### Organizers

This workshop addresses the broad class of imaging problems in the life sciences that rely on shape or geometry to characterize biological processes and parameters. Of course, the strategy of observing shape and its relationships to biology is a classical undertaking, but in recent years, the availability of 3D imaging and better computational tools has opened up new possibilities for systematic, quantitative analyses of biological shape. This, in turn, has resulted in new demands for more fundamental approaches, based in mathematics, for quantifying and analyzing geometric objects. The problem of quantifying shapes arises in clinical science, where the shapes of neurological or musculoskeletal structures are thought to be related to growth, function, pathology, and degeneration. More recently, computational strategies for shape analysis have become widespread throughout the life sciences, with compelling applications in anthropology, cell and tissue biology, botany, etc. The mathematical contributions to shape analysis have resulted in new tools for modeling or characterizing shapes and for analyzing both shape dynamics and the statistics of populations of shapes. However, the applications of these methods are typically limited by somewhat strong assumptions about the classes of shapes, such as smoothness, correspondence, and homogeneity or underlying simplifications in morphogenetic processes. This workshop focuses on the frontiers of this technology with an eye toward new applications, such as cell biology and biological morphogenesis, which have yet to benefit from robust, comprehensive approaches. Of particular interest are more general tools for handling nonmanifold shapes, such as networks or trees, as well as tools that can handle relatively heterogeneous collections of objects, such as those seen in cell or tissue biology. Also important is the analysis of dynamic shapes as in morphogenesis and regeneration, and the links to other data such as lineage, genomics, and proteomics. Participants will consist of life scientists with compelling scientific and clinical examples, engineers with computational tools for shape analysis, and mathematicians with insights into fundamental approaches for representing and quantifying shape.

### Accepted Speakers

Monday, February 10, 2014 | |
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Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 08:45 AM | Breakfast |

08:45 AM 09:00 AM | Greetings and info from MBI - Marty Golubitsky |

09:00 AM 09:40 AM | Raghu Machiraju - Describing Phenotypical Differences with Extracted Shapes In this talk I will present examples of visualizing phenotypical changes arising from genotypical changes in a variety of biological contexts from cancer and developmental biology. The emphasis will be on visual analytic tools that were developed to detect group-wise and individual (sample) changes in shapes of structures at various scales. I will describe the various computational tools that were used to delineate these changes and how they could be used to generate novel hypotheses. In one recently completed work, I will describe how we explore spatiotemporal patterns of gene expression in a developing mouse brain over the six pre-adulthood stages. I will especially describe how we associate changes in gene expression to preferential growth patterns of structures. In another example, I describe how we detect group-wise changes in the shape of nuclei of salient cells in the microenvironment as noted in knockout mouse and wound-impairment studies. Finally, in the last example, I will describe how changes in shape of the tissue interfaces can be used to explain genotypical changes. |

09:45 AM 10:25 AM | Rohit Bhargava - Extending the concept of shape beyond structural morphology with chemical imaging Microscopic structural features are critical to the diagnosis of solid cancers and form the current clinical gold standard on which much of the followup therapy relies. Complementing the physical form is the chemical makeup of tissue. We have developed chemical imaging - an approach combining spectroscopy and microscopy - to provide a molecular view of tissues, without the use of dyes or stains. This chemical "shape" in tissue has major implications for diagnostic and prognostic activities but is limited by rather primitive analysis. Here we provide an overview of chemical imaging, its applications to cancer and potential for analysis of data that can greatly enhance our ability to understand and counteract solid tumors in humans. |

10:25 AM 11:10 AM | Break |

11:10 AM 11:50 AM | Robert Marc - Unpacking neuronal form and neighborhoods from connectomes Mapping neural networks in brain, retina and spinal cord requires (1) comprehensive parts lists (vertex types), (2) nanometer scale connection detection (edge types), and (3) millimeter scale network tracing. Connectomics based on high-resolution automated transmission electron microscope imaging merges these operations and allows discovery of network modules and motifs as well as the their geometric patterning cell shapes. The mammalian retina contains â‰ˆ 70 classes of neurons assembled into â‰ˆ 15 different network modules, with significant motif overlap. We analyzed mammalian retinal connectome RC1 to unpack this mesh of neurons. A key question that emerges in tracing networks is how neurons and patterns are regulated. I will describe the scales and modes of patterning (packing, tiling, covering) adopted by different neurons and discuss the implications for developmental regulation. |

11:50 AM 02:00 PM | Lunch Break |

02:00 PM 02:40 PM | Murat Maga - Maternal alcohol exposure: impact on genetic control of craniofacial phenotype Varying amounts of structural and functional defects can be seen in individuals exposed to alcohol prenatally. The whole range of these defects is termed as "Fetal Alcohol Spectrum Disorders" (FASD), among which the “Fetal Alcohol Syndrome" (FAS) represents the most extreme case. The reasons for this wide range of outcomes remains elusive, and is thought to be a combination of consumption amount, timing, influence maternal health and age, as well as the genetic background (susceptibility). Using an animal model in a longitudinal study combining high-resolution tomographic imaging (both optical projection and micro computed tomography) and genomic techniques, our goal is to document and understand how and when prenatal alcohol begins to impact the craniofacial form. We collect samples from mid-fetal stages (11.5 days after plugging) to later development (90 post-natal days). Challenges in this study involve rapid shape changes occurring in early time series and the effect of change of imaging modality (from soft tissue to hard tissue). |

02:45 PM 03:25 PM | Kishore Rao Mosaliganti - Inner ear size and shape is regulated by pressure, transport, and tissue mechanics How do animals develop similar organ sizes and shapes despite large fluctuations in initial growth conditions? How is size and shape control achieved across molecular-cellular-tissue scales? We answer this question in the context of early ear development that exhibits a highly stereotyped pattern of assembly and growth. Using in toto imaging technologies in the zebrafish embryo, we reconstructed morphogenetic patterns of cellular movements, cell number and shape changes, and tissue topology changes. We show that otic vesicle growth and regeneration is characterized by endolymph pressure and tissue stretching forces that provide feedback to circuits responsible for generating endolymph fluid. To systematically investigate how otic vesicle growth is controlled, we developed a minimal mathematical model linking tissue geometry and mechanics to tissue stretching forces, thus illuminating how size control to stage-specific volumes is accomplished. Because ear development shares many features with other developmental (eye, heart, kidney) and disease processes (tissue tumor formation), our results and mathematical model will inform understanding of the morphogenesis of other organs. |

