surface to grow too far, the user can manually steer the growth by applying a 3D paintbrush to the surface’s incorrect portion. This in turn modifies the underlying attributes and guides the level set in a new direction. We manage the domain knowledge about geologic features by storing scalar-data volumes of the attributes that highlight faults, channels, and geobodies for a given seismic data set. Alongside each attribute volume, we store upper and lower threshold values based on an expert’s determination of
∂φ/∂t = ∇φ V + A⋅∇φ
φ
Figure 4. Attributes serve as speed values that determine how the surface evolves. Attributes are looked at in a narrow band around the surface (top left) such that the surface evolves into features of interest (bottom right) and shrinks from false positives and nonfeatures.
what range of values best represents a particular feature for an entire data set. The code that computes the level-set evolution chooses the appropriate preferred growth directions and level-set terms, as we described previously. Surface evolution continues for a user-specified number of iterations or until the visualization shows a satisfactory result. Users can adjust these default thresholds and parameters on the basis of what they see when visualizing the segmentation. The level-set evolution employs a GPU-based implementation (see the “GPU Implementation” sidebar), which renders the surface immediately after every iteration. When computing each voxel of the level-set surface, if that voxel lies on the isovalue of interest, we reuse derivatives from the level set’s calculation to generate the triangles forming that portion of the surface. Because we’ve already computed the surface normal for the level set, we don’t need to recompute it for the triangle. IEEE Computer Graphics and Applications
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Knowledge-Assisted Visualization
(a)
(b)
(c) Figure 5. Segmenting a (a) geobody, (b) fault, and (c) channel, starting with user-defined seed points (the left column). The seed points evolve for 200 iterations; growth occurs from left to right along the rows.
The level-set representation guarantees that the collection of all triangles extracted at a particular isovalue will render the isosurface of interest.
User Study To demonstrate our approach’s effectiveness in a real-world setting, we conducted a user study. We aimed to determine how long participants took to segment geologic features using our techniques, ■■ determine the segmentations’ accuracy, and ■■ compare the participants’ speed and accuracy to those of an expert performing manual interpretation. ■■
To determine whether our method can produce volumetric delineations comparable to features 36
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manually interpreted by experts, we had the participants segment faults and geobodies. Because these features vary in seismic data, we needed to provide further specification. The domain knowledge we provided for faults was a fault-likelihood attribute volume with values thresholded to correspond with a high likelihood of a fault at that point in the data set. The geobodies were visible as connected bodies of voxels with similar amplitude in a seismic-amplitude volume; the initial thresholds defined the range of values containing the bodies. The participants’ goal was to segment the bounding surfaces of three different faults and three different geobodies, all from the same 2563 subvolume from a Gulf of Mexico data set.
Participants, Preparation, and Procedure Eight University of Colorado undergraduate and
Feature
Not feature Information color map
Initial growth
Leaking into nonfeature
Adjusting growth
Final segmentation
Figure 6. Our approach renders knowledge of fault likelihood on the evolving surface to show the user when the segmentation leaks into regions that don’t contain a fault (green) instead of a region that does (red). The top and bottom rows show two different perspectives.
graduate science students participated. None of them had studied geosciences or worked in that field, and they had little or no experience with 3D visualization tools and seismic data. So, the participants can be considered nonexperts and naïve in the field of 3D seismic interpretation. Before beginning the study, we gave each participant a five-minute introduction to the software and explained how to identify and segment faults and geobodies from a test data set. At the beginning of each feature interpretation, we briefly showed the participants a 2D slice of the feature so that they knew which feature to segment. We then removed this display, and it wasn’t visible during the study’s timed portion. Time started when we directed the participant to each feature’s location and stopped when the participant was satisfied with the solution obtained. The investigator conducting the study sat beside each participant to provide immediate answers to any questions or help with difficulties related to working with the software. Participants rarely requested help; such requests usually involved the participant forgetting how to do something trivial in the software that didn’t relate to the study itself.
Results For each feature, we recorded the segmented surfaces and the time to complete the segmentation for each participant and compared this data to the expert’s. We computed the accuracy of participant results relative to the expert interpretation on a volumetric basis such that 100 percent accuracy implies that the participant’s and expert’s results were identical.
