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IBM Research Report Reverse Engineering Methods for Digital RC23991 (W0606-132) June 28, 2006 Computer Science IBM Research Report Reverse Engineering Methods for Digital Restoration Applications Ioana Boier-Martin IBM Research Division Thomas J. Watson Research Center P.O. Box 704 Yorktown Heights, NY 10598 Holly Rushmeier Yale University New Haven, CT Research Division Almaden - Austin - Beijing - Haifa - India - T. J. Watson - Tokyo - Zurich LIMITED DISTRIBUTION NOTICE: This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. I thas been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g ,. payment of royalties). Copies may be requested from IBM T. J. Watson Research Center , P. O. Box 218, Yorktown Heights, NY 10598 USA (email: [email protected]). Some reports are available on the internet at http://domino.watson.ibm.com/library/CyberDig.nsf/home . Reverse Engineering Methods for Digital Restoration Applications Ioana Boier-Martin Holly Rushmeier IBM T. J. Watson Research Center Yale University Hawthorne, New York, USA New Haven, Connecticut, USA [email protected] [email protected] Abstract In this paper we focus on the demands of restoring dig- ital objects for cultural heritage applications. However, the In this paper we discuss the challenges of processing methods we present are relevant to many other areas. and converting 3D scanned data to representations suit- This is a revised and extended version of our previous pa- able for interactive manipulation in the context of virtual per [12]. In that paper we specifically considered the prob- restoration applications. We present a constrained parame- lem of converting a triangle mesh to a Catmull-Clark mul- terization approach that allows us to represent 3D scanned tiresolution subdivision surface. Here we place that work models as parametric surfaces defined over polyhedral do- in the context of cultural heritage restoration applications. mains. A combination of normal- and spatial-based cluster- This context motivates the problem of partitioning to fa- ing techniques is used to generate a partition of the model cilitate texture map editing in addition to the partitioning into regions suitable for parameterization. Constraints can needed for conversion to a subdivision surface. We refor- be optionally imposed to enforce a strict correspondence mulate our techniques to deal with the different partitions between input and output features. We consider two types of needed for intuitive texture map and shape editing. virtual restoration methods: (a) a paint restoration method that takes advantage of the normal-based coarse partition 1.1. Related Work to identify large regions of reduced metric distortion suit- able for texture mapping and (b) a shape restoration ap- Our work is motivated by experiences in virtual restora- proach which relies on a refined partition used to convert tion applications and we build on previous work in ge- the input model to a multiresolution subdivision represen- ometriy processing. tation suitable for intuitive interactive manipulation during digital studies of historical artifacts. Scanning and virtual restoration. The pipeline for process- ing to form a texture mapped triangle mesh from sensed data is well established [7]. Commercial products (e.g., Polyworks R , RapidForm R are available to convert point 1. Introduction clouds to meshes. These products also include some stan- dard CAE/CAD analysis tools such as measurements on Reverse engineering is the process of taking an object surfaces and comparisons of as-built to originally digitally apart for the purpose of analyzing its workings in detail, designed parts. However, the needs of cultural heritage usually with the intention of constructing a new object of applications [21, 33, 27, 7] are different from traditional similar or extended functionality. In the case of 3D scan- CAE/CAD in several different respects. First, the objects ning, the objects are physical items for which digital repli- of interest are typically not regularly machined objects, but cas are created so that the original objects can be further rather complex free-form shapes that were produced manu- studied, manipulated, and / or reproduced with the help of ally and have been worn or broken over time through nat- the computer. Today, 3D scanning has become a commod- ural processes. Second, while shape alone is sometimes of ity service, with multiple applications, ranging from indus- interest, the material appearance of the object as well as its trial design, to retail, to entertainment, to archeology and shape are being studied. Third, several alteration iterations cultural heritage. Most often, the scanner software allows are needed to evaluate the validity of a change. Often times, for the acquired data to be converted to an unstructured 3D judgments are made on the basis of appearance and match- mesh. This representation is typically difficult to manipu- ing images and textual