03:25 PM 04:00 PM | Break |

04:00 PM 04:40 PM | Julie Thierot - Cell Shape Determination in Single-Cell Motility Julie Thierot's talk onCell Shape Determination in Single-Cell Motility |

04:45 PM 05:30 PM | Jaap Eldering - A distance on curves using orthogonal transformations We construct a geometric method to directly quantify the difference between curves. That is, we construct a distance for parametrized curves in R^n modulo Euclidean transformations. This distance measures the local dissimilarity of k-jets (Taylor polynomials) of the curves. The distance is obtained from a variational principle, and can be constructed by solving a boundary value problem for a second-order ODE. As such it may prove to be computationally less expensive than EPdiff methods if one is only interested in a distance measure. |

05:30 PM 07:00 PM | Reception and poster session in MBI Lounge |

07:00 PM | Shuttle pick-up from MBI |

Tuesday, February 11, 2014 | |
---|---|

Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 09:00 AM | Breakfast |

09:00 AM 09:40 AM | Aasa Feragen - Airway tree-shape modeling through large-scale tree-space statistics Anatomical trees appear as transportation systems distributing blood, water or air. Due to their critical role, statistics on populations of trees is essential to understanding disease. This is difficult due to anatomical variation in branching structure across subjects. I will present a geometric tree-space framework for leaf-labeled trees, discuss how statistics can be defined and performed in tree-space, and present applications to anatomical labeling of airway trees and large-scale statistics on the effect of Chronic Obstructive Pulmonary Disease on airway trees. |

09:45 AM 10:25 AM | Mirza Faisel Beg - Computational Neuroanatomy: Mapping brain structure for differential discrimination in Dementia Computational Neuroanatomy: Mapping brain structure for differential discrimination in Dementia |

10:25 AM 11:10 AM | Break |

11:10 AM 11:50 AM | Alain Trouve - Diffeomorphometry of f-shapes Shape spaces have emerged as a natural mathematical setting to think about shapes as a structured space. In that setting, group actions of diffeomorphisms provide nice vehicles to build a full processing framework called here diffeomorphometry. This talks will present a recently developed framework embedding the situation of geometrical shapes carrying a functional information called here f-shapes. |

11:50 AM 02:00 PM | Lunch Break |

02:00 PM 02:40 PM | Miriam Zelditch - Comparative analyses of mandibular growth using Procrustes-based geometric methods Evolutionary biologists study ontogeny both to dissect the modifications of development that generate morphological diversity and to obtain a comprehensive view of phenotypes. The central concept in comparative quantitative studies is the "ontogenetic trajectory", which quantifies the relationship between changes in size, shape and age. These trajectories represent a sequence of age-specific shapes, and the optimal trajectory may be a compromise among optimal age-specific shapes. A still open question is whether ontogenetic trajectories evolve more rapidly in groups that have biphasic life-cycles because metamorphosis allows resetting the trajectory, making each developmental phase independently evolvable. In contrast, trajectories of species that have continuous life-cycles may be more constrained because developing organisms must reconcile conflict between the demands of their current life-history stage and those of maturation from one stage to the next. One plausible constraint on the evolution of post-weaning ontogenies in mammals is the biomechanical demands of feeding. To analyze the ontogeny of form in relationship to the biomechanical demands of feeding, we compare six species of rodents, first to determine what changes in mandibular form appear to be common to all, then to quantify the divergence of the trajectories. The differences among trajectories are relatively modest; measured as an angle between pairs of trajectories, none exceeds 45 degrees. A common feature of all the trajectories is the deepening of the mandible, notable expansion of the angular process, and reorientation plus broadening of the coronoid process. A striking difference is the consequence of the difference in the relationship between tooth development and weaning in the house mouse and the squirrels. In the house mouse, tooth development and weaning occur in relatively narrower intervals with minimal overlap. In squirrels, tooth and jaw development are more protracted processes and so is mandibular development. Eruption of the second molar marks the beginning of weaning in both mice and squirrels. However, the development of functional teeth in squirrels continues long after weaning; the third molar and the adult premolar may not complete development until the following spring whereas mice lack a premolar and the third molar is rudimentary, erupting very soon after the second molar. Partly because of this difference, mandibles of mice at weaning are closer to their adult size and shape than are mandibles of squirrels. Additionally, muscle development and associated changes in the pattern of bone growth overlap the interval of tooth development more broadly in squirrels than in mice. |

02:45 PM 03:25 PM | Anuj Srivastava - Metric-Based Approaches for shape analysis Shape analysis of objects intrinsically involves registration of points across objects. While registration is historically treated as a pre-processing step, a more recent trend is to incorporate it as an integral step in shape comparison. There are two distinct approaches for shape registration -- model based and metric based. (1) In the first case, one assumes a model upfront that is generally of the type: The goal then is to estimate the template and individual deformations given multiple observations. (2) The second approach does not start with a model but uses a metric that forms an objective function for both: registration of points across objects and quantification of difference in shapes. This metric facilitates a consistent framework where registration and ensuing shape analysis (summarization, modes of variations, etc) are all performed under the same metric (and not as either pre- and/or post-processing). It is the second approach that I will elaborate upon in this talk. The key property of valid metrics for registration is that the re-parameterization group acts by isometries under this metric. While such metrics are beginning to emerge for shape analysis of curves, surfaces, and even images, they are often too difficult to allow efficient solutions. In some cases a simple change of variable converts these invariant metrics into standard Euclidean metrics, the classical computational solutions apply. Examples include square-root velocity functions for curves and square-root normal fields for surfaces. I will demonstrate these ideas using different types of objects: curves in Euclidean spaces, trajectories on Riemannian manifolds, 2D surfaces, and vector-valued images. |

