2D Image Morphing Algorithms

1. 2 Published Algorithms for Warping

• Mesh warping
• Feature-Based (Field) morphing

 

2. Mesh Warping[1]

Source Image

Destination Imge

 
                                                       Figure3 Images with Control Points

Then two imges are processed through 2-pass warping with 2 output intermediate images I1 and I2. The first pass is responsible for resampling each row independently. It maps all initial image points coordinates (u, v) to their (x, v) coordinates in the intermediate image , thereby positioning each input point into its proper output column.The second pass then resamples each column in intermediate image, mapping every (x, v) point to its final (x, y) position in I1/I2. The 2D arrays in which the control points are stored to impose a topology to the mesh.

More detail is that each frame in the transformation uses an interpolated mesh M as the set of target positions for the input mesh points. M is computed by performing linear interpolation between respective points in S and D. The "warp" program actually plays an important role here since both I1 and I2 are each warped using M as the target mesh. Thus, I1 is warped using meshes S and M. In addition, I2 is warped using meshes D and M. Now that the landmarks of the source and target images are aligned, they are cross-dissolved to generate a morph frame. Catmull-Rom cubic spline is used to implement bicubic interpolation in [3] because it offers local control, although any spline wourld suffice.

Result:
 

Makefile:       dependency rules for creating "warp" and "morph"
meshwarp.h      header file
warp.c:         main function for "warp"
morph.c:        main function for "morph"
meshwarp.c:     workhorse mesh warping code
util.c:         image I/O and memory allocation functions
catmullrom.c:   Catmull-Rom cubic spline interpolation.

Pros and Cons:
 

Pro

Con

Fast and intuitive Efficient algorithms exist for computing the mapping of each pixel from the control grid

Trying to position dozens of mesh points around is like trying to push a rope; something is always forced where you don’t want it to go. The animator must specify in advance how many control points to use to control the image, then take those given points and move them to the correct locations.  Points left unmodified or points for which the animator could not find an associating feature are still used by the warping algorithm.

 

3. Feature-Based Image Morphing [2]

[ Note: There are 2 ways to warp an image. The first, called forward mapping, scans through the source image pixel by pixel, and copies them to teh apprpriate place in the destination image. The second, reverse mapping, goes through the destination image pixel by pixel, and samples the correct pixel from the source image. The most important feature of inverse mapping is that every pixel in the destination image gets set to something appropriate. In the forward mapping case, some pixels in the destination might not get painted, and would have to be interpolated.]
 

Transformation between one pair of lines

where u is the position along the line, and v is the distance from the line

The algorithms transforms each pixel coordinate by a rotation, translation, and/or a scale, thereby transforming the whole image.
 

Transformation between multiple pairs of lines

 

where length is the length of a line, dist is the distance from the pixel to the line, and a, b, and p are constants that can be used to change the relative effect of the lines

For each pixel X in the destination
        DSUM=0
        weightsum = 0
        For each line PiQi
             calculate u, v based on PiQi
             calculate X’i based on u, v and P’iQ’i
             calculate displacement Di=X’i-Xi for this line
             dist= shortest distance from X to PiQi
             weight = (lengthP / (a + dist))b
             DSUM  += Di * weight
             weightsum += weigth
        X’ = X + DSUM / weightsum
        destinationImage(X) = sourceImage(X’)

Process of Morphing between Two images

• Define corresponding lines in source image I0 and destination image I1.
• Each intermediate frame I of the metamorphosis is defined by creating a new set of line segments by interpolating the lines from their positions in I0 to the positions in I1.
• Both images I0 and I1 are distorted toward the position of the lines in I. These two resulting images are cross-dissolved throughout the metamorphosis.

 

Example

Source Image

Destination Image

	Left figure is the first face distorted to the intermediate position without the grid or lines.
	Same as above figures with lines drawn over the faces.
	Left figure is the second face distorted to the intermediate position without the grid or lines.
	Same as above figures with lines drawn over the faces.
	Left figure shows the morphed image (right figure) with the interpolated lines drawn over it.

Advantage and disadvantage