Venkataraman A, Van Dijk KRA, Buckner RL, Golland P. Exploring Functional Connectivity in fMRI via Clustering. Proc IEEE Int Conf Acoust Speech Signal Process. 2009;2009 :441-4.Abstract
In this paper we investigate the use of data driven clustering methods for functional connectivity analysis in fMRI. In particular, we consider the K-Means and Spectral Clustering algorithms as alternatives to the commonly used Seed-Based Analysis. To enable clustering of the entire brain volume, we use the Nyström Method to approximate the necessary spectral decompositions. We apply K-Means, Spectral Clustering and Seed-Based Analysis to resting-state fMRI data collected from 45 healthy young adults. Without placing any a priori constraints, both clustering methods yield partitions that are associated with brain systems previously identified via Seed-Based Analysis. Our empirical results suggest that clustering provides a valuable tool for functional connectivity analysis.
Sabuncu MR, Balci SK, Shenton ME, Golland P. Image-driven population analysis through mixture modeling. IEEE Trans Med Imaging. 2009;28 (9) :1473-87.Abstract
We present iCluster, a fast and efficient algorithm that clusters a set of images while co-registering them using a parameterized, nonlinear transformation model. The output of the algorithm is a small number of template images that represent different modes in a population. This is in contrast with traditional, hypothesis-driven computational anatomy approaches that assume a single template to construct an atlas. We derive the algorithm based on a generative model of an image population as a mixture of deformable template images. We validate and explore our method in four experiments. In the first experiment, we use synthetic data to explore the behavior of the algorithm and inform a design choice on parameter settings. In the second experiment, we demonstrate the utility of having multiple atlases for the application of localizing temporal lobe brain structures in a pool of subjects that contains healthy controls and schizophrenia patients. Next, we employ iCluster to partition a data set of 415 whole brain MR volumes of subjects aged 18 through 96 years into three anatomical subgroups. Our analysis suggests that these subgroups mainly correspond to age groups. The templates reveal significant structural differences across these age groups that confirm previous findings in aging research. In the final experiment, we run iCluster on a group of 15 patients with dementia and 15 age-matched healthy controls. The algorithm produces two modes, one of which contains dementia patients only. These results suggest that the algorithm can be used to discover subpopulations that correspond to interesting structural or functional "modes."
Goodman AA, Rosolowsky EW, Borkin MA, Foster JB, Halle M, Kauffmann J, Pineda JE. A role for self-gravity at multiple length scales in the process of star formation. Nature. 2009;457 (7225) :63-6.Abstract
Self-gravity plays a decisive role in the final stages of star formation, where dense cores (size approximately 0.1 parsecs) inside molecular clouds collapse to form star-plus-disk systems. But self-gravity's role at earlier times (and on larger length scales, such as approximately 1 parsec) is unclear; some molecular cloud simulations that do not include self-gravity suggest that 'turbulent fragmentation' alone is sufficient to create a mass distribution of dense cores that resembles, and sets, the stellar initial mass function. Here we report a 'dendrogram' (hierarchical tree-diagram) analysis that reveals that self-gravity plays a significant role over the full range of possible scales traced by (13)CO observations in the L1448 molecular cloud, but not everywhere in the observed region. In particular, more than 90 per cent of the compact 'pre-stellar cores' traced by peaks of dust emission are projected on the sky within one of the dendrogram's self-gravitating 'leaves'. As these peaks mark the locations of already-forming stars, or of those probably about to form, a self-gravitating cocoon seems a critical condition for their existence. Turbulent fragmentation simulations without self-gravity-even of unmagnetized isothermal material-can yield mass and velocity power spectra very similar to what is observed in clouds like L1448. But a dendrogram of such a simulation shows that nearly all the gas in it (much more than in the observations) appears to be self-gravitating. A potentially significant role for gravity in 'non-self-gravitating' simulations suggests inconsistency in simulation assumptions and output, and that it is necessary to include self-gravity in any realistic simulation of the star-formation process on subparsec scales.