03:25 PM 04:00 PM | Break |

04:00 PM 04:40 PM | Gustavo Rohde - Transport-based morphometry for modeling and discrimination of image data Numerous applications in science and technology depend on quantitative information extraction from data whose dimension is large compared to the number of samples available. We describe a novel image analysis framework that, in contrast to deformation-based morphometry, can be used for modeling and discrimination of shape and intensity (e.g. texture) information for a wide variety of imaging problems. The approach consists of an analysis as well as a synthesis operation (i.e. a signal transform) which not only provides a linear embedding isometric to a linearized version of the well known optimal transport metric, but is also invertible. Computational methods for implementing the framework will be described. The approach will be demonstrated in modeling and discrimination in image databases of cells and faces. We show that the method can not only achieve high discrimination accuracies, but also allow for straightforward visualization and interpretation of the information present in such databases. We will also describe our efforts in modeling cellular phenomena from microscopy images using deformation and transport-based methods. The models described are implemented or being implemented in our open source system, CellOrganizer, which can learn generative models of cell organization and synthesize new images drawn from those models. |

04:40 PM 05:15 PM | Discussion |

05:15 PM | Shuttle pick-up from MBI |

Wednesday, February 12, 2014 | |
---|---|

Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 09:00 AM | Breakfast |

09:00 AM 09:40 AM | L. Mahadevan - Gut patterning, brain gyrification and wing shape Gut patterning, brain gyrification and wing shape. |

09:45 AM 10:25 AM | Laurent Younes - Statistical Shape Analysis in Computational Anatomy We will describe a shape analysis pipeline in medical imaging that starts from a dataset containing segmented regions of interest (such as brain subvolumes, or cardiac ventricles), computes a population average, or template, then registers all shapes on the template using large deformation diffeomorphic metric mapping algorithm (LDDMM) in order to derive anatomical biomarkers that are finally used in statistical analyses. The approach is illustrated by specific examples, involving Alzheimer's disease (BIOCARD, ADNI), Huntington disease (PREDICT) and hypertrophic cardiomyopathy. |

10:25 AM 11:10 AM | Break |

11:10 AM 11:50 AM | Sebastian Kurtek - Statistical analysis of shapes of 3D objects We present a Riemannian framework for comprehensive statistical shape analysis of 3D objects represented by their boundaries, which form parameterized surfaces. This framework provides tools for registration, comparison, averaging, summarizing variability, and statistical modeling of shapes. It is based on a special representation of surfaces called square root normal fields (SRNFs) and a related elastic Riemannian metric. The main advantages of this method are: (1) the elastic metric provides an intuitive interpretation of shape deformations that are being quantified; (2) this metric is invariant to re-parameterizations of surfaces; (3) under the SRNF representation, the complicated elastic metric becomes the standard L2 metric, simplifying parts of the implementation. We present numerous examples of shape comparisons for various types of surfaces in different application areas including medical imaging and graphics. We also compute average shapes, covariances and perform principal component analysis. These quantities are used to define generative shape models and for random sampling. |

12:00 PM 02:00 PM | Pizza Lunch |

02:00 PM 02:40 PM | Sharon Gerbode |

02:45 PM 03:25 PM | TBD |

03:25 PM 04:00 PM | Break |

04:00 PM 04:40 PM | Megan Owen - Mean and Variance of Metric Trees Data generated in such areas as medical imaging and evolutionary biology are frequently tree-shaped, and thus non-Euclidean in nature. As a result, standard techniques for analyzing data in Euclidean spaces become inappropriate, and new methods must be used. One such framework is the space of metric trees constructed by Billera, Holmes, and Vogtmann. This space is non-positively curved (hyperbolic), so there is a unique geodesic path (shortest path) between any two trees and a well-defined notion of a mean tree for a given set of trees. Furthermore, this geodesic path can be computed in polynomial time, leading to a practical algorithm for computing the mean and variance. We look at the mean and variance of distributions of phylogenetic trees that arise in tree inference, and compare with them with existing measures of consensus and variance. No prior knowledge of phylogenetic inference will be assumed. This is joint work with Daniel Brown. |

04:40 PM 05:15 PM | Discussion |

05:15 PM | Shuttle pick-up from MBI |

Thursday, February 13, 2014 | |
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Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 09:00 AM | Breakfast |

09:00 AM 09:40 AM | Tom Fletcher - Probabilistic Modeling of Shape Probabilistic Modeling of Shape |

09:45 AM 10:25 AM | Xiaolei (Sharon) Huang - 3D Actin Network Centerline Extraction with Multiple Active Contours Fluorescence microscopy is frequently used to study two and three dimensional network structures formed by cytoskeletal polymer fibers such as actin filaments and actin cables. While these cytoskeletal structures are often dilute enough to allow imaging of individual filaments or bundles of them, quantitative analysis of these images is challenging. To facilitate quantitative, reproducible and objective analysis of the image data, we present an automated method to extract actin networks and retrieve their topology in 3D. Our method uses multiple Stretching Open Active Contours (SOACs) that are automatically initialized at image intensity ridges and then evolve along the centerlines of filaments in the network. SOACs can merge, stop at junctions, and reconfigure with others to allow smooth crossing at junctions of filaments. The proposed approach is generally applicable to images of curvilinear networks with low SNR. We demonstrate its potential by extracting the centerlines of synthetic meshwork images, actin networks in 2D Total Internal Reflection Fluorescence Microscopy images, and 3D actin cable meshworks of live fission yeast cells imaged by spinning disk confocal microscopy. |

10:25 AM 11:10 AM | Break |

11:10 AM 11:50 AM | Carola Wenk - Geometric algorithms for shapes and trajectories This talk will give an introduction to geometric algorithms for comparing and matching discrete geometric shapes such as point sets, polygonal curves, and graphs. We will study distance measures for shapes, approaches for matching shapes under transformations, and algorithms for reconciling sets of shapes by constructing simpler representative shapes. We will consider theoretical results as well as real-world applications including biomedical imaging and GPS trajectory analysis. |

