Mihailo Alic
Electronic Visualization Lab,
University of Illinois at Chicago
851 S Morgan St., Room 1120 SEO
Chicago, Ill, 60607-7053
1 Abstract
This paper presents a method for the metamorphosis of solid 3D objects based on their geometric features. It is an extension of a feature-based image metamorphosis technique by Beier and Neely[2]. Mentioned approach allows the operator to treat 3D geometry the same way as 2D image: identifying features of the object enables it's manipulation. Metamorphosis could be done with one object (warping) or with two, where the transformation of one into another is created. A Virtual Environment called The CAVE was chosen for animator's interface because it provides the most intuitive way of selecting features in corresponding objects and for viewing results.
Keywords: Computer Animation, Interpolation, Shape Transformation.
2 Introduction
2.1 Metamorphosis - the word
The word metamorphosis is of the Greek
origin, and is composed of two words: Meta, meaning between or after, and
Morphosis, the way form or structure changes. It has its roots in biology,
signifying development of organisms, and since it is a continuous and never
ending process of matter transformation, the use of the word Meta with
two meanings is justified. We will be using the term morphing as a shorten
form of the word metamorphosis.
2.2 Morphing as a visual effect
From its early infancy film industry
has embraced morphing as one of the most powerful special effects. Techniques
have evolved ranging from optical dissolves, use of lap photography like
in traditional animation of immobile objects, to the use of computer graphics.
Stop-motion animation is still a basic approach, in which the subject is
progressively transformed in each successive frame. Classical horror movies
are the best examples of effects that elaborate makeup change can make
combined with stop-motion animation filming.
2.3 2D Computer Graphics Techniques - image morphing
Morphing of one image into another is usually done by combining image warping with cross-dissolving between two series of animation steps. The animator specifies a warp that would distort the first image into the second and the inverse that would produce steps of transforming the second image into the first. Morphing animation starts with the first image that is gradually distorted and faded out, while the second image starts out totally distorted toward the first and is faded in. Two series of images are produced, having the same number of transformation steps as the final animation, and then an interpolation of their pixel values is used to cross-dissolve them. As a result, the middle image of the animation is the average of the first image distorted halfway toward the second one and the second image distorted halfway back toward the first one.
Other methods for image morphing might
involve particle systems with pixel tiles flying around, or mesh warping
technique described by Wolberg[15].
2.4 3D Computer Graphics Techniques - object morphing
Morphing 3D objects is a bit more difficult. In most cases one can get away with using scanned photographs of the scene to which 2D morphing is applied. This approach is appropriate for objects that are hard to model and render realistically using computer graphics. On the other hand, even objects that have a 3D computer representation might have a problem: it is fairly easy to make two images to contain the same number of pixels, but not as easy for 3D objects to have the same number of vertices and/or polygons. Also there is a problem of finding corresponding vertices in both objects that would during morphing interpolate into each other.
Apart from this direct point-interpolation
technique where vertex correspondence could be established easily, other
methods for object morphing are using solid deformations [1] [12] and particle
systems [10].
3 Feature - Based Morphing
3.1 Algorithm Fundamentals and Extension to 3D
The key to this algorithm is animator's recognition of features in the image content or on the object that we want to transform, and specifying expected change. Most of the time the image is just a 2D projection of the 3D object, and features are important edges that describe object's shape. Morphing between two objects is enabled by identifying corresponding features in both, and doing their interpolation. The animator is specifying a feature by laying down a control line along or near the edge that needs to be moved, and another line that shows a desired new position. The strongest influence of a control line is on image pixels that are close, and falls off with distance.
Extending the algorithm to 3D could be done in several ways. Usually, going up one dimension would mean using lines instead of points, planes instead of lines. In this case we would have planes as control primitives that would be placed near edges of the 3D object. That would certainly make distance calculation much more complicated, and expensive for very detailed objects.
The other approach is much simpler, and treats an object as a collection of vertices that could be influenced by control lines. The result is very much like a free - form deformation, and control lines could be viewed as having a field of influence, which is why this technique might be also called Field Morphing.
8 References
[1] Barr, A. H., Global and Local Deformations of Solid Primitives. In "Proc. SIGGRAPH'84" (Minneapolis, July 23-27, 1984). Published as "Computer Graphics", 18(3) (July 1984), pp. 21-30.
[2] Beier, T., Neely, S., Feature-Based Image Metamorphosis. In "Proc. SIGGRAPH'92 "(Chicago, July 26-31, 1992). Published as "Computer Graphics", 26(2) (July 1992), pp. 35-42.
[8] Oka, M., Tsutsui, K., Akio, O., Yoshitaka, K. Takashi, T., Real-Time Manipulation of Texture-Mapped Surfaces. In "Proc. SIGGRAPH'87" (Anaheim, July 27-31, 1987). Published as "Computer Graphics", 21(4) (July 1987), pp. 181-188.
[10] Reeves, W. T., Particle Systems: A Technique for Modeling a Class of Fuzzy Objects. "ACM Transactions on Graphics", 2(2) (April 1983). (Reprinted in "Proc. SIGGRAPH'83 (Detroit, July 25-29, 1983). Published as "Computer Graphics", 17(3) (July 1983), pp. 359-376.)
[11] Rosenfeld, M., Special Effects Production with Computer Graphics and Video Techniques. In "SIGGRAPH '87 Course Notes #8 - Special Effects with Computer Graphics" (Anaheim, July 27-31, 1987)
[12] Sederberg, T. W. and Parry, S. R., Free-Form Deformation of Solid Geometric Models. In "Proc. SIGGRAPH '86 (Dallas, August 18-22, 1986). Published as "Computer Graphics, 20(4) (August 1986). pp. 151-160.
[14] Smith, A. R., Planar 2-Pass Texture Mapping and Warping. In Proc. SIGGRAPH'87" (Anaheim, July 27-31, 1987). Published as "Computer Graphics", 21(4) (July 1987), p. 263-272.
[15] Wolberg, G., "Digital Image Warping" IEEE Computer Society Press, 1990.