Figure 7 shows six pairs of zoomed-in images showing the region of interest around features. In each pair, the left image is the expert manual
GPU Implementation
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o allow for fast computation of surface evolution, we implement our approach (see the main article) using CUDA (Compute Unified Device Architecture )1 on an Nvidia Quadro FX 5600 GPU. We leverage the GPU for its many parallel processors and the ease with which results can be visualized directly on the GPU. Compared to a standard single-core CPU (an AMD Opteron 280), the GPU shows significant speedup through reduced runtimes (see Table A). The increased speed allows for the technique’s computation at interactive rates for moderate-sized subvolumes (2563). This lets users observe the evolution of surfaces in real time and adjust runtime parameters on the fly to guide surfaces toward features. Table A. The visualization system’s performance on a single-core CPU (an AMD Opteron 280) and a GPU (an Nvidia Quadro FX 5600), for 200 iterations. CPU
GPU
No. of faces
Runtime (sec.)
Runtime (sec.)
Frames per sec.
Speedup
1,729 K
1,978.2
62.43
3.20
~32×
Fault
744 K
1,382.5
38.24
5.23
~36×
Channel
432 K
1,816.0
49.06
4.10
~37×
Data set Geobody
Reference 1. Nvidia Compute Unified Device Architecture, Programming Guide, Version Beta 2.0, Nvidia, 2. Apr. 2008.
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(a)
(b) Figure 7. Six interpretation tasks undertaken in the user study: (a) faults and (b) geobodies. In each pair of images, the left image shows the expert hand-drawn result and the right image is the consensus result obtained by averaging the eight participants’ results. Overall similarities between the expert and consensus results attest to this technique’s accuracy. Differences between the edges of the shapes result from users not fully extending their segmentations to the feature boundary. 70 60
Participant A Participant B Participant C Participant D Participant E Participant F Participant G Participant H
Minutes
50 40 30 20
Expert
10 0 Fault 1
Fault 2
Fault 3
Geobody 1
Geobody 2
Geobody 3
Figure 8. The time to interpret three faults and three geobodies. The participants segmented the features many times faster than the expert did.
interpretation and the right image is the consensus result obtained by averaging the participants’ segmentations. This consensus result is valid owing to the low variance between user segmentations. Figure 8 shows the time taken to interpret the features. The participants obviously could segment the features many times faster than the expert could. Figure 9 shows the participants’ accuracy. Their average accuracy was approximately 85 percent for faults and 90 to 95 percent for geobodies. Figure 10 indicates our approach’s reliability by comparing how similar each participant’s results were to each other. The participants’ results were 85 to 95 percent similar for faults and over 95 percent similar for geobodies. This shows the approach has little interuser variability, thus resulting in highly consistent segmentations. 38
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Compared to simpler segmentation approaches, such as using a 3D paintbrush, ours is fast, intuitive, and easy. Because we provide specific expert knowledge through our streamlined visualization environment, users can easily understand a data set’s geology without having to manage a separate knowledge database. Finally, because our approach accurately segments complex shapes, users don’t have to onerously follow detailed feature boundaries using precise brush movements, which could cause repetitive-strain injuries.
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rom the results, we infer that our approach transfers knowledge quickly and with high accuracy from experts to novices. However, although the novices’ results were excellent, they weren’t production quality. Fortunately, when a trained
100
Accuracy (%)
90 Participant A Participant B Participant C Participant D Participant E Participant F Participant G Participant H
80 70 60 50 40 Fault 1
Fault 2
Fault 3
Geobody 1
Geobody 2
Geobody 3
Figure 9. Participant accuracy. A score of 100 percent means that the participant matched the expert’s interpretation. The participants’ average accuracy was approximately 85 percent for faults and 90 to 95 percent for geobodies. 100 90 Reliability (%)
geoscientist uses our approach, it easily generates segmentations comparable to an expert’s. The approach also successfully captures user knowledge during segmentation, thereby allowing intelligent adjustments to parameters that produce immediately visible effects. We plan to apply our approach to other application areas with similar goals, such as 3D medical imaging.
80 70 60 50 40
Acknowledgments David Yuen, William Hammon, Jonathon Marbach, Francis M. Coady, and James Carlson all influenced this research. TerraSpark Geosciences provided support.
References 1. S. Osher and J.A. Sethian, “Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,” J. Computational Physics, vol. 79, 1988, pp. 12–49; http://math.berkeley. edu/~sethian/2006/Papers/sethian.osher.88.pdf. 2. M. Chen et al., “Data, Information, and Knowledge in Visualization,” IEEE Computer Graphics and Applications, vol. 29, no. 1, pp. 12–19.
