The problem of how to efficiently display a polyhedral scene over a pathof viewpoints is cast as a problem of computing visual events along that path.A visual event is a viewpoint that causes a change in the structure ofthe image structure graph, a model's projected line drawing.The information stored with a visual event is sufficient to updatea representation of the image structure graph.Thus the visible lines of a scene can be displayed as viewpoint changesby first precomputing and storing visual events, and then using those eventsat display time to interactively update the image structure graph.Display rates comparable to wire-frame display are achieved for largepolyhedral models.<P>The rim appearance representation is a new, viewer-centered, exactrepresentation of the occluding contour of polyhedra.We present an algorithm based on the geometry of polyhedral self-occlusionand on visual events for computing a representation of the exact appearanceof occluding contour edges.The rim appearance representation, organized as a multi-level model of theoccluding contour, is used to constrain the viewpoints ofa three-dimensional model that can produce a set of detectedoccluding-contour features.Implementation results demonstrate that precomputed occluding-contourinformation efficiently and tightly constrains the pose of a model whileconsistently accounting for detected occluding-contour features.</blockquote></UL><HR><P><H2><A NAME="snakes">Deformable Contours</A></H2><UL><LI><B><A NAME="pami94-lai">     Deformable Contours: Modeling and Extraction</A></B><BR>     K. F. Lai and R. T. Chin,     <CITE>IEEE Trans. Pattern Analysis and Machine Intell.</CITE> <B>17</B>,     1995, 1084-1090.       (<!WA80><!WA80><!WA80><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/pami94-lai.ps">postscript</A>     or <!WA81><!WA81><!WA81><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/pami94-lai.ps.gz">350K gzip'ed postscript</A>)<BR>     (An earlier version appeared in     <CITE>Proc. Computer Vision and Pattern Recognition Conf.</CITE>,     1994, 601-608     (<!WA82><!WA82><!WA82><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr94-lai.ps">postscript</A>     or <!WA83><!WA83><!WA83><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr94-lai.ps.gz">220K gzip'ed postscript</A>).)<P><blockquote>This paper considers the problem of modeling and extracting arbitrary deformable contours from noisy images. We propose a global contour model based on a stable and regenerative shape matrix, which is invariant and unique under rigid motions. Combined with Markov random field to model local deformations, this yields prior distribution that exerts influence over a global model while allowing for deformations. We then cast the problem of extraction into posterior estimation and show its equivalence to energy minimization of a generalized active contour model. We discuss pertinent issues in shape training, energy minimization, line search strategies, minimax regularization and initialization by generalized Hough transform. Finally, we present experimental results and compare its performance to rigid template matching.</blockquote><LI> <B><A NAME="icarcv94-lai">     On Classifying Deformable Contours Using the Generalized     Active Contour Model</A></B><BR>     K. F. Lai and R. T. Chin,     <CITE>Proc. Int. Conf. Automation, Robotics and Computer Vision</CITE>,       Singapore, 1994.       (<!WA84><!WA84><!WA84><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/icarcv94-lai.ps">postscript</A>     or <!WA85><!WA85><!WA85><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/icarcv94-lai.ps.gz">150K gzip'ed postscript</A>)<P><blockquote>Recently, we proposed the generalized active contour model (g-snake) to model and extract deformable contours from noisy images. This paper demonstrates the usefulness of g-snake in classifying among several candidate deformable contours. The g-snake is suitable for this task because its shape representation is unique, affine invariant and possessesmetric properties. We derive the optimal classification test and show that this requires marginalization of the distribution. However, as the summation is peaked around the posterior estimate in most practical applications, only small regions need to be considered.  Finally, we performed extensive experimentations and report significant improvement over matched template in handwritten numeral recognition.</blockquote><LI> <B><A NAME="thesis-lai">     Deformable Contours: Modeling, Extraction,     Detection and Classification</A></B><BR>     Ph.D. Dissertation, K. F. Lai,     Electrical and Computer Engineering Department,     August 1994.     (<!WA86><!WA86><!WA86><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/thesis-lai.ps">postscript</A>     or <!WA87><!WA87><!WA87><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/thesis-lai.ps.gz">820K gzip'ed postscript</A>)<P><blockquote>This thesis presents an integrated approach in modeling, extracting, detecting and classifying deformable contours directly from noisy images. We begin by conducting a case study on regularization, formulation and initialization ofthe active contour models (snakes). Using minimax principle, we derive a regularization criterion whereby the values can be automatically and implicitly determined along the contour. Furthermore, we formulate a set of energy functionals which yield snakes that contain Hough transform as a special case. Subsequently, we consider the problem of modeling and extracting arbitrary deformable contours from noisy images. We combine a stable, invariant andunique contour model with Markov random field to yield priordistribution that exerts influence over an arbitrary global model while allowing for deformation. Under the Bayesian framework, contour extraction turns into posterior estimation, which is in turn equivalent to energy minimization in a generalized active contour model. Finally, we integrate these lower level visual tasks withpattern recognition processes of detection and classification. Based on the Nearman-Pearson lemma, we derive the optimal detection and classificationtests.  As the summation is peaked in most practical applications,only small regions need to be considered in marginalizing the distribution. The validity of our formulation have been confirmed by extensive and rigorous experimentations.</blockquote><LI> <B><A NAME="accv93-lai">     On Regularization, Formulation and Initialization of     Active Contour Models (Snakes)</A></B><BR>     K. F. Lai and R. T. Chin,     <CITE>Proc. 1st Asian Conf. on Computer Vision</CITE>,       1993, 542-545.       (<!WA88><!WA88><!WA88><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/accv93-lai.ps">postscript</A>     or <!WA89><!WA89><!WA89><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/accv93-lai.ps.gz">150K gzip'ed postscript</A>)<P><blockquote>In snake formulation, large regularization enhances the robustness against noise and incomplete data, while small values increase the accuracy in capturing boundary variations. We present a local minimax criterion which automatically determines the optimal regularization at every locations along the boundary with no added computation cost. We also modify existing energy formulations to repair deficiencies in internal energy and improve performance in external energy. This yields snakes that contain Hough transform as a special case. We can therefore initialize the snake efficiently and reliably using Hough transform.</blockquote></UL><HR><P><H2><A NAME="visualization">Visualization</A></H2><UL><LI><B><A NAME="thesis-hibbard">     Visualizing Scientific Computations: A System based on     Lattice-Structured Data and Display Models</A></B><BR>     W. L. Hibbard, Ph.D. Dissertation,     Computer Sciences Department Technical Report 1226,     University of Wisconsin-Madison, 1995.     (<!WA90><!WA90><!WA90><A HREF="ftp://iris.ssec.wisc.edu/pub/lattice">600K compress'ed postscript</A>)<P><blockquote>In this thesis we develop a system that makes scientificcomputations visible and enables physical scientists to perform visualexperiments with their computations.  Our approach is unique in the wayit integrates visualization with a scientific programming language.  Dataobjects of any user-defined data type can be displayed, and can bedisplayed in any way that satisfies broad analytic conditions, withoutrequiring graphics expertise from the user.  Furthermore, the system ishighly interactive.<P>In order to achieve generality in our architecture, we first analyzethe nature of scientific data and displays, and the visualization mappingsbetween them.  Scientific data and displays are usually approximations tomathematical objects (i.e., variables, vectors and functions) and thisprovides a natural way to define a mathematical lattice structure on datamodels and display models.  Lattice-structured models provide a basis forintegrating certain forms of scientific metadata into the computational anddisplay semantics of data, and also provide a rigorous interpretation ofcertain expressiveness conditions on the visualization mapping from datato displays.  Visualization mappings satisfying these expressivenessconditions are lattice isomorphisms.  Applied to the data types of ascientific programming language, this implies that visualization mappingsfrom data aggregates to display aggregates can always be decomposedinto mappings of data primitives to display primitives.<P>These results provide very flexible data and display models, andprovide the basis for flexible and easy-to-use visualization of data objectsoccurring in scientific computations.</blockquote><LI> <B><A NAME="computer94-hibbard">     Interactive Visualization of Earth and Space Science Computations</A></B><BR>     W. L. Hibbard, B. E. Paul, A. L. Battaiola, D. A. Santek,     M-F. Voidrot-Martinez, and C. R. Dyer,     <CITE>Computer</CITE><B> 27</B>, No. 7, July 1994, 65-72.     (<!WA91><!WA91><!WA91><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/computer94-hibbard.ps">postscript</A>     or <!WA92><!WA92><!WA92><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/computer94-hibbard.ps.gz">20K gzip'ed postscript</A>)<P><blockquote>We describe techniques that enable Earth and space scientiststo interactively visualize and experiment with their computations.Numerical simulations of the Earth's atmosphere and oceans generatelarge and complex data sets, which we visualize in a highly interactivevirtual Earth environment.  We use data compression and distributedcomputing to maximize the size of simulations that can be explored,and a user interface tuned to the needs of environmental modelers.For the broader class of computations used by scientists we havedeveloped more general techniques, integrating visualization with anenvironment for developing and executing algorithms.  The key isproviding a flexible data model that lets users define data typesappropriate for their algorithms, and also providing a display modelthat lets users visualize those data types without placing a substantialburden of graphics knowledge on them.</blockquote><LI> <B><A NAME="vis94-hibbard">     A Lattice Model for Data Display</A></B><BR>     W. L. Hibbard, C. R. Dyer, and B. E. Paul,     <CITE>Proc. Visualization '94</CITE>, 1994, 310-317.     (<!WA93><!WA93><!WA93><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/vis94-hibbard.ps">postscript</A>     or <!WA94><!WA94><!WA94><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/vis94-hibbard.ps.gz">60K gzip'ed postscript</A>)<P><blockquote>In order to develop a foundation for visualization, we developlattice models for data objects and displays that focus on the fact thatdata objects are approximations to mathematical objects and realdisplays are approximations to ideal displays.  These lattice modelsgive us a way to quantize the information content of data and displaysand to define conditions on the visualization mappings from data todisplays.  Mappings satisfy these conditions if and only if they arelattice isomorphisms.  We show how to apply this result to scientificdata and display models, and discuss how it might be applied torecursively defined data types appropriate for complex informationprocessing.</blockquote><LI> <B><A NAME="vis92-hibbard">     Display of Scientific Data Structures for Algorithm Visualization</A></B><BR>     W. Hibbard, C. R. Dyer, and B. Paul,     <CITE>Proc. Visualization '92</CITE>, 1992, 139-146.     (<!WA95><!WA95><!WA95><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/vis92-hibbard.ps">postscript</A>     or <!WA96><!WA96><!WA96><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/vis92-hibbard.ps.gz">60K gzip'ed postscript</A>)<P><blockquote>We present a technique for defining graphical depictions for allthe data types defined in an algorithm.  The ability to display arbitrarycombinations of an algorithm's data objects in a common frame ofreference, coupled with interactive control of algorithm execution,provides a powerful way to understand algorithm behavior.  Typedefinitions are constrained so that all primitive values occurring in dataobjects are assigned scalar types.  A graphical display, including userinteraction with the display, is modeled by a special data type.Mappings from the scalar types into the display model type provide asimple user interface for controlling how all data types are depicted,without the need for type-specific graphics logic.</blockquote></UL></BODY></HTML>