11:50 AM 02:00 PM | Lunch Break |

02:00 PM 02:40 PM | Jens Rittscher - The Role of Imaging in Phenotypic Screening To set the stage I will introduce the phenotypic screening and the relevance of this approach to drug discovery. The talk will highlight a number of image analysis techniques that play an increasingly important role in phenotypic screening. In particular it will review algorithms for cell tracking and cell cycle estimation as well as image analysis based approaches for tissue mapping. Apart from discussing the image analysis algorithms the presentation will also outline what work will be necessary to integrated the high-content information in the overall workflow. The ongoing work at the newly established Target Discovery Institute (TDI) at the University of Oxford will also be presented. The overall goal and the research objectives of the different groups at TDI will be discussed. |

02:45 PM 03:15 PM | Cindy Grimm - Shape Analysis for Biomedical Applications Shape and function are intricately related in biology. We present three biological case studies where the goal is to quantify shape change in order to analyze how shape informs function. The biologists have specific questions they are interested in answering, and have domain knowledge that should be incorporated into the the shape correspondence algorithm. We show how we incorporate these constraints into the shape matching algorithms in order to provide our collaborators with biologically-meaningful shape correspondences. Case study 1: Using strain to track ferret brain development. Case study 2: Using geodesic distances and an approximate medial axis to track an in-vivo beating chicken hearts at an early stage of development (peristaltic motion). Case study 3: Shape space based on natural neighbor coordinates for bat pinnae and noseleaves. |

03:15 PM 03:30 PM | Break |

03:30 PM 04:15 PM | Filipa Alves - Quantifying and modelling patterned cell fate determination in butterfly wings Quantifying and modelling patterned cell fate determination in butterfly wings |

04:15 PM 05:00 PM | Ross Whitaker - Data Driven Methods for Shape Analysis and Visualization Data Driven Methods for Shape Analysis and Visualization |

05:00 PM | Shuttle pick-up from MBI |

06:00 PM 07:00 PM | Cash Bar |

07:00 PM 09:00 PM | Banquet in the Fusion Room at Crowne Plaza |

Friday, February 14, 2014 | |
---|---|

Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 09:00 AM | Breakfast |

09:00 AM 10:00 AM | Discussion 1 |

10:00 AM 10:30 AM | Break |

10:30 AM 12:00 PM | Discussion 2 |

12:00 PM | Shuttle pick-up from MBI (One to Hotel / One to Airport) |

Name | Affiliation | |
---|---|---|

Alves, Filipa | filipaalves@igc.gulbenkian.pt | Physics, Instituto Gulbenkian Ciencia |

Beg, Mirza Faisal | mfbeg@sfu.ca | School of Engineering Science, Simon Fraser University |

Bhargava, Rohit | rxb@illinois.edu | Bioengineering, University of Illinois at Urbana-Champaign |

Bruveris, Martins | martins.bruveris@epfl.ch | Mathematics, Ãƒâ€°cole Polytechnique FÃƒÂ©dÃƒÂ©rale de Lausanne |

Eldering, Jaap | j.eldering@imperial.ac.uk | Math, Imperial College London |

Elhabian, Shireen | shireen@sci.utah.edu | Scientific Computing and Imaging Institute, University of Utah |

Ellingson, Leif | leif.ellingson@ttu.edu | Mathematics and Statistics, Texas Tech University |

Feragen, Aasa | aasa@diku.dk | Department of Computer Science, University of Copenhagen, Department of Computer Science |

Fletcher, Tom | fletcher@sci.utah.edu | School of Computing, University of Utah |

Gasparovic, Ellen | gasparovic@math.upenn.edu | Mathematics, Duke University |

Grimm, Cindy | grimmc@engr.oregonstate.edu | Mechanical and industrial engineering, Oregon State University |

Huang, Xiaolei (Sharon) | xih206@lehigh.edu | Computer Science and Engineering, Lehigh University |

Hurdal, Monica | mhurdal@math.fsu.edu | Department of Mathematics, Florida State University |

Kavanagh, Kathryn | kkavanagh@umassd.edu | Biology, University of Massachusetts Dartmouth |

Kurtek, Sebastian | kurtek.1@stat.osu.edu | Statistics, The Ohio State University |

Lubkin, Sharon | lubkin@ncsu.edu | Mathematics, North Carolina State University |

Machiraju, Raghu | machiraju.1@osu.edu | Computer Science and Engineering, The Ohio State University |

Maga, Murat | maga@uw.edu | Pediatrics, University of Washington |

Mahadevan, L. | lm@seas.harvard.edu | School of Engineering and Applied Sciences, Harvard University |

Marc, Robert | robert.marc@hsc.utah.edu | Ophthalmology, University of Utah School of Medicine |

Mosaliganti, Kishore Rao | Kishore_mosaliganti@hms.harvard.edu | Department of Systems Biology, Harvard Medical School |

Mukherjee, Prateep | mukherjeeprateep@gmail.com | School of Computing, Scientific Computing and Imaging Institute, University of Utah |

Muralidharan, Prasanna | prasanna@sci.utah.edu | School of Computing, University of Utah |

Narayan, Akil | akil.narayan@umassd.edu | Mathematics, University of Massachusetts Dartmouth |

Owen, Megan | megan.owen@uwaterloo.ca | Computer Science, University of Waterloo |

Rittscher, Jens | Jens@rittscher.org | IBME, University of Oxford |

Rohde, Gustavo | gustavor@cmu.edu | Biomedical Engineering, Carnegie Mellon University |

Sheets, H. David | hsheets@buffalo.edu | Geology, SUNY at Buffalo |

Srivastava, Anuj | anuj@stat.fsu.edu | Statistics, Florida State University |

Su, Jingyong | jingyong.su@ttu.edu | Mathematics and Statistics, Texas Tech University |