Benjamin J. Kadlec is a partner and computational scientist at TerraSpark Geosciences. His research focuses on scientific visualization and computation, 3D modeling, and image processing. Kadlec has a PhD in computer science from the University of Colorado. Contact him at [email protected]. Henry M. Tufo is an associate professor of computer science and the director of the University of Colorado’s Computational Science Center. He’s also the head of the Computer Science Section in the Computational and Information Systems Laboratory at the US National Center for Atmospheric Research. He conducts research in high-performance scientific computing,
Fault 1
Fault 2
Fault 3
Geobody 1 Geobody 2 Geobody 3
Figure 10. The approach’s reliability as determined by the standard deviation of participant results. We computed this as the average percentage of the difference between the participant segmentations and the mean of all participant segmentations. A value of 0 percent means participant segmentations were orthogonal to each other; 100 percent means that all participants produced the same segmentation. The results show that our approach has little interuser variability, thus resulting in highly consistent segmentations.
parallel algorithms and architectures, Linux clusters, Grid computing, scalable solvers, high-order numerical methods, computational fluid dynamics, climate modeling, and flow visualization. Tufo has a PhD in applied mathematics from Brown University. Contact him at [email protected]. Geoffrey A. Dorn is the president and a general partner of TerraSpark Geosciences and is an adjoint professor in the University of Colorado’s Department of Geological Sciences and Department of Computer Sciences. His research is in 3D and 4D seismic interpretation and visualization for energy exploration and development. Dorn has a PhD in geophysics from the University of California, Berkeley. Contact him at [email protected]. Selected CS articles and columns are also available for free at http://ComputingNow.computer.org. IEEE Computer Graphics and Applications
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Knowledge-Assisted Visualization and Segmentation of Geologic Features Benjamin J. Kadlec and Henry M. Tufo ■ University of Colorado Geoffrey A. Dorn ■ TerraSpark Geosciences
S
cientists have been using 3D seismic data to explore the Earth’s crust for over 30 years. Interpreting seismic data is an important component of oil and gas exploration that’s challenging owing to the data sets’ scale and complexity. In addition, few geoscientists have the expert skills necessary to interpret the increasing number of these data sets. In particular, segmenting the 3D bounding surface of many complex geologic features remains A 3D visualization difficult. The opportunity thus environment contains domain exists to harness the knowledge information about geologic of experts to facilitate easier segfeatures in seismic data and mentation of geologic features. lets users interactively steer Traditional interpretation apsegmentations on the basis of proaches generate attribute data visual sources of information sets that try to highlight specific geologic features to aid and knowledge. A user study identification. These approaches demonstrates this approach’s then segment the features using ability to transfer domain manual drawing tools along 2D knowledge to nonexperts. slices of the data sets while referencing these attributes. To reduce the need to acquire knowledge about seismic data and attributes, our technique uses steered surfaces that grow into the known shapes of geologic features. As surfaces evolve toward geologic features, our approach renders visual feedback on the surface to provide users with simple information they can use to generate knowledgeable modifications of the segmentation. The result is a knowledge-assisted visualization and segmentation system that lets nonexperts quickly segment 30
January/February 2010
geologic features in complex seismic data sets (see Figure 1).
Background Most published research in this area of segmentation has used explicit surfaces constructed from triangles. (For more information on other research, see the “Related Work” sidebar.) Deforming triangulated surfaces requires extreme care when discontinuous topological changes occur, and guaranteeing the surface’s smoothness is difficult. In addition, there’s no guarantee that the result of a deformed explicit surface will be physically realizable. Implicit surfaces are represented volumetrically using level-set methods. Compared to explicit surfaces, they allow easier computation of dynamic topological changes and geometric quantities. Level-set simulations produce physically realizable surface models, which are desirable when you’re trying to represent real-life geologic features. Dynamic implicit surfaces, which are implicit surfaces in motion, have shown great potential in the computational sciences for applications such as modeling, simulation, and segmentation. Levelset methods allow implicit handling of complex topologies deformed by operations where large changes can occur, without destroying the levelset representation. The challenge remains in devising level-set methods to represent unique geologic shapes and to devise a surface evolution that follows features imaged by seismic data attributes. Unfortunately, fully automated surface evolution can’t take into account the variability of real-
Published by the IEEE Computer Society
0272-1716/10/$26.00 © 2010 IEEE
Related Work in Level-Set Segmentation and Seismic Interpretation
B
ecause of the main article’s interdisciplinary nature, previous related research falls into two general categories: interactive level-set segmentation and seismic interpretation. Although no one has attempted to conduct seismic interpretation using guided surfaces and knowledge visualization, some previous researchers have made contributions that motivate our research. Regarding level-set segmentation, Aaron Lefohn and his colleagues describe a GPU-based technique for interactively visualizing level-set evolutions for segmenting tumors.1 They use real-time volume rendering to visualize the level-set surface as it deforms, and they expose controls to allow interactive modification of parameters. Regarding seismic interpretation, researchers have developed techniques for extracting geologic features such as channels and geobodies2 and faults3 (for more on these features, see the “Geologic Features in Seismic Data Sets” sidebar). Randolph Pepper and Gaston Bejarano present an extensive review of automatic fault extraction techniques.4 Daniel Patel and his colleagues developed the Seismic Analyzer, a toolbox for interpreting and illustrating 2D seismic data sets. 5 To support the visualization of geology, the toolbox uses horizon structures to improve searching for features and provides multiattribute visualizations for annotating geologic structures. Patel and his colleagues’ techniques add knowledge to the visualization of seismic data sets and reduce the need for seismic illustrators and interpreters to generate this same information. Commercial software used
Seismic data
in oil companies includes Petrel and VoxelGeo. Previously, we presented a technique for segmenting faults using level sets.6 However, unlike the approach we describe in the main article, that research didn’t use domain knowledge for visualization, steering, or interaction during segmentation.