Levitt JJ, Styner M, Niethammer M, Bouix S, Koo M-S, Voglmaier MM, Dickey CC, Niznikiewicz MA, Kikinis R, McCarley RW, et al. Shape abnormalities of caudate nucleus in schizotypal personality disorder. Schizophr Res. 2009;110 (1-3) :127-39.Abstract
BACKGROUND: Previously, we reported abnormal volume and global shape in the caudate nucleus in schizotypal personality disorder (SPD). Here, we use a new shape measure which importantly permits local in addition to global shape analysis, as well as local correlations with behavioral measures. METHODS: Thirty-two female and 15 male SPDs, and 29 female and 14 male normal controls (NCLs), underwent brain magnetic resonance imaging (MRI). We assessed caudate shape measures using spherical harmonic-point distribution model (SPHARM-PDM) methodology. RESULTS: We found more pronounced global shape differences in the right caudate in male and female SPD, compared with NCLs. Local shape differences, principally in the caudate head, survived statistical correction on the right. Also, we performed correlations between local surface deformations with clinical measures and found significant correlations between local shape deflated deformations in the anterior medial surface of the caudate with verbal learning capacity in female SPD. CONCLUSIONS: Using SPHARM-PDM methodology, we found both global and local caudate shape abnormalities in male and female SPD, particularly right-sided, and largely restricted to limbic and cognitive anterior caudate. The most important and novel findings were bilateral statistically significant correlations between local surface deflations in the anterior medial surface of the head of the caudate and verbal learning capacity in female SPD. By extension, these local caudate correlation findings implicate the ventromedial prefrontal cortex (vmPFC), which innervates that area of the caudate, and demonstrate the utility of local shape analysis to investigate the relationship between specific subcortical and cortical brain structures in neuropsychiatric conditions.
Nunnery G, Hershkovits E, Tannenbaum A, Tannenbaum R. Adsorption of poly(methyl methacrylate) on concave Al2O3 surfaces in nanoporous membranes. Langmuir. 2009;25 (16) :9157-63.Abstract
The objective of this study was to determine the influence of polymer molecular weight and surface curvature on the adsorption of polymers onto concave surfaces. Poly(methyl methacrylate) (PMMA) of various molecular weights was adsorbed onto porous aluminum oxide membranes having various pore sizes, ranging from 32 to 220 nm. The surface coverage, expressed as repeat units per unit surface area, was observed to vary linearly with molecular weight for molecular weights below approximately 120,000 g/mol. The coverage was independent of molecular weight above this critical molar mass, as was previously reported for the adsorption of PMMA on convex surfaces. Furthermore, the coverage varied linearly with pore size. A theoretical model was developed to describe curvature-dependent adsorption by considering the density gradient that exists between the surface and the edge of the adsorption layer. According to this model, the density gradient of the adsorbed polymer segments scales inversely with particle size, while the total coverage scales linearly with particle size, in good agreement with experiment. These results show that the details of the adsorption of polymers onto concave surfaces with cylindrical geometries can be used to calculate molecular weight (below a critical molecular weight) if pore size is known. Conversely, pore size can also be determined with similar adsorption experiments. Most significantly, for polymers above a critical molecular weight, the precise molecular weight need not be known in order to determine pore size. Moreover, the adsorption developed and validated in this work can be used to predict coverage also onto surfaces with different geometries.
Van Leemput K, Bakkour A, Benner T, Wiggins G, Wald LL, Augustinack J, Dickerson BC, Golland P, Fischl B. Automated segmentation of hippocampal subfields from ultra-high resolution in vivo MRI. Hippocampus. 2009;19 (6) :549-57.Abstract
Recent developments in MRI data acquisition technology are starting to yield images that show anatomical features of the hippocampal formation at an unprecedented level of detail, providing the basis for hippocampal subfield measurement. However, a fundamental bottleneck in MRI studies of the hippocampus at the subfield level is that they currently depend on manual segmentation, a laborious process that severely limits the amount of data that can be analyzed. In this article, we present a computational method for segmenting the hippocampal subfields in ultra-high resolution MRI data in a fully automated fashion. Using Bayesian inference, we use a statistical model of image formation around the hippocampal area to obtain automated segmentations. We validate the proposed technique by comparing its segmentations to corresponding manual delineations in ultra-high resolution MRI scans of 10 individuals, and show that automated volume measurements of the larger subfields correlate well with manual volume estimates. Unlike manual segmentations, our automated technique is fully reproducible, and fast enough to enable routine analysis of the hippocampal subfields in large imaging studies.