Swiderski, Donald | dlswider@umich.edu | Kresge Hearing Research Institute, University of Michigan |

Theriot, Julie | theriot@stanford.edu | Biochemistry, Stanford University School of Medicine |

Trouve, Alain | trouve@cmla.ens-cachan.fr | Mathematics, 'Ecole Normale Sup'erieure de Cachan |

Wenk, Carola | cwenk@tulane.edu | Computer Science, Tulane University |

Whitaker, Ross | whitaker@cs.utah.edu | School of Computing, University of Utah |

Xie, Qian | qxie@stat.fsu.edu | Statistics, Florida State University |

Xu, Qiuping | qxu@math.fsu.edu | Department of Mathematics, Florida State University |

Younes, Laurent | younes@cis.jhu.edu | Applied Mathematics and Statistics, Johns Hopkins University |

Zelditch, Miriam | zelditch@umich.edu | Museum of Paleontology, University of Michigan |

Zhang, Miaomiao | bonny1986@gmail.com | School of Computing, University of Utah |

Quantifying and modelling patterned cell fate determination in butterfly wings

Microscopic structural features are critical to the diagnosis of solid cancers and form the current clinical gold standard on which much of the followup therapy relies. Complementing the physical form is the chemical makeup of tissue. We have developed chemical imaging - an approach combining spectroscopy and microscopy - to provide a molecular view of tissues, without the use of dyes or stains. This chemical "shape" in tissue has major implications for diagnostic and prognostic activities but is limited by rather primitive analysis. Here we provide an overview of chemical imaging, its applications to cancer and potential for analysis of data that can greatly enhance our ability to understand and counteract solid tumors in humans.

We construct a geometric method to directly quantify the difference between curves. That is, we construct a distance for parametrized curves in R^n modulo Euclidean transformations. This distance measures the local dissimilarity of k-jets (Taylor polynomials) of the curves. The distance is obtained from a variational principle, and can be constructed by solving a boundary value problem for a second-order ODE. As such it may prove to be computationally less expensive than EPdiff methods if one is only interested in a distance measure.

Anatomical trees appear as transportation systems distributing blood, water or air. Due to their critical role, statistics on populations of trees is essential to understanding disease. This is difficult due to anatomical variation in branching structure across subjects. I will present a geometric tree-space framework for leaf-labeled trees, discuss how statistics can be defined and performed in tree-space, and present applications to anatomical labeling of airway trees and large-scale statistics on the effect of Chronic Obstructive Pulmonary Disease on airway trees.

Probabilistic Modeling of Shape

We introduce "medial/skeletal linking structures" for configurations of multiple objects, which build upon the individual skeletal structures of the objects in a minimal way, and which enable us to analyze the "positional geometry" of the configuration along with the shapes of the individual objects. We use the skeletal linking structure to introduce and compute volumetric invariants of the positional geometry of the collection, which include measures of relative closeness and geometric significance of the individual objects. The invariants are computed via "skeletal linking integrals" computed directly on the skeletal sets, and we use them to construct a "tiered linking graph."

When given thresholds of closeness and significance are applied to this graph, they yield subgraph(s) identifying subconfigurations and provide a hierarchical ordering of the objects.

Shape and function are intricately related in biology. We present three biological case studies where the goal is to quantify shape change in order to analyze how shape informs function. The biologists have specific questions they are interested in answering, and have domain knowledge that should be incorporated into the the shape correspondence algorithm. We show how we incorporate these constraints into the shape matching algorithms in order to provide our collaborators with biologically-meaningful shape correspondences.

Case study 1: Using strain to track ferret brain development.

Case study 2: Using geodesic distances and an approximate medial axis to track an in-vivo beating chicken hearts at an early stage of development (peristaltic motion).

Case study 3: Shape space based on natural neighbor coordinates for bat pinnae and noseleaves.

Fluorescence microscopy is frequently used to study two and three dimensional network structures formed by cytoskeletal polymer fibers such as actin filaments and actin cables. While these cytoskeletal structures are often dilute enough to allow imaging of individual filaments or bundles of them, quantitative analysis of these images is challenging. To facilitate quantitative, reproducible and objective analysis of the image data, we present an automated method to extract actin networks and retrieve their topology in 3D. Our method uses multiple Stretching Open Active Contours (SOACs) that are automatically initialized at image intensity ridges and then evolve along the centerlines of filaments in the network. SOACs can merge, stop at junctions, and reconfigure with others to allow smooth crossing at junctions of filaments. The proposed approach is generally applicable to images of curvilinear networks with low SNR. We demonstrate its potential by extracting the centerlines of synthetic meshwork images, actin networks in 2D Total Internal Reflection Fluorescence Microscopy images, and 3D actin cable meshworks of live fission yeast cells imaged by spinning disk confocal microscopy.

The tetrapod limb has become an important model system for studying developmental regulation of morphogenesis and variation in size proportions. Phalanges (finger and toe bones) develop by sequential outgrowth and segmentation of the digit pre-chondrogenic condensation during a 4-day embryonic period. Among taxa, phalangesâ€™ sizes covary in a highly predictable way. However, decades of advances in genetic regulatory studies of the limb have been unable to accurately model regulation of digit segmentation using developmental genetic signaling interactions alone. In this talk, I will discuss alternative models of morphogenesis of segmented structures such as the digits, in which physical tension between cells, evolutionary origins, and high-level network dynamics should be considered.

We present a Riemannian framework for comprehensive statistical shape analysis of 3D objects represented by their boundaries, which form parameterized surfaces. This framework provides tools for registration, comparison, averaging, summarizing variability, and statistical modeling of shapes. It is based on a special representation of surfaces called square root normal fields (SRNFs) and a related elastic Riemannian metric. The main advantages of this method are: (1) the elastic metric provides an intuitive interpretation of shape deformations that are being quantified; (2) this metric is invariant to re-parameterizations of surfaces; (3) under the SRNF representation, the complicated elastic metric becomes the standard L2 metric, simplifying parts of the implementation. We present numerous examples of shape comparisons for various types of surfaces in different application areas including medical imaging and graphics. We also compute average shapes, covariances and perform principal component analysis. These quantities are used to define generative shape models and for random sampling.