References 1. A. Lefohn et al., “Interactive Deformation and Visualization of Level Set Surfaces Using Graphics Hardware,” Proc. 2003 IEEE Visualization Conf. (VIS 03), IEEE Press, 2003, pp. 75–82. 2. J. Carlson, “Surface Wrapping: A Deformable Mesh Approach to Semi-automatic 3D Volume Segmentation,” PhD thesis, Univ. of Colorado at Boulder, 2009. 3. W.K. Jeong, R. Whitaker, and M. Dobin, “Interactive 3D Seismic Fault Detection on the Graphics Hardware,” Proc. 2006 Eurographics/IEEE VGTC Workshop Volume Graphics (VG 06), Eurographics Assoc., 2006. 4. R. Pepper and G. Bejarano, “Advances in Seismic Fault Inter pretation Automation,” Search and Discovery Article 40170, 2005; www.searchanddiscovery.net/documents/2005/pepper/ index.htm. 5. D. Patel et al., “The Seismic Analyzer: Interpreting and Illustrating 2D Seismic Data,” IEEE Trans. Visualization and Computer Graphics, vol. 14, no. 6, 2008, pp. 1571–1578. 6. B.J. Kadlec et al., “Interactive 3-D Computation of Fault Surfaces Using Level Sets,” Visual Geosciences, vol. 13, no. 1, 2008, pp. 133–138.
Information-guided surface growth
Information visualization
∂φ/∂t φ
Knowledge-assisted visualization
Final segmentation
φ
Domain knowledge User knowledge Figure 1. Knowledge-assisted visualization and segmentation for geologic features in 3D seismic data. The system uses domain information about geologic features to transfer knowledge to users in an interactive environment.
world geologic features, which requires a trained eye and the subjective analysis of experts. Similar problems occur in other imaging fields when an evolving surface segmentation requires human knowledge, possibly owing to poor imaging or a highly complex feature. To account for unknowns in data, it’s necessary to employ domain knowledge to provide visual monitoring and user control of the segmentation.
So, an opportunity exists to incorporate knowledge of seismic attributes with level-set surface evolution into an interactive environment for 3D segmentation. This article presents a unified approach in the form of an interactive technique designed to efficiently segment geologic features with high accuracy. The interactive environment unifies seismic attributes and implicit-surface modeling as a surface-driven solution that provides users with IEEE Computer Graphics and Applications
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Geologic Features in Seismic Data Sets
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he fundamentals of seismic interpretation are based on interpreting changes in the amplitude signal of seismic traces. Because large impedance contrasts at geologic boundaries will generally have higher amplitudes in a seismic trace, changes in seismic amplitudes coincide with changes in geology.1 To visualize seismic data, scientists first used wiggle traces, and then color-mapped amplitude slices (see Figure A). Traditionally, for color-mapped amplitude data, negative amplitudes are in the blue spectrum, positive amplitudes are in the red spectrum, and zero amplitude is white. Geobodies are sets of connected voxels in seismic data that have the same impedance characteristics and therefore similar amplitudes.
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amplitude data. Strata appear as consistent positive (red) or negative (blue) amplitudes that can be connected horizontally across the data.
Seismic-Interpretation Knowledge Research and commercial systems have implemented a variety of seismic-interpretation techniques. Although fully automated techniques exist, their results aren’t accurate enough to use directly for many interpretation tasks. So, most geoscientists still rely on some level of manual segmentation to generate their interpretations. To do this, they typically enhance geologic features from a seismic-amplitude data set using various mathematical algorithms to generate attribute volumes highlighting specific features. To conduct manual segmentation, they visualize the original seismic-amplitude data alongside the attribute data and manually draw or track feature boundaries. Visualization of the final segmentation is usually available only as a postprocessing step, creating a January/February 2010
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Figure A. Wiggle traces overlain on standard color-mapped seismic-
visualizations of expert knowledge for the segmentation of geologic features in 3D seismic data.