Kaban LB, Seldin EB, Kikinis R, Yeshwant K, Padwa BL, Troulis MJ. Clinical application of curvilinear distraction osteogenesis for correction of mandibular deformities. J Oral Maxillofac Surg. 2009;67 (5) :996-1008.Abstract
PURPOSE: To report the use of a semiburied curvilinear distraction device, with a 3-dimensional (3D) computed tomography treatment planning system, for correction of mandibular deformities. MATERIALS AND METHODS: This was a retrospective evaluation of 13 consecutive patients, with syndromic and nonsyndromic micrognathia, who underwent correction by curvilinear distraction osteogenesis. A 3D computed tomography scan was obtained for each patient and imported into a 3D treatment planning system (Slicer/Osteoplan). Surgical guides were constructed to localize the osteotomy and to drill holes to secure the distractor's proximal and distal footplates to the mandible. Postoperatively, patients were followed by clinical examination and plain radiographs to ensure the desired vector of movement. At end distraction, when possible, a 3D computed tomography scan was obtained to document the final mandibular position. RESULTS: Of the 13 patients, 8 were females and 5 were males, with a mean age of 11.9 years (range 15 months to 39 years). All 13 underwent bilateral mandibular curvilinear distraction. Of the 13 patients, 8 were 16 years old or younger and 5 were younger than 6 years of age. The diagnoses included Treacher Collins syndrome (n = 3), Nager syndrome (n = 3), craniofacial microsomia (n = 2), post-traumatic ankylosis (n = 1), and micrognathia (syndromic, n = 3; nonsyndromic, n = 1). The correct distractor placement, vector of movement, and final mandibular position were achieved in 10 of 13 patients. In the other 3 patients, the desired jaw position was achieved by "molding" the regenerate. CONCLUSIONS: The use of a semiburied curvilinear distraction device, with 3D treatment planning, is a potentially powerful tool to correct complex mandibular deformities.
Yeo TBT, Vercauteren T, Fillard P, Peyrat J-M, Pennec X, Golland P, Ayache N, Clatz O. DT-REFinD: diffusion tensor registration with exact finite-strain differential. IEEE Trans Med Imaging. 2009;28 (12) :1914-28.Abstract
In this paper, we propose the DT-REFinD algorithm for the diffeomorphic nonlinear registration of diffusion tensor images. Unlike scalar images, deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme. Current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently, these methods often approximate the gradient of the objective function. In the case of the finite-strain (FS) reorientation strategy, we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function. By utilizing the closed-form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms, the resulting registration algorithm is diffeomorphic and fast. We contrast the algorithm with a traditional FS alternative that ignores the reorientation in the gradient computation. We show that the exact gradient leads to significantly better registration at the cost of computation time. Independently of the choice of Euclidean or Log-Euclidean interpolation and sum of squared differences dissimilarity measure, the exact gradient achieves better alignment over an entire spectrum of deformation penalties. Alignment quality is assessed with a battery of metrics including tensor overlap, fractional anisotropy, inverse consistency and closeness to synthetic warps. The improvements persist even when a different reorientation scheme, preservation of principal directions, is used to apply the final deformations.
Oun W, Numënmaa A, Hämäläinen M, Golland P. Multimodal functional imaging using fMRI-informed regional EEG/MEG source estimation. Inf Process Med Imaging. 2009;21 :88-100.Abstract
We propose a novel method, fMRI-Informed Regional Estimation (FIRE), which utilizes information from fMRI in E/MEG source reconstruction. FIRE takes advantage of the spatial alignment between the neural and the vascular activities, while allowing for substantial differences in their dynamics. Furthermore, with the regional approach, FIRE can be efficiently applied to a dense grid of sources. Inspection of our optimization procedure reveals that FIRE is related to the re-weighted minimum-norm algorithms, the difference being that the weights in the proposed approach are computed from both the current estimates and fMRI data. Analysis of both simulated and human fMRI-MEG data shows that FIRE reduces the ambiguities in source localization present in the minimum-norm estimates. Comparisons with several joint fMRI-E/MEG algorithms demonstrate robustness of FIRE in the presence of sources silent to either fMRI or E/MEG measurements.
