SCIENTIFIC COMPUTING AND IMAGING INSTITUTE
at the University of Utah

Morse decomposition provides a numerically stable topological representation of vector fields that is crucial for their rigorous interpretation. However, Morse decomposition is not unique, and its granularity directly impacts its computational cost. In this paper, we propose an automatic refinement scheme to construct the Morse Connection Graph (MCG) of a given vector field in a hierarchical fashion. Our framework allows a Morse set to be refined through a local update of the flow combinatorialization graph, as well as the connection regions between Morse sets. The computation is fast because the most expensive computation is concentrated on a small portion of the domain. Furthermore, the present work allows the generation of a topologically consistent hierarchy of MCGs, which cannot be obtained using a global method. The classification of the extracted Morse sets is a crucial step for the construction of the MCG, for which the Poincaré index is inadequate. We make use of an upper bound for the Conley index, provided by the Betti numbers of an index pair for a translation along the flow, to classify the Morse sets. This upper bound is sufficiently accurate for Morse set classification and provides supportive information for the automatic refinement process. An improved visualization technique for MCG is developed to incorporate the Conley indices. Finally, we apply the proposed techniques to a number of synthetic and real-world simulation data to demonstrate their utility.

We present a system for visualizing memory reference traces, the records of the memory transactions performed by a program at runtime. The visualization consists of a structured layout representing the levels of a cache and a set of data glyphs representing the pieces of data in memory being operated on during application runtime. The data glyphs move in response to events generated by a cache simulator, indicating their changing residency in the various levels of the memory hierarchy. Within the levels, the glyphs arrange themselves into higher-order shapes representing the structure of the cache levels, including the composition of their associative cache sets and eviction ordering. We make careful use of different visual channels, including structure, motion, color, and size, to convey salient events as they occur. Our abstract visualization provides a high-level, global view of memory behavior, while giving insight about important events that may help students or software engineers to better understand their software’s performance and behavior.

Seamless image cloning has become one of the most important editing operation for photomontage. Recent coordinate-based methods have lessened considerably the computational cost of image cloning, thus enabling interactive applications. However, those techniques still bear severe limitations as to concavities and dynamic shape deformation. In this paper we present novel methodology for image cloning that turns out to be highly efficient in terms of computational times while still being more flexible than existing techniques. Our approach builds on combinatorial Laplacian and fast Cholesky factorization to ensure interactive image manipulation, handling holes, concavities, and dynamic deformations during the cloning process. The provided experimental results show that the proposed technique outperforms existing methods in requisites such as accuracy and flexibility.

An ensemble of biological shapes can be represented and analyzed with a dense set of point correspondences. In previous work, optimal point placement was determined by optimizing an information theoretic criterion that depends on relative spatial locations on different shapes combined with pairwise Euclidean distances between nearby points on the same shape. These choices have prevented such methods from effectively characterizing shapes with complex geometry such as thin or highly curved features. This paper extends previous methods for automatic shape correspondence by taking into account the underlying geometry of individual shapes. This is done by replacing the Euclidean distance for intrashape pairwise particle interactions by the geodesic distance. A novel set of numerical techniques for fast distance computations on curved surfaces is used to extract these distances. In addition, we introduce an intershape penalty term that incorporates surface normal information to achieve better particle correspondences near sharp features. Finally, we demonstrate this new method on synthetic and biological datasets.

Keywords: namic

The anterior-inferior glenohumeral capsule is the primary passive stabilizer to the glenohumeral joint during anterior dislocation. Physical examinations following dislocation are crucial for proper diagnosis of capsule pathology; however,they are not standardized for joint position which may lead to misdiagnoses and poor outcomes. To suggest joint positions for physical examinations where the stability provided by the capsule may be consistent among patients, the objective of this study was to evaluate the distribution of maximum principal strain on the anterior-inferior capsule using two validated subject-specific finite element models of the glenohumeral joint at clinically relevant joint positions. The joint positions with 25 N anterior load applied at 60° of glenohumeral abduction and 10°, 20°, 30° and 40° of external rotation resulted in distributions of strain that were similar between shoulders(r²≥0.7). Furthermore, those positions with 20-40° of external rotation resulted in capsule strains on the glenoid side of the anterior band of the inferior glenohumeral ligament that were significantly greater than in all other capsule regions. These findings suggest that anterior stability provided by the anterior-inferior capsule may be consistent among subjects at joint positions with 60° of glenohumeral abduction and a mid-range (20-40°) of external rotation, and that the glenoid side has the greatest contribution to stability at these joint positions. Therefore, it may be possible to establish standard joint positions for physical examinations that clinicians can use to effectively diagnose pathology in the anterior-inferior capsule following dislocation and lead to improved outcomes.

This paper aims at quantifying ontogenetic differences between bonobo (Pan paniscus) and chimpanzee (Pan troglodytes) endocrania, using dental development as a timeline. We utilize a methodology based on smooth and invertible deformations combined with a metric of "currents" that defines a distance between endocranial surfaces and does not rely on correspondence between landmarks. This allows us to perform a temporal surface regression that estimates typical endocranial ontogenetic trajectories separately for bonobos and chimpanzees. We highlight non-linear patterns of endocranial ontogenetic change and significant differences between species at local anatomical levels rather than considering the endocranium as a uniform entity. A spatiotemporal registration permits the quantification of inter-species differences decomposed into a morphological deformation (accounting for size and shape differences independently of age) and a time warp (accounting for changes in the dynamics of development). Our statistical simulations suggest that patterns of endocranial volume (EV) increase may differ significantly between bonobos and chimpanzees, with an earlier phase of a relatively rapid increase (preferentially at some endocranial subdivisions) in the former and a much later phase of relatively rapid increase in the latter. As a consequence, the chimpanzee endocranium appears to reach its adult size later. Moreover, the time warp indicates that juvenile bonobos develop much slower than juvenile chimpanzees, suggesting that inter-specific ontogenetic shifts do not only concern EV increase, but also the rate of shape changes over time. Our method provides, for the first time, a quantitative estimation of inter-specific ontogenetic shifts that appear to differentiate non-linearly.