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Structural Features The most common structural features interpreted in seismic data are faults. A fault is a fracture in the Earth’s crust along which displacement has occurred. This displacement can have vertical and horizontal components. Faults are important for interpreting seismic data because they provide clues to the relative location of depositional layers in a survey and act as traps for oil and gas reservoirs. In particular, faults can be sealing and block fluid flow through rocks, or they can provide a path for fluid to flow. So, geoscientists spend considerable time mapping out faults, which can number in the thousands for a moderate-sized survey. Figure B shows a vertical slice with multiple faults, which appear as linear discontinuous features moving vertically through the data. Viewing multiple slices at once can reveal how the faults extend in 3D. However, it’s a challenge to identify and segment these fault discontinuities and to determine the 3D envelope around a fault plane
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two-stage process in which the scientists typically can’t observe a feature’s 3D extents during manual interpretation. This disconnect prevents geoscientists from fully using their geologic insight because they must focus on localized 2D regions of the data set rather than a global view of the entire 3D feature. In general, previous research has also offered little realtime interaction or live editing capabilities, such as we present here. Attributes store information about seismic data, such as edges, orientations, textures, and shapes. The proper application of attributes to interpreting specific features in seismic data requires geologic knowledge. So, we can accomplish knowledgeassisted visualization of seismic data by visualizing these attributes to provide insight about a data set’s geology. The “Geologic Features in Seismic Data Sets” sidebar describes how geologic faults, channels, and geobodies are imaged in seismic-
(1)
(2)
Figure C. Channels. (1) Vertical cross-sections of three typical layering structures that form channels and (2) a horizontal slice of a 3D volume, with red arrows pointing to channel features. The geoscientist’s task is to segment the 3D bounding surface of these structures. Figure B. A vertical slice of a 3D seismic data set, with black arrows pointing to many crossing faults. The geoscientist’s task is to segment a 3D envelope around the fault plane.
that coincides with the thickness of the damage zone near the fault.
Stratigraphic Features Stratigraphy studies the ancient layering or deposition of rock layers on top of each other. Features in seismic data sets represented in this way are called stratigraphic features. Channels are stratigraphic features having a sedimentary structure often formed by flowing water; they have a distinctive morphology or shape. Figure C1 shows a vertical cross-section of the three most
amplitude data sets. Figure 2 illustrates the attributes we use to identify these features. In the case of faults (see Figure 2a), we align a vertical structuring element to the local strata and compute horizontal differences, which produces a strong response at the location of faults. For channels (see Figure 2b), we align a horizontal structuring element with the local strata to compute a measure of curvature associated with the existence of channels. Geobodies are regions with similar seismic amplitude characteristics; the attribute to identify them uses the stratigraphic orientation to highlight connected amplitude regions (see Figure 2c). To create these attributes, seismic-processing experts have tuned a number of data-dependent parameters from combinations of algorithms that highlight one geologic feature in a data set. Ideally, an attribute describes a particular type of feature for a given survey; that attribute is stored as a par
common types of layering that form channels. Although channels might form under other situations, channel structure always displays some curvature. This layering is reflected in the channel feature’s structure in a 3D data volume. You can most easily recognize these features by looking at a stratal slice that approximates a depositional surface at some time in the past (see Figure C2). Stratigraphic segmentation aims to extract the bounding surfaces of channels or other stratigraphic features (for example, sand bars) with similar characteristics.
Reference 1. A. Brown, Interpretation of Three-Dimensional Seismic Data, Soc. of Exploration Geophysicists, 1999.
allel volume of the input data set. If the seismicprocessing expert gleans new information about the survey, such as from the drilling of a well or feedback from other experts, he or she can feed it back into an updated attribute calculation. The result of these volumetric attributes is a value that gives a particular geologic feature’s likelihood at a given voxel. So, an attribute with a high value is likely to contain a feature, and an attribute with a low value is unlikely to contain one. Using these predefined attributes, the challenge remains to effectively transfer this geologic knowledge to first-time users tasked with segmenting complex features.