Tokuda J, Fischer GS, Papademetris X, Yaniv Z, Ibanez L, Cheng P, Liu H, Blevins J, Arata J, Golby AJ, et al. OpenIGTLink: an open network protocol for image-guided therapy environment. Int J Med Robot. 2009;5 (4) :423-34.Abstract
BACKGROUND: With increasing research on system integration for image-guided therapy (IGT), there has been a strong demand for standardized communication among devices and software to share data such as target positions, images and device status. METHOD: We propose a new, open, simple and extensible network communication protocol for IGT, named OpenIGTLink, to transfer transform, image and status messages. We conducted performance tests and use-case evaluations in five clinical and engineering scenarios. RESULTS: The protocol was able to transfer position data with submillisecond latency up to 1024 fps and images with latency of <10 ms at 32 fps. The use-case tests demonstrated that the protocol is feasible for integrating devices and software. CONCLUSION: The protocol proved capable of handling data required in the IGT setting with sufficient time resolution and latency. The protocol not only improves the interoperability of devices and software but also promotes transitions of research prototypes to clinical applications.
Mamisch TC, Kim Y-J, Richolt J, Zilkens C, Kikinis R, Millis M, Kordelle J. Range of motion after computed tomography-based simulation of intertrochanteric corrective osteotomy in cases of slipped capital femoral epiphysis: comparison of uniplanar flexion osteotomy and multiplanar flexion, valgisation, and rotational osteotomies. J Pediatr Orthop. 2009;29 (4) :336-40.Abstract
BACKGROUND: Various osteotomy techniques have been developed to correct the deformity caused by slipped capital femoral epiphysis (SCFE) and compared by their clinical outcomes. The aim of the presented study was to compare an intertrochanteric uniplanar flexion osteotomy with a multiplanar osteotomy by their ability to improve postoperative range of motion as measured by simulation of computed tomographic data in patients with SCFE. METHODS: We examined 19 patients with moderate or severe SCFE as classified based on slippage angle. A computer program for the simulation of movement and osteotomy developed in our laboratory was used for study execution. According to a 3-dimensional reconstruction of the computed tomographic data, the physiological range was determined by flexion, abduction, and internal rotation. The multiplanar osteotomy was compared with the uniplanar flexion osteotomy. Both intertrochanteric osteotomy techniques were simulated, and the improvements of the movement range were assessed and compared. RESULTS: The mean slipping and thus correction angles measured were 25 degrees (range, 8-46 degrees) inferior and 54 degrees (range, 32-78 degrees) posterior. After the simulation of multiplanar osteotomy, the virtually measured ranges of motion as determined by bone-to-bone contact were 61 degrees for flexion, 57 degrees for abduction, and 66 degrees for internal rotation. The simulation of the uniplanar flexion osteotomy achieved a flexion of 63 degrees, an abduction of 36 degrees, and an internal rotation of 54 degrees. CONCLUSIONS: Apart from abduction, the improvement in the range of motion by a uniplanar flexion osteotomy is comparable with that of the multiplanar osteotomy. However, the improvement in flexion for the simulation of both techniques is not satisfactory with regard to the requirements of normal everyday life, in contrast to abduction and internal rotation. LEVEL OF EVIDENCE: Level III, Retrospective comparative study.
Wang X, Grimson EWL, Westin C-F. Tractography segmentation using a hierarchical Dirichlet processes mixture model. Inf Process Med Imaging. 2009;21 :101-13.Abstract
In this paper, we propose a new nonparametric Bayesian framework to cluster white matter fiber tracts into bundles using a hierarchical Dirichlet processes mixture (HDPM) model. The number of clusters is automatically learnt from data with a Dirichlet process (DP) prior instead of being manually specified. After the models of bundles have been learnt from training data without supervision, they can be used as priors to cluster/classify fibers of new subjects. When clustering fibers of new subjects, new clusters can be created for structures not observed in the training data. Our approach does not require computing pairwise distances between fibers and can cluster a huge set of fibers across multiple subjects without subsampling. We present results on multiple data sets, the largest of which has more than 120, 000 fibers.
Toews M, Wells III WM. Bayesian Registration via Local Image Regions: Information, Selection and Marginalization. Inf Process Med Imaging. 2009;21 :435-46.Abstract

We propose a novel Bayesian registration formulation in which image location is represented as a latent random variable. Location is marginalized to determine the maximum a priori (MAP) transform between images, which results in registration that is more robust than the alternatives of omitting locality (i.e. global registration) or jointly maximizing locality and transform (i.e. iconic registration). A mathematical link is established between the Bayesian registration formulation and the mutual information (MI) similarity measure. This leads to a novel technique for selecting informative image regions for registration, based on the MI of image intensity and spatial location. Experimental results demonstrate the effectiveness of the marginalization formulation and the MI-based region selection technique for ultrasound (US) to magnetic resonance (MR) registration in an image-guided neurosurgical application.