In this talk I will present examples of visualizing phenotypical changes arising from genotypical changes in a variety of biological contexts from cancer and developmental biology. The emphasis will be on visual analytic tools that were developed to detect group-wise and individual (sample) changes in shapes of structures at various scales. I will describe the various computational tools that were used to delineate these changes and how they could be used to generate novel hypotheses. In one recently completed work, I will describe how we explore spatiotemporal patterns of gene expression in a developing mouse brain over the six pre-adulthood stages. I will especially describe how we associate changes in gene expression to preferential growth patterns of structures. In another example, I describe how we detect group-wise changes in the shape of nuclei of salient cells in the microenvironment as noted in knockout mouse and wound-impairment studies. Finally, in the last example, I will describe how changes in shape of the tissue interfaces can be used to explain genotypical changes.

Varying amounts of structural and functional defects can be seen in individuals exposed to alcohol prenatally. The whole range of these defects is termed as "Fetal Alcohol Spectrum Disorders" (FASD), among which the â€œFetal Alcohol Syndrome" (FAS) represents the most extreme case. The reasons for this wide range of outcomes remains elusive, and is thought to be a combination of consumption amount, timing, influence maternal health and age, as well as the genetic background (susceptibility). Using an animal model in a longitudinal study combining high-resolution tomographic imaging (both optical projection and micro computed tomography) and genomic techniques, our goal is to document and understand how and when prenatal alcohol begins to impact the craniofacial form. We collect samples from mid-fetal stages (11.5 days after plugging) to later development (90 post-natal days). Challenges in this study involve rapid shape changes occurring in early time series and the effect of change of imaging modality (from soft tissue to hard tissue).

Gut patterning, brain gyrification and wing shape.

Mapping neural networks in brain, retina and spinal cord requires (1) comprehensive parts lists (vertex types), (2) nanometer scale connection detection (edge types), and (3) millimeter scale network tracing. Connectomics based on high-resolution automated transmission electron microscope imaging merges these operations and allows discovery of network modules and motifs as well as the their geometric patterning cell shapes.

The mammalian retina contains Ã¢â€°Ë† 70 classes of neurons assembled into Ã¢â€°Ë† 15 different network modules, with significant motif overlap. We analyzed mammalian retinal connectome RC1 to unpack this mesh of neurons. A key question that emerges in tracing networks is how neurons and patterns are regulated. I will describe the scales and modes of patterning (packing, tiling, covering) adopted by different neurons and discuss the implications for developmental regulation.

How do animals develop similar organ sizes and shapes despite large fluctuations in initial growth conditions? How is size and shape control achieved across molecular-cellular-tissue scales? We answer this question in the context of early ear development that exhibits a highly stereotyped pattern of assembly and growth. Using in toto imaging technologies in the zebrafish embryo, we reconstructed morphogenetic patterns of cellular movements, cell number and shape changes, and tissue topology changes. We show that otic vesicle growth and regeneration is characterized by endolymph pressure and tissue stretching forces that provide feedback to circuits responsible for generating endolymph fluid. To systematically investigate how otic vesicle growth is controlled, we developed a minimal mathematical model linking tissue geometry and mechanics to tissue stretching forces, thus illuminating how size control to stage-specific volumes is accomplished. Because ear development shares many features with other developmental (eye, heart, kidney) and disease processes (tissue tumor formation), our results and mathematical model will inform understanding of the morphogenesis of other organs.

Data generated in such areas as medical imaging and evolutionary biology are frequently tree-shaped, and thus non-Euclidean in nature. As a result, standard techniques for analyzing data in Euclidean spaces become inappropriate, and new methods must be used. One such framework is the space of metric trees constructed by Billera, Holmes, and Vogtmann. This space is non-positively curved (hyperbolic), so there is a unique geodesic path (shortest path) between any two trees and a well-defined notion of a mean tree for a given set of trees. Furthermore, this geodesic path can be computed in polynomial time, leading to a practical algorithm for computing the mean and variance. We look at the mean and variance of distributions of phylogenetic trees that arise in tree inference, and compare with them with existing measures of consensus and variance. No prior knowledge of phylogenetic inference will be assumed. This is joint work with Daniel Brown.

To set the stage I will introduce the phenotypic screening and the relevance of this approach to drug discovery. The talk will highlight a number of image analysis techniques that play an increasingly important role in phenotypic screening. In particular it will review algorithms for cell tracking and cell cycle estimation as well as image analysis based approaches for tissue mapping. Apart from discussing the image analysis algorithms the presentation will also outline what work will be necessary to integrated the high-content information in the overall workflow. The ongoing work at the newly established Target Discovery Institute (TDI) at the University of Oxford will also be presented. The overall goal and the research objectives of the different groups at TDI will be discussed.

Numerous applications in science and technology depend on quantitative information extraction from data whose dimension is large compared to the number of samples available. We describe a novel image analysis framework that, in contrast to deformation-based morphometry, can be used for modeling and discrimination of shape and intensity (e.g. texture) information for a wide variety of imaging problems. The approach consists of an analysis as well as a synthesis operation (i.e. a signal transform) which not only provides a linear embedding isometric to a linearized version of the well known optimal transport metric, but is also invertible. Computational methods for implementing the framework will be described. The approach will be demonstrated in modeling and discrimination in image databases of cells and faces. We show that the method can not only achieve high discrimination accuracies, but also allow for straightforward visualization and interpretation of the information present in such databases. We will also describe our efforts in modeling cellular phenomena from microscopy images using deformation and transport-based methods. The models described are implemented or being implemented in our open source system, CellOrganizer, which can learn generative models of cell organization and synthesize new images drawn from those models.

Shape analysis of objects intrinsically involves registration of points across objects. While registration is historically treated as a pre-processing step, a more recent trend is to incorporate it as an integral step in shape comparison. There are two distinct approaches for shape registration -- model based and metric based.

