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We present a new approach for establishing correspondence between two homeomorphic 3D polyhedral models. The user can specify corresponding feature pairs on the polyhedra with a simple and intuitive interface. Based on these features, our algorithm decomposes the boundary of each polyhedron into the same number of morphing patches. A 2D mapping for each morphing patch is computed in order to merge the topologies of the polyhedra one patch at a time. We create a morph by defining morphing trajectories between the feature pairs and by interpolating them across the merged polyhedron. The user interface provides high-level control as well as local refinement to improve the morph. The implementation has been applied to several complex polyhedra composed of thousands of polygons. The system can also handle non-simple polyhedra that have holes.

Image metamorphosis as an animation tool has mostly been employed in the context of the entire image. This work explores the use of isolated and focused image based metamorphosis between two-dimensional objects, while capturing the features, colors, and textures of the objects. This pinpointed approach allows one to independently overlay several such dynamic shapes, without any bleeding of one shape into another. Hence, shape blending and metamorphosis of two-dimensional objects can be exploited as animated sequences of clip arts. 1. Introduction The continuous evolution from a source object into a target object is generally known as metamorphosis, or morphing. Metamorphosis can produce compelling transitions between objects, and thus have numerous applications in scientific visualization and in animations in the film and advertising industries. Many morphing algorithms have been proposed. Some are based on two dimensional polylines or piecewise linear curves 7; 11; 14; 26; 27 ...

Polyhedron realization is the transformation of a polyhedron into a convex polyhedron with an isomorphic vertex neighborhood graph. We present in this paper a novel algorithm for polyhedron realization, which is general, practical, efficient, and works for any zero–genus polyhedron. We show how the algorithm can be used for finding a correspondence for shape transformation. After the two given polyhedra are being realized, it is easy to merge their vertex–neighborhood graphs into a common graph. This graph is then induced back onto the original polyhedra. The common vertex–neighborhood graph allows the interpolation of the corresponding vertices.

In this paper we consider the problem of reconstructing triangular surfaces from given contours. An algorithm solving this problem has to decide which contours of two successive slices should be connected by the surface (branching problem), and, given that, which vertices of the assigned contours should be connected for the triangular mesh (correspondence problem).

Figure 1: Surface reconstruction with our new method. (left) 35 input contours from a CT scan of the pelvis area bones, resolution 420 × 300. (middle) Input contours overlaid on the surface reconstruction. (right) The reconstructed surface alone, resolution 420 × 300 × 347. We present a robust method for 3D reconstruction of closed surfaces from sparsely sampled parallel contours. A solution to this problem is especially important for medical segmentation, where manual contouring of 2D imaging scans is still extensively used. Our proposed method is based on a morphing process applied to neighboring contours that sweeps out a 3D surface. Our method is guaranteed to produce closed surfaces that exactly pass through the input contours, regardless of the topology of the reconstruction. Our general approach consecutively morphs between sets of input contours using an Eulerian formulation (i.e. fixed grid) augmented with Lagrangian particles (i.e. interface tracking). This is numerically accomplished by propagating the input contours as 2D level sets with carefully constructed continuous speed functions. Specifically this involves particle advection to estimate distances between the contours, monotonicity constrained spline interpolation to compute continuous speed functions without overshooting, and stateof-the-art numerical techniques for solving the level set equations. We demonstrate the robustness of our method on a variety of medical, topographic and synthetic data sets.

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A method for shape reconstruction from contours is presented using isotopic deformation. The reconstructed shape is free of self-intersection and it can incorporate given feature correspondences. The method automatically adds vertices, where necessary, to satisfy these requirements. A new method for handling bifurcation is also proposed, which can handle cases that are problematic for some other algorithms. The method proposed is suitable for terrain modeling, since reconstructed shapes generated by the method do not have overhangs. The running time of the algorithm is dependent on the complexity of the input scene and is shown to be worst-case optimal for the class of task defined. Experimental results are included to illustrate the feasibility of the approach. Keywords: shape reconstruction, terrain modeling, isosurface, isotopy. 1 Introduction Shape reconstruction from contours is the problem of constructing a 3D polyhedral shape that has a given pair of contours as its to...

A metamorphosis or a (3D) morphing is the process of continuously transforming one object into another. 2D and 3D morphing are popular in computer animation, industrial design or growth simulation. Since there is no intrinsic solution to the morphing problem, user interaction can be a key component of a morphing software. Many morphing techniques have been proposed in the recent years for 2D or 3D objects. We present a survey of the different approaches in 3D giving a special attention to the user interface. We show how the approaches are intimately related to the object representations. We conclude by sketching some morphing strategies for the future. Key Words: metamorphosis, shape transformation, interpolation, computer animation, geometric modeling. 1 Introduction Shape interpolation is the process of transforming one shape into another. A metamorphosis or a (3D) morphing of 3D graphical objects [GCDV96] includes the interpolation of their shapes as well as an interpolation of th...

This paper presents a technique for creating a smooth, closed surface from a set of 2D contours, which have been extracted from a 3D scan. The technique interprets the pixels that make up the contours as points in R 3 and employs Multi-level Partition of Unity (MPU) implicit models to create a surface that approximately fits to the 3D points. Since MPU implicit models additionally require surface normal information at each point, an algorithm that estimates normals from the contour data is also described. Contour data frequently contains noise from the scanning and delineation process. MPU implicit models provide a superior approach to the problem of contour-based surface reconstruction, especially in the presence of noise, because they are based on adaptive implicit functions that locally approximate the points within a controllable error bound. We demonstrate the effectiveness of our technique with a number of example datasets, providing images and error statistics generated from our results. Key words: Surface reconstruction, contours, implicit models, Multi-level Partition of Unity, normal estimation