Lashkari D, Golland P. Exploratory fMRI analysis without spatial normalization. Inf Process Med Imaging. 2009;21 :398-410.Abstract
We present an exploratory method for simultaneous parcellation of multisubject fMRI data into functionally coherent areas. The method is based on a solely functional representation of the fMRI data and a hierarchical probabilistic model that accounts for both intersubject and intra-subject forms of variability in fMRI response. We employ a Variational Bayes approximation to fit the model to the data. The resulting algorithm finds a functional parcellation of the individual brains along with a set of population-level clusters, establishing correspondence between these two levels. The model eliminates the need for spatial normalization while still enabling us to fuse data from several subjects. We demonstrate the application of our method on a visual fMRI study.
Risholm P, Samsett E, Talos I-F, Wells III WM. A Non-rigid Registration Framework that Accommodates Resection and Retraction. Inf Process Med Imaging. 2009;21 :447-58.Abstract

Traditional non-rigid registration algorithms are incapable of accurately registering intra-operative with pre-operative images whenever tissue has been resected or retracted. In this work we present methods for detecting and handling retraction and resection. The registration framework is based on the bijective Demons algorithm using an anisotropic diffusion smoother. Retraction is detected at areas of the deformation field with high internal strain and the estimated retraction boundary is integrated as a diffusion boundary in the smoother to allow discontinuities to develop across the resection boundary. Resection is detected by a level set method evolving in the space where image intensities disagree. The estimated resection is integrated into the smoother as a diffusion sink to restrict image forces originating inside the resection from being diffused to surrounding areas. In addition, the deformation field is continuous across the diffusion sink boundary which allow us to move the boundary of the diffusion sink without changing values in the deformation field (no interpolation or extrapolation is needed). We present preliminary results on both synthetic and clinical data which clearly shows the added value of explicitly modeling these processes in a registration framework.

Sampat MP, Berger AM, Healy BC, Hildenbrand P, Vass J, Meier DS, Chitnis T, Weiner HL, Bakshi R, Guttmann CRG. Regional white matter atrophy--based classification of multiple sclerosis in cross-sectional and longitudinal data. AJNR Am J Neuroradiol. 2009;30 (9) :1731-9.Abstract
BACKGROUND AND PURPOSE: The different clinical subtypes of multiple sclerosis (MS) may reflect underlying differences in affected neuroanatomic regions. Our aim was to analyze the effectiveness of jointly using the inferior subolivary medulla oblongata volume (MOV) and the cross-sectional area of the corpus callosum in distinguishing patients with relapsing-remitting multiple sclerosis (RRMS), secondary-progressive multiple sclerosis (SPMS), and primary-progressive multiple sclerosis (PPMS). MATERIALS AND METHODS: We analyzed a cross-sectional dataset of 64 patients (30 RRMS, 14 SPMS, 20 PPMS) and a separate longitudinal dataset of 25 patients (114 MR imaging examinations). Twelve patients in the longitudinal dataset had converted from RRMS to SPMS. For all images, the MOV and corpus callosum were delineated manually and the corpus callosum was parcellated into 5 segments. Patients from the cross-sectional dataset were classified as RRMS, SPMS, or PPMS by using a decision tree algorithm with the following input features: brain parenchymal fraction, age, disease duration, MOV, total corpus callosum area and areas of 5 segments of the corpus callosum. To test the robustness of the classification technique, we applied the results derived from the cross-sectional analysis to the longitudinal dataset. RESULTS: MOV and central corpus callosum segment area were the 2 features retained by the decision tree. Patients with MOV >0.94 cm(3) were classified as having RRMS. Patients with progressive MS were further subclassified as having SPMS if the central corpus callosum segment area was <55.12 mm(2), and as having PPMS otherwise. In the cross-sectional dataset, 51/64 (80%) patients were correctly classified. For the longitudinal dataset, 88/114 (77%) patient time points were correctly classified as RRMS or SPMS. CONCLUSIONS: Classification techniques revealed differences in affected neuroanatomic regions in subtypes of multiple sclerosis. The combination of central corpus callosum segment area and MOV provides good discrimination among patients with RRMS, SPMS, and PPMS.