(1) In the first case, one assumes a model upfront that is generally of the type:

observation = deformed template & noise.

The goal then is to estimate the template and individual deformations given multiple observations.

(2) The second approach does not start with a model but uses a metric that forms an objective function for both: registration of points across objects and quantification of difference in shapes. This metric facilitates a consistent framework where registration and ensuing shape analysis (summarization, modes of variations, etc) are all performed under the same metric (and not as either pre- and/or post-processing).

It is the second approach that I will elaborate upon in this talk. The key property of valid metrics for registration is that the re-parameterization group acts by isometries under this metric. While such metrics are beginning to emerge for shape analysis of curves, surfaces, and even images, they are often too difficult to allow efficient solutions. In some cases a simple change of variable converts these invariant metrics into standard Euclidean metrics, the classical computational solutions apply.

Examples include square-root velocity functions for curves and square-root normal fields for surfaces.

I will demonstrate these ideas using different types of objects: curves in Euclidean spaces, trajectories on Riemannian manifolds, 2D surfaces, and vector-valued images.

Julie Thierot's talk onCell Shape Determination in Single-Cell Motility

Shape spaces have emerged as a natural mathematical setting to think about shapes as a structured space. In that setting, group actions of diffeomorphisms provide nice vehicles to build a full processing framework called here diffeomorphometry. This talks will present a recently developed framework embedding the situation of geometrical shapes carrying a functional information called here f-shapes.

This talk will give an introduction to geometric algorithms for comparing and matching discrete geometric shapes such as point sets, polygonal curves, and graphs. We will study distance measures for shapes, approaches for matching shapes under transformations, and algorithms for reconciling sets of shapes by constructing simpler representative shapes. We will consider theoretical results as well as real-world applications including biomedical imaging and GPS trajectory analysis.

Data Driven Methods for Shape Analysis and Visualization

Sonic hedgehog (Shh) is a protein whose signaling plays an essential role in interactions that control facial development. Shh is first expressed in the forebrain prior to development of the facial features. As neural crest cells migrate into the midface, Shh is activated in the adjacent region, and this frontonasal ectodermal zone (or â€˜FEZâ€™) acts as a signaling center that controls growth. Despite its potential explanatory power of FEZ in facial growth and shape, this idea has never been quantitatively assessed.

In this work, through analyses of shapes of the Shh domain in the FEZ and facial shapes of chicks, ducks and chimeras, we tackled the challenges caused by irregularity and large variability of FEZ shapes and built a regression model between FEZ and facial shapes.

We will describe a shape analysis pipeline in medical imaging that starts from a dataset containing segmented regions of interest (such as brain subvolumes, or cardiac ventricles), computes a population average, or template, then registers all shapes on the template using large deformation diffeomorphic metric mapping algorithm (LDDMM) in order to derive anatomical biomarkers that are finally used in statistical analyses. The approach is illustrated by specific examples, involving Alzheimer's disease (BIOCARD, ADNI), Huntington disease (PREDICT) and hypertrophic cardiomyopathy.

Evolutionary biologists study ontogeny both to dissect the modifications of development that generate morphological diversity and to obtain a comprehensive view of phenotypes. The central concept in comparative quantitative studies is the "ontogenetic trajectory", which quantifies the relationship between changes in size, shape and age. These trajectories represent a sequence of age-specific shapes, and the optimal trajectory may be a compromise among optimal age-specific shapes. A still open question is whether ontogenetic trajectories evolve more rapidly in groups that have biphasic life-cycles because metamorphosis allows resetting the trajectory, making each developmental phase independently evolvable. In contrast, trajectories of species that have continuous life-cycles may be more constrained because developing organisms must reconcile conflict between the demands of their current life-history stage and those of maturation from one stage to the next. One plausible constraint on the evolution of post-weaning ontogenies in mammals is the biomechanical demands of feeding. To analyze the ontogeny of form in relationship to the biomechanical demands of feeding, we compare six species of rodents, first to determine what changes in mandibular form appear to be common to all, then to quantify the divergence of the trajectories. The differences among trajectories are relatively modest; measured as an angle between pairs of trajectories, none exceeds 45 degrees. A common feature of all the trajectories is the deepening of the mandible, notable expansion of the angular process, and reorientation plus broadening of the coronoid process. A striking difference is the consequence of the difference in the relationship between tooth development and weaning in the house mouse and the squirrels. In the house mouse, tooth development and weaning occur in relatively narrower intervals with minimal overlap. In squirrels, tooth and jaw development are more protracted processes and so is mandibular development. Eruption of the second molar marks the beginning of weaning in both mice and squirrels. However, the development of functional teeth in squirrels continues long after weaning; the third molar and the adult premolar may not complete development until the following spring whereas mice lack a premolar and the third molar is rudimentary, erupting very soon after the second molar. Partly because of this difference, mandibles of mice at weaning are closer to their adult size and shape than are mandibles of squirrels. Additionally, muscle development and associated changes in the pattern of bone growth overlap the interval of tooth development more broadly in squirrels than in mice.

Principal geodesic analysis (PGA) is a generalization of principal component anal- ysis (PCA) for dimensionality reduction of data on a Riemannian manifold. Cur- rently PGA is defined as a geometric fit to the data, rather than as a probabilistic model. Inspired by probabilistic PCA, we present a latent variable model for PGA that provides a probabilistic framework for factor analysis on manifolds. To com- pute maximum likelihood estimates of the parameters in our model, we develop a Monte Carlo Expectation Maximization algorithm, where the expectation is ap- proximated by Hamiltonian Monte Carlo sampling of the latent variables. We demonstrate the ability of our method to recover the ground truth parameters in simulated sphere data, as well as its effectiveness in analyzing shape variability of a corpus callosum data set from human brain images.