Instability is a significant concern in total hip arthroplasty (THA), particularly when there is structural compromise of the capsule due to pre-existing pathology or due to necessities of surgical approach. An experimentally grounded fiber-direction-based finite element model of the hip capsule was developed, and was integrated with an established three-dimensional model of impingement/dislocation. Model validity was established by close similarity to results from a cadaveric experiment in a servohydraulic hip simulator. Parametric computational runs explored effects of graded levels of capsule thickness, of regional detachment from the capsule's femoral or acetabular insertions, of surgical incisions of capsule substance, and of capsule defect repairs. Depending strongly upon the specific site, localized capsule defects caused varying degrees of construct stability compromise, with several specific situations involving over 60\% decrement in dislocation resistance. Construct stability was returned substantially toward intact-capsule levels following well-conceived repairs, although the suture sites involved were often at substantial risk of failure. These parametric model results underscore the importance of retaining or robustly repairing capsular structures in THA, in order to maximize overall construct stability. © 2011 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 29:1642–1648, 2011

Identification of electrical activation or depolarization times on sparsely-sampled complex heart surfaces is of importance to clinicians and researchers in cardiac electrophysiology. We introduce a spatiotemporal approach for activation time estimation which combines prior results using spatial and temporal methods with our own progress on gradient estimation on triangulated surfaces. Results of the method applied to simulated and canine heart data suggest that improvements are possible using this novel combined approach.

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly-available isosurface codes.

Longitudinal shape analysis often relies on the estimation of a realistic continuous growth scenario from data sparsely distributed in time. In this paper, we propose a new type of growth model parameterized by acceleration, whereas standard methods typically control the velocity. This mimics the behavior of biological tissue as a mechanical system driven by external forces. The growth trajectories are estimated as smooth flows of deformations, which are twice differentiable. This differs from piecewise geodesic regression, for which the velocity may be discontinuous. We evaluate our approach on a set of anatomical structures of the same subject, scanned 16 times between 4 and 8 years of age. We show our acceleration based method estimates smooth growth, demonstrating improved regularity compared to piecewise geodesic regression. Leave-several-out experiments show that our method is robust to missing observations, as well as being less sensitive to noise, and is therefore more likely to capture the underlying biological growth.

Keywords: na-mic

Differences in the level, timing, or location of gene expression can contribute to alternative phenotypes at the molecular and organismal level. Understanding the origins of expression differences is complicated by the fact that organismal morphology and gene regulatory networks could potentially vary even between closely related species. To assess the scope of such changes, we used high-resolution imaging methods to measure mRNA expression in blastoderm embryos of Drosophila yakuba and Drosophila pseudoobscura and assembled these data into cellular resolution atlases, where expression levels for 13 genes in the segmentation network are averaged into species-specific, cellular resolution morphological frameworks. We demonstrate that the blastoderm embryos of these species differ in their morphology in terms of size, shape, and number of nuclei. We present an approach to compare cellular gene expression patterns between species, while accounting for varying embryo morphology, and apply it to our data and an equivalent dataset for Drosophila melanogaster. Our analysis reveals that all individual genes differ quantitatively in their spatio-temporal expression patterns between these species, primarily in terms of their relative position and dynamics. Despite many small quantitative differences, cellular gene expression profiles for the whole set of genes examined are largely similar. This suggests that cell types at this stage of development are conserved, though they can differ in their relative position by up to 3-4 cell widths and in their relative proportion between species by as much as 5-fold. Quantitative differences in the dynamics and relative level of a subset of genes between corresponding cell types may reflect altered regulatory functions between species. Our results emphasize that transcriptional networks can diverge over short evolutionary timescales and that even small changes can lead to distinct output in terms of the placement and number of equivalent cells.

This paper presents an efficient, fine-grained parallel algorithm for solving the Eikonal equation on triangular meshes. The Eikonal equation, and the broader class of Hamilton–Jacobi equations to which it belongs, have a wide range of applications from geometric optics and seismology to biological modeling and analysis of geometry and images. The ability to solve such equations accurately and efficiently provides new capabilities for exploring and visualizing parameter spaces and for solving inverse problems that rely on such equations in the forward model. Efficient solvers on state-of-the-art, parallel architectures require new algorithms that are not, in many cases, optimal, but are better suited to synchronous updates of the solution. In previous work [W. K. Jeong and R. T. Whitaker, SIAM J. Sci. Comput., 30 (2008), pp. 2512–2534], the authors proposed the fast iterative method (FIM) to efficiently solve the Eikonal equation on regular grids. In this paper we extend the fast iterative method to solve Eikonal equations efficiently on triangulated domains on the CPU and on parallel architectures, including graphics processors. We propose a new local update scheme that provides solutions of first-order accuracy for both architectures. We also propose a novel triangle-based update scheme and its corresponding data structure for efficient irregular data mapping to parallel single-instruction multiple-data (SIMD) processors. We provide detailed descriptions of the implementations on a single CPU, a multicore CPU with shared memory, and SIMD architectures with comparative results against state-of-the-art Eikonal solvers.