Pohl KM, Sabuncu MR. A unified framework for MR based disease classification. Inf Process Med Imaging. 2009;21 :300-13.Abstract
In this paper, we employ an anatomical parameterization of spatial warps to reveal structural differences between medical images of healthy control subjects and disease patients. The warps are represented as structure-specific 9-parameter affine transformations, which constitute a global, non-rigid mapping between the atlas and image coordinates. Our method estimates the structure-specific transformation parameters directly from medical scans by minimizing a Kullback-Leibler divergence measure. The resulting parameters are then input to a linear Support Vector Machine classifier, which assigns individual scans to a specific clinical group. The classifier also enables us to interpret the anatomical differences between groups, as we can visualize the discriminative warp that best differentiates the two groups. We test the accuracy of our approach on a data set consisting of Magnetic Resonance scans from 16 first episode schizophrenics and 17 age-matched healthy control subjects. The data set also contains manual labels for four regions of interest in both hemispheres: superior temporal gyrus, amygdala, hippocampus, and para-hippocampal gyrus. On this small size data set, our approach, which performs classification based on the MR images directly, yields a leave-one-out cross-validation accuracy of up to 90%. This compares favorably with the accuracy achieved by state-of-the-art techniques in schizophrenia MRI research.
Tao R, Fletcher TP, Gerber S, Whitaker RT. A variational image-based approach to the correction of susceptibility artifacts in the alignment of diffusion weighted and structural MRI. Inf Process Med Imaging. 2009;21 :664-75.Abstract
This paper presents a method for correcting the geometric and greyscale distortions in diffusion-weighted MRI that result from inhomogeneities in the static magnetic field. These inhomogeneities may due to imperfections in the magnet or to spatial variations in the magnetic susceptibility of the object being imaged--so called susceptibility artifacts. Echo-planar imaging (EPI), used in virtually all diffusion weighted acquisition protocols, assumes a homogeneous static field, which generally does not hold for head MRI. The resulting distortions are significant, sometimes more than ten millimeters. These artifacts impede accurate alignment of diffusion images with structural MRI, and are generally considered an obstacle to the joint analysis of connectivity and structure in head MRI. In principle, susceptibility artifacts can be corrected by acquiring (and applying) a field map. However, as shown in the literature and demonstrated in this paper, field map corrections of susceptibility artifacts are not entirely accurate and reliable, and thus field maps do not produce reliable alignment of EPIs with corresponding structural images. This paper presents a new, image-based method for correcting susceptibility artifacts. The method relies on a variational formulation of the match between an EPI baseline image and a corresponding T2-weighted structural image but also specifically accounts for the physics of susceptibility artifacts. We derive a set of partial differential equations associated with the optimization, describe the numerical methods for solving these equations, and present results that demonstrate the effectiveness of the proposed method compared with field-map correction.
Gholami B, Haddad WM, Tannenbaum AR. Agitation and pain assessment using digital imaging. Conf Proc IEEE Eng Med Biol Soc. 2009;2009 :2176-9.Abstract
Pain assessment in patients who are unable to verbally communicate with medical staff is a challenging problem in patient critical care. The fundamental limitations in sedation and pain assessment in the intensive care unit (ICU) stem from subjective assessment criteria, rather than quantifiable, measurable data for ICU sedation and analgesia. This often results in poor quality and inconsistent treatment of patient agitation and pain from nurse to nurse. Recent advancements in pattern recognition techniques using a relevance vector machine algorithm can assist medical staff in assessing sedation and pain by constantly monitoring the patient and providing the clinician with quantifiable data for ICU sedation. In this paper, we show that the pain intensity assessment given by a computer classifier has a strong correlation with the pain intensity assessed by expert and non-expert human examiners.
Banks DC, Beason KM. Decoupling illumination from isosurface generation using 4D light transport. IEEE Trans Vis Comput Graph. 2009;15 (6) :1595-602.Abstract
One way to provide global illumination for the scientist who performs an interactive sweep through a 3D scalar dataset is to pre-compute global illumination, resample the radiance onto a 3D grid, then use it as a 3D texture. The basic approach of repeatedly extracting isosurfaces, illuminating them, and then building a 3D illumination grid suffers from the non-uniform sampling that arises from coupling the sampling of radiance with the sampling of isosurfaces. We demonstrate how the illumination step can be decoupled from the isosurface extraction step by illuminating the entire 3D scalar function as a 3-manifold in 4-dimensional space. By reformulating light transport in a higher dimension, one can sample a 3D volume without requiring the radiance samples to aggregate along individual isosurfaces in the pre-computed illumination grid.