Attribute-Guided Level-Set Segmentation An implicit representation of a surface consists of all points S = {i | f(i) = 0}, where f: R3 ⇒ R. Level sets relate the motion on the surface S to a partial differential equation on the image as IEEE Computer Graphics and Applications
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Knowledge-Assisted Visualization
Equation 1 is sometimes called the level-set equation, the name with which Stanley Osher and James Sethian introduced it.1 For segmenting geologic features using our technique, the velocity equation consists of two data-dependent terms and a mean-curvature term. So, we define the level-set evolution on a 3D image I as the combination of three terms: f = t
f fD ( I ) + f
×
÷ f÷ ÷ ÷ ÷+ f( A ( I ) × f) . ÷ ÷ ÷ f÷÷
(2)
(a)
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(c) Figure 2. Previous research has developed a number of attributes for imaging the structure of geologic features such as (a) faults, (b) channels, and (c) geobodies. Attributes enhance features by using structuring elements aligned to the 3D shape of these features.
f = V × f, t
(1)
where V describes the surface’s motion in space and time. This framework lets us implement a variety of deformations by defining an appropriate V. We can combine the velocity (or speed) term with several other terms such as geometric terms (for example, mean curvature) and image-dependent terms. 34
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D is a propagation-speed term defined by an attribute’s intensity in the surface normal’s direction. The term ×( f f) is the surface’s mean curvature. The final term, A × f, is the dot product of the gradient vector of the advecting force, defined by a feature edge, with the surface normal. Each term’s influence is set by the scalar values a, b, and g. Figure 3 illustrates their contributions. The propagation term for level-set surface evolution is given by the likelihood value in the attribute volume for each respective geologic feature. This lets the surface evolve into regions with a high likelihood of a feature and shrink from regions with low feature likelihood. An expert predefines the initial threshold that determines whether an attribute value causes growth or shrinkage, although users can adjust the threshold during runtime to account for data variability. The mean-curvature term helps keep the surface smooth during evolution and prevents it from leaking into noisy regions. The advection force is given by magnitude changes in the attribute volume; it prevents the evolving surface from crossing edges that separate features. Domain knowledge about geologic features describes the existence of a preferred orientation for faults, channels, and geobodies, which can serve as additional knowledge to assist visualization and segmentation. For instance, stratigraphic features such as channels and geobodies extend further horizontally than vertically through a volume. The opposite is true for faults, which have a much more extensive vertical orientation. We use this knowledge to restrain the growth of features to their preferred orientation by applying a global advection force to the surface evolution. This additional restraint helps users visualize and segment complex features by leveraging geologic expertise to further guide surfaces. Figure 4 illustrates how a surface evolves according to speed values given by a seismic-data attribute. Figure 5 shows the approach for segmenting three geologic features by first placing seed points,
Intensity propagation flow
Mean curvature flow
Edge advection flow
Combined result
Figure 3. The contribution of level-set terms in Equation 2 for a surface (or contour) that evolves toward a bright intensity feature. Propagation flow moves the surface in the normal direction toward the feature attribute. Mean curvature flow maintains a smooth surface and prevents leaking into nonfeatures. Advection flow moves the surface toward an edge attribute but prevents it from crossing. The combination of flows causes an initial surface to evolve into the geologic feature of interest.
then letting those seeds evolve into geologic features. During the surface’s growth, users can adjust parameters and rotate the 3D visualization on the fly.
Knowledge-Assisted Visualization Min Chen and his colleagues define knowledge in the computational space as “data that represents the transcripts of some knowledge acquired by human beings.”2 This best describes how human knowledge enters our visualization process. To help obtain satisfactory results, we want to utilize knowledge captured both from domain experts and from the user’s visualization of an interactive segmentation process. Our process begins with the user exploring the space of a seismic data set by using 2D slices to interactively search the 3D volume for possible features of interest. After locating them, the user places seed points inside the features. The user then decides what type of feature (fault, channel, or geobody) he or she is trying to find. Next, the surface evolves into the geologic feature of interest, using the appropriate level-set terms and attributes representing expert knowledge. As the surface evolves, our approach renders the attribute values onto the surface to provide visual feedback to users about the segmentation’s quality (see Figure 6). If the visual feedback’s color indicates that the surface is leaking into a nonfeature, the user can adjust the level set’s threshold values to steer the surface back toward the feature of interest. If the attribute guiding the evolution has an inaccuracy that causes the surface to grow too far, the user can manually steer the growth by applying a 3D paintbrush to the surface’s incorrect portion. This in turn modifies the underlying attributes and guides the level set in a new direction. We manage the domain knowledge about geologic features by storing scalar-data volumes of the attributes that highlight faults, channels, and geobodies for a given seismic data set. Alongside each attribute volume, we store upper and lower threshold values based on an expert’s determination of
∂φ/∂t = ∇φ V + A⋅∇φ
φ
Figure 4. Attributes serve as speed values that determine how the surface evolves. Attributes are looked at in a narrow band around the surface (top left) such that the surface evolves into features of interest (bottom right) and shrinks from false positives and nonfeatures.