### Posters

Longitudinal data arises in many applications in which the goal is to understand changes in individual entities over time. We present a method for analyzing longitudinal data that take values in a Riemannian manifold. A driving application is to characterize anatomical shape changes and to distinguish between trends in anatomy that are healthy versus those that are due to disease. We present a generative hierarchical model in which each individual is modeled by a geodesic trend, which in turn is considered as a perturbation of the mean geodesic trend for the population. Each geodesic in the model can be uniquely parameterized by a starting point and velocity, i.e., a point in the tangent bundle. Comparison between these parameters is achieved through the Sasaki metric, which provides a natural distance metric on the tangent bundle. We also develop a statistical hypothesis test for differences between two groups of longitudinal data by generalizing the Hotelling T^2 statistic to manifolds. We demonstrate the ability of these methods to distinguish differences in shape changes in a comparison of longitudinal corpus callosum data in subjects with dementia versus healthily aging controls.

Longitudinal data arises in many applications in which the goal is to understand changes in individual entities over time. We present a method for analyzing longitudinal data that take values in a Riemannian manifold. A driving application is to characterize anatomical shape changes and to distinguish between trends in anatomy that are healthy versus those that are due to disease. We present a generative hierarchical model in which each individual is modeled by a geodesic trend, which in turn is considered as a perturbation of the mean geodesic trend for the population. Each geodesic in the model can be uniquely parameterized by a starting point and velocity, i.e., a point in the tangent bundle. Comparison between these parameters is achieved through the Sasaki metric, which provides a natural distance metric on the tangent bundle. We also develop a statistical hypothesis test for differences between two groups of longitudinal data by generalizing the Hotelling T^2 statistic to manifolds. We demonstrate the ability of these methods to distinguish differences in shape changes in a comparison of longitudinal corpus callosum data in subjects with dementia versus healthily aging controls.

Patterns in the human dentition are often used in forensic post mortem identification and in bite-mark analysis. While victim identification based on the whole dentition, including dental work, is non-controversial, bitemark identification has been strongly criticized (NAS, 2009) as lacking a substantial, systematic scientific background. Systematic documentation of the general patterns of human dental variation is lacking, as is evidence that a bitemark impression, a record of the incisal surface configuration of the anterior dentition, is adequate to uniquely link an individual to a bitemark.

Statistical shape analysis develops methods for comparisons, deformations, summarizations, and modeling of shapes in given data sets. These tasks require a fundamental tool called parallel transport of tangent vectors along arbitrary paths. This tool is essential for: (1) computation of geodesic paths using either shooting or path-straightening method, (2) transferring deformations across objects, and (3) modeling of statistical variability in shapes. Using the square-root normal field (SRNF) representation of parameterized surfaces, we present a method for transporting deformations along paths in the shape space. This is difficult despite the underlying space being a vector space because the chosen (elastic) Riemannian metric is non-standard.

Using a finite-basis for representing SRNFs of shapes, we derive expressions for Christoffel symbols that enable parallel transports. We demonstrate this framework using examples from shape analysis of parameterized spherical surfaces, in the three contexts mentioned above.

**Data Driven Methods for Shape Analysis and Visualization**

Ross Whitaker

Data Driven Methods for Shape Analysis and Visualization

**Shape Analysis for Biomedical Applications**

Cindy Grimm

Shape and function are intricately related in biology. We present three biological case studies where the goal is to quantify shape change in order to analyze how shape informs function. The biologists have specific questions they are intere

**The Role of Imaging in Phenotypic Screening**

Jens Rittscher

To set the stage I will introduce the phenotypic screening and the relevance of this approach to drug discovery. The talk will highlight a number of image analysis techniques that play an increasingly important role in phenotypic screening.

**Geometric algorithms for shapes and trajectories**

Carola Wenk

This talk will give an introduction to geometric algorithms for comparing and matching discrete geometric shapes such as point sets, polygona

**3D Actin Network Centerline Extraction with Multiple Active Contours**

Xiaolei (Sharon) Huang

Fluorescence microscopy is frequently used to study two and three dimensional network structures formed by cytoskeletal polymer fibers such as actin filaments and actin cables. While these cytoskeletal structures are often dilute enough to a

**Probabilistic Modeling of Shape**

Tom Fletcher

Probabilistic Modeling of Shape

**Gut patterning, brain gyrification and wing shape**

L. Mahadevan

Gut patterning, brain gyrification and wing shape.

**Metric-Based Approaches for shape analysis**

Anuj Srivastava

Shape analysis of objects intrinsically involves registration of points across objects. While registration is historically treated as a pre-processing step, a more recent trend is to incorporate it as an integral step in shape comparison. Th

**A distance on curves using orthogonal transformations**

Jaap Eldering

We construct a geometric method to directly quantify the difference between curves. That is, we construct a distance for parametrized curves in R^n modulo Euclidean transformations. This distance measures the local dissimilarity of k-jets (Taylor

**Airway tree-shape modeling through large-scale tree-space statistics**

Aasa Feragen

Anatomical trees appear as transportation systems distributing blood, water or air. Due to their critical role, statistics on populations of trees is essential to understanding disease. This is difficult due to anatomical variation in branching st

**Diffeomorphometry of f-shapes**

Alain Trouve

Shape spaces have emerged as a natural mathematical setting to think about shapes as a structured space. In that setting, group actions of diffeomorphisms provide nice vehicles to build a full processing framework called here diffeomorphomet

**Cell Shape Determination in Single-Cell Motility**

Julie Theriot

Julie Thierot's talk onCell Shape Determination in Single-Cell Motility

**Inner ear size and shape is regulated by pressure, transport, and tissue mechanics**

Kishore Rao Mosaliganti

How do animals develop similar organ sizes and shapes despite large fluctuations in initial growth conditions? How is size and shape control achieved across molecular-cellular-tissue scales? We answer this question in the context of early ea

**Unpacking neuronal form and neighborhoods from connectomes**

Robert Marc

Mapping neural networks in brain, retina and spinal cord requires (1) comprehensive parts lists (vertex types), (2) nanometer scale connection detection (edge types), and (3) millimeter scale network tracing. Connectomics based on high-resol