Publication Abstracts
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`A Two-Pass Mesh Warping Implementation of Morphing
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`Dr. Dobb's Journal, no. 202, July 1993.
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`The files in this directory contain the code necessary to implement a morph (metamorphosis) sequence. The
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`process is based on a mesh warping algorithm first introduced for a special effect sequence in the movie "Willow"
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`in 1988 [Smythe 90]. The algorithm, described in [Smythe 90] and [Wolberg 90], has since been used in several
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`films and commercials. The self-contained code given here is adapted fiom a program listing in [Wolberg 90].
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`The mesh warping algorithm is used to deform one image into another. The input includes a source iimge 11 and
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`two meshes, M1 and M2. Mesh M1 is used to select landnmk positions in 11, and M2 identifies their
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`corresponding positions in the output image. In this manner, arbitrary points in 11 can be "pulled" to new
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`positions. Although the use of a (parametric) mesh might seem to place unnecessary constraints on the positions
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`ofthese points, a large class ofusefi11 transformations is poss1ble. It is important, though, that the mesh not self-
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`interesect in order to avoid the iimge fiom folding upon itself The benefit ofusing a mesh derives from the
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`simplicity in interpolating the new positions of intermediate points (between the mesh points). A bilinear or
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`bicubic fiinction can be used. We use a Catmull-Rom cubic spline to implement bicubic interpolation here.
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`There are two executables that the user can compile: warp and morph. They are created by typing "make warp"
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`and "make morph", respectively. In "warp", 11 is simply deformed based on the correspondence points given in
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`meshes M1 and M2. In "morph", a second image 12 is used to designate the target image. Not only is 11
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`deformed, but it simultaneously undergoes a cross— dissolve with a warped version of12 to create the illusion of a
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`metamorphosis. The user must specify the number of frames to generate in this transformation. The basic idea is
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`that each fiame in the transforrmtion uses an interpolated mesh M3 as the set oftarget positions for the input
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`mesh points. M3 is computed by performing linear interpolation between respective points in M1 and M2. The
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`"warp" program actually plays an important role here since both 11 and 12 are each warped using M3 as the
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`target mesh. Thus, 11 is warped using meshes M1 and M3. In addition, 12 is warped using meshes M2 and M3.
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`Now that the landmarks ofthe source and target images are aligned, they are cross-dissolved to generate a
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`morph fiame.
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`FILES:
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`Makefile:
`meshwarp.h
`warp.c:
`morph.c:
`meshwarp.c:
`util.c:
`catmullrom.c:
`face.bw:
`cat.bw:
`face.XY:
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`dependency rules for creating "warp" and "morph"
`header file
`main function for "warp"
`main function for "morph"
`workhorse mesh warping code
`image I/O and memory allocation functions
`Catmull—Rom cubic spline interpolation.
`source image
`target image
`source mesh
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`cat.XY:
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`target mesh
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`RUNNING THE PROGRAMS:
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`WARP:
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`After you type "make warp", an executable file called "warp" will be created. You can invoke it by typing: warp
`face.bw laceXY cat.XY out.bw
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`Publication Abstracts
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`You may notice that the output has a distorted grid- like pattern on it. This is not an artifact ofthe algorithm, but
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`rather it is due to the grid pattern that appears in the input after scanning it fiom a magazine.
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`MORPH:
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`After you type "make morph", an executable file called "morph" will be created. You can invoke it by typing:
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`morph ficebw cat.bw ficeXY cat.XY 10 out
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`This will create a lO-frame animation stored in files out_000.bw, out_001.bw, out_002.bw,
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`out_009.bw
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`COMMENTS:
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`This code works on grayscale irmges only. Extending the program to handle 3 RGB color channels is
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`straightforward.
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`The code is missing a program to help the user create and edit meshes. A good mesh editor is a critical
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`component to any mesh warping program That code is not given here because it falls outside ofthe scope ofthis
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`presentation. Instead, sample meshes face.XY and cat.XY are provided.
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`The reader should be aware that such an interfice should allow the user to control the cross-dissolve schedule at
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`each mesh point, as well as its position. This permits the intensities in dilferent regions ofthe image to interpolate
`at difierent rates.
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`REFERENCES:
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`[Smythe 90]
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`Smythe, Douglas B., "A Two-Pass Mesh Warping Algorithm for Object Transformation and Irmge
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`Interpolation," ILM Technical Memo #1030, Computer Graphics Department, Lucasfilm Ltd., 1990.
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`[Wolberg 90]
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`Wolberg, George, Digmllmage Warping , IEEE Computer Society Press, Los Alamitos, CA, 1990.
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`WMN-cs.ccny.cuny.edu/~wo|berg/abstracts.html#dobb393
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