what range of values best represents a particular feature for an entire data set. The code that computes the level-set evolution chooses the appropriate preferred growth directions and level-set terms, as we described previously. Surface evolution continues for a user-specified number of iterations or until the visualization shows a satisfactory result. Users can adjust these default thresholds and parameters on the basis of what they see when visualizing the segmentation. The level-set evolution employs a GPU-based implementation (see the “GPU Implementation” sidebar), which renders the surface immediately after every iteration. When computing each voxel of the level-set surface, if that voxel lies on the isovalue of interest, we reuse derivatives from the level set’s calculation to generate the triangles forming that portion of the surface. Because we’ve already computed the surface normal for the level set, we don’t need to recompute it for the triangle. IEEE Computer Graphics and Applications
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Knowledge-Assisted Visualization
(a)
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(c) Figure 5. Segmenting a (a) geobody, (b) fault, and (c) channel, starting with user-defined seed points (the left column). The seed points evolve for 200 iterations; growth occurs from left to right along the rows.
The level-set representation guarantees that the collection of all triangles extracted at a particular isovalue will render the isosurface of interest.
User Study To demonstrate our approach’s effectiveness in a real-world setting, we conducted a user study. We aimed to determine how long participants took to segment geologic features using our techniques, ■■ determine the segmentations’ accuracy, and ■■ compare the participants’ speed and accuracy to those of an expert performing manual interpretation. ■■
To determine whether our method can produce volumetric delineations comparable to features 36
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manually interpreted by experts, we had the participants segment faults and geobodies. Because these features vary in seismic data, we needed to provide further specification. The domain knowledge we provided for faults was a fault-likelihood attribute volume with values thresholded to correspond with a high likelihood of a fault at that point in the data set. The geobodies were visible as connected bodies of voxels with similar amplitude in a seismic-amplitude volume; the initial thresholds defined the range of values containing the bodies. The participants’ goal was to segment the bounding surfaces of three different faults and three different geobodies, all from the same 2563 subvolume from a Gulf of Mexico data set.
Participants, Preparation, and Procedure Eight University of Colorado undergraduate and
Feature
Not feature Information color map
Initial growth
Leaking into nonfeature
Adjusting growth
Final segmentation
Figure 6. Our approach renders knowledge of fault likelihood on the evolving surface to show the user when the segmentation leaks into regions that don’t contain a fault (green) instead of a region that does (red). The top and bottom rows show two different perspectives.
graduate science students participated. None of them had studied geosciences or worked in that field, and they had little or no experience with 3D visualization tools and seismic data. So, the participants can be considered nonexperts and naïve in the field of 3D seismic interpretation. Before beginning the study, we gave each participant a five-minute introduction to the software and explained how to identify and segment faults and geobodies from a test data set. At the beginning of each feature interpretation, we briefly showed the participants a 2D slice of the feature so that they knew which feature to segment. We then removed this display, and it wasn’t visible during the study’s timed portion. Time started when we directed the participant to each feature’s location and stopped when the participant was satisfied with the solution obtained. The investigator conducting the study sat beside each participant to provide immediate answers to any questions or help with difficulties related to working with the software. Participants rarely requested help; such requests usually involved the participant forgetting how to do something trivial in the software that didn’t relate to the study itself.
Results For each feature, we recorded the segmented surfaces and the time to complete the segmentation for each participant and compared this data to the expert’s. We computed the accuracy of participant results relative to the expert interpretation on a volumetric basis such that 100 percent accuracy implies that the participant’s and expert’s results were identical.
Figure 7 shows six pairs of zoomed-in images showing the region of interest around features. In each pair, the left image is the expert manual
GPU Implementation
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o allow for fast computation of surface evolution, we implement our approach (see the main article) using CUDA (Compute Unified Device Architecture )1 on an Nvidia Quadro FX 5600 GPU. We leverage the GPU for its many parallel processors and the ease with which results can be visualized directly on the GPU. Compared to a standard single-core CPU (an AMD Opteron 280), the GPU shows significant speedup through reduced runtimes (see Table A). The increased speed allows for the technique’s computation at interactive rates for moderate-sized subvolumes (2563). This lets users observe the evolution of surfaces in real time and adjust runtime parameters on the fly to guide surfaces toward features. Table A. The visualization system’s performance on a single-core CPU (an AMD Opteron 280) and a GPU (an Nvidia Quadro FX 5600), for 200 iterations. CPU
GPU
No. of faces
Runtime (sec.)
Runtime (sec.)
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Speedup
1,729 K
1,978.2
62.43
3.20
~32×
Fault
744 K
1,382.5
38.24
5.23
~36×
Channel
432 K
1,816.0
49.06
4.10
~37×
Data set Geobody
Reference 1. Nvidia Compute Unified Device Architecture, Programming Guide, Version Beta 2.0, Nvidia, 2. Apr. 2008.