descriptions of appearance, rather late beyond basic display and conversions to other repre- than on more readily quantified requirements such as mak- sentations are needed. ing parts fit together or minimizing weight. Fourth, the pop- ulation using digital models in cultural heritage is much dif- Levoy [31] to fit tensor-product B-spline patches to irregu- ferent from the population using CAE/CAD tools. While lar meshes and that of Guskov et al. [24] to build quad base cultural heritage specialists may have extensive technical domains as part of their hybrid mesh representation. Tech- training, their primary interest is in the history of the ob- niques for converting given models to quadrilateral meshes jects being studied and the people that used them, and not have also been proposed in the mesh generation commu- in the technology itself. The cost of hiring technical special- nity. Advancing front and packing are among the most com- ists and the difficulty of working through a mediator make mon strategies [38, 5]). Typically, the resulting meshes it impractical to include pure technicians on most teams. Fi- have a large number of quads and are not suitable as pa- nally, the hardware and software resources available to cul- rameterization domains. tural heritage projects are generally much more limited than Also related to our approach are mesh partitioning meth- those of engineering design projects. ods. The fuzzy clustering technique of [28] produces patches which are not homeomorphic to disks and can- Geometry processing. Considerable literature exists on not be directly used for parameterization. Other methods building high-quality parameterizations over triangu- generate disk-like patches according to various crite- lated base domains (see [30] for a recent example and refer- ria (e.g., [20, 41, 34, 16]), but no single method ad- ences). In contrast, very little work has been done on deriv- dresses the combination of patch shape, distortion, number ing quadrilateral base complexes for arbitrary meshes. The of neighbors, alignment to features, and constraints. most recent work is that of Levy et al. [40]. Their periodic Surazhsky et al. [43] use centroidal Voronoi tessellations parameterizations are used to derive high-quality quadri- to generate dense isotropic triangulations. The centroid up- lateral meshes. However, these meshes may be dense (the dates are performed in 2D and require computing local pa- size of the quads is directly related to the size of the small- rameterizations of model regions. This is a remeshing ap- est tubular feature) and typically contain T-junctions so proach which does not produce a parameterization domain they are not directly usable as base meshes for subdi- for the input model. vision surfaces. Eck et al. [19] describe an automatic method for fitting B-splines to meshes of arbitrary topol- ogy. A quad base domain is generated indirectly from 1.2. Goals and Contribution a triangulated one by simplification followed by pair- The consideration of the needs of cultural heritage leads ing of neighboring triangles. In general, approaches based us to the following goals: on mesh simplification suffer from several shortcom- ings: it is not clear how to determine when to stop the sim- • Object representations should make minimal demands plification, geometric error typically drives the process with on computational resources during editing. little or no control over the resulting topology and con- • Editing operations should be as direct as possible on nectivity, the simplified mesh is a triangle mesh for which the target representation. a quadrilateral decomposition has to be found, and con- straints are difficult to enforce [29]. Generating quadrilat- The first goal requires that we have representations that eral meshes by pairing of triangles (see also 4 − 8 subdi- do not require loading the full model to make edits. The sec- vision schemes [44]) pose additional problems: complete ond goal requires that we have representations that make pairings may not always exist and finding ones that mini- sense to a viewer. In the case of the material or texture, mize distortion is expensive. Arbitrary meshes are typically we want textures that are partitioned along features that are parameterized by cutting and flattening. An extreme ex- meaningful to the user and are not distorted. This allows ample is the parameterization of an entire mesh over a the user to update the texture map directly in a standard im- square [22]. Maintaining consistency across seams is diffi- age editor (such as PhotoShop R or PaintShopPro R ). cult, especially if the model is to be modified (e.g., edited, To achieve these goals we propose a segmentation ap- compressed). In [23] conformal parameterizations of com- proach that allows the user to focus on minimal represen- plex surfaces are computed without cutting. However, the tations of the object necessary to achieve a particular task.
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