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(a)
(b) Figure 7. Six interpretation tasks undertaken in the user study: (a) faults and (b) geobodies. In each pair of images, the left image shows the expert hand-drawn result and the right image is the consensus result obtained by averaging the eight participants’ results. Overall similarities between the expert and consensus results attest to this technique’s accuracy. Differences between the edges of the shapes result from users not fully extending their segmentations to the feature boundary. 70 60
Participant A Participant B Participant C Participant D Participant E Participant F Participant G Participant H
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Figure 8. The time to interpret three faults and three geobodies. The participants segmented the features many times faster than the expert did.
interpretation and the right image is the consensus result obtained by averaging the participants’ segmentations. This consensus result is valid owing to the low variance between user segmentations. Figure 8 shows the time taken to interpret the features. The participants obviously could segment the features many times faster than the expert could. Figure 9 shows the participants’ accuracy. Their average accuracy was approximately 85 percent for faults and 90 to 95 percent for geobodies. Figure 10 indicates our approach’s reliability by comparing how similar each participant’s results were to each other. The participants’ results were 85 to 95 percent similar for faults and over 95 percent similar for geobodies. This shows the approach has little interuser variability, thus resulting in highly consistent segmentations. 38
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Compared to simpler segmentation approaches, such as using a 3D paintbrush, ours is fast, intuitive, and easy. Because we provide specific expert knowledge through our streamlined visualization environment, users can easily understand a data set’s geology without having to manage a separate knowledge database. Finally, because our approach accurately segments complex shapes, users don’t have to onerously follow detailed feature boundaries using precise brush movements, which could cause repetitive-strain injuries.
F
rom the results, we infer that our approach transfers knowledge quickly and with high accuracy from experts to novices. However, although the novices’ results were excellent, they weren’t production quality. Fortunately, when a trained
100
Accuracy (%)
90 Participant A Participant B Participant C Participant D Participant E Participant F Participant G Participant H
80 70 60 50 40 Fault 1
Fault 2
Fault 3
Geobody 1
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Figure 9. Participant accuracy. A score of 100 percent means that the participant matched the expert’s interpretation. The participants’ average accuracy was approximately 85 percent for faults and 90 to 95 percent for geobodies. 100 90 Reliability (%)
geoscientist uses our approach, it easily generates segmentations comparable to an expert’s. The approach also successfully captures user knowledge during segmentation, thereby allowing intelligent adjustments to parameters that produce immediately visible effects. We plan to apply our approach to other application areas with similar goals, such as 3D medical imaging.
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Acknowledgments David Yuen, William Hammon, Jonathon Marbach, Francis M. Coady, and James Carlson all influenced this research. TerraSpark Geosciences provided support.
References 1. S. Osher and J.A. Sethian, “Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,” J. Computational Physics, vol. 79, 1988, pp. 12–49; http://math.berkeley. edu/~sethian/2006/Papers/sethian.osher.88.pdf. 2. M. Chen et al., “Data, Information, and Knowledge in Visualization,” IEEE Computer Graphics and Applications, vol. 29, no. 1, pp. 12–19.
Benjamin J. Kadlec is a partner and computational scientist at TerraSpark Geosciences. His research focuses on scientific visualization and computation, 3D modeling, and image processing. Kadlec has a PhD in computer science from the University of Colorado. Contact him at [email protected]. Henry M. Tufo is an associate professor of computer science and the director of the University of Colorado’s Computational Science Center. He’s also the head of the Computer Science Section in the Computational and Information Systems Laboratory at the US National Center for Atmospheric Research. He conducts research in high-performance scientific computing,
Fault 1
Fault 2
Fault 3
Geobody 1 Geobody 2 Geobody 3
Figure 10. The approach’s reliability as determined by the standard deviation of participant results. We computed this as the average percentage of the difference between the participant segmentations and the mean of all participant segmentations. A value of 0 percent means participant segmentations were orthogonal to each other; 100 percent means that all participants produced the same segmentation. The results show that our approach has little interuser variability, thus resulting in highly consistent segmentations.
parallel algorithms and architectures, Linux clusters, Grid computing, scalable solvers, high-order numerical methods, computational fluid dynamics, climate modeling, and flow visualization. Tufo has a PhD in applied mathematics from Brown University. Contact him at [email protected]. Geoffrey A. Dorn is the president and a general partner of TerraSpark Geosciences and is an adjoint professor in the University of Colorado’s Department of Geological Sciences and Department of Computer Sciences. His research is in 3D and 4D seismic interpretation and visualization for energy exploration and development. Dorn has a PhD in geophysics from the University of California, Berkeley. Contact him at [email protected]. Selected CS articles and columns are also available for free at http://ComputingNow.computer.org. IEEE Computer Graphics and Applications
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