Mesh Warping

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1. 2 Published Algorithms for Warping

Mesh warpingFeature-Based (Field) morphing

2. Mesh Warping[1]

The mesh-warping algorithm relates features with nonuniform mesh in the source and destination images,

i.e., the images are broken up into small regions that are mapped onto each other for the morph.

The algorithm accepts a source image, a destination image and two 2D arrays of coordinates. The first

array, S, specifies the coordinates of control points in the source image. The second array, D, specifies

their corresponding positions in the destination image. Both S and D must have the same dimensions in

order to establish a one-to-one correspondence.

Source Image

Destination Imge

Figure2 Original Images for morphing

file:///C:/Documents and Settings/897514501/Desktop/2d.htm

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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 respectivepoints 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:

Source code for Mesh-morphing: (Some changes are made to the image morphing source codes written by

George Wolberg in order to morphing the color images. )

1. Transform a RGB format file to three BW format files in term of different color channel [code]

2. Morphing Source Code (written by George Wolberg,1993.) [see detail athttp://www.engr.ccny.cuny.edu/CSCWWW/faculty/wolberg/abstracts.html#cga97 ]

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.

3. Merging three channel's BW format images into one RGB color image[code]

Pros and Cons:


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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 dont 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 animatorcould not find an associating feature are still used by the

warping algorithm.

3. Feature-Based Image Morphing [2]

The field morphing algorithm uses lines to relate features in the source image to features in the destination

image. It is based upon fields of influence surrounding two-dimensional control primitives. It applies thereverse mapping as its ways of warping.

[ 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

A pair of lines (one defined relative to the source image, the other defined relative to the destinationimage) defines a mapping from one image to the other.

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

Normally there are many features in images where transformation between multiple pairs of lines are

applied. It specifies more complex transformations. A weighting of the coordinate transformations for

each line is performed. The weight is determined by the distance from X to the line.


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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

The multiple line algorithm is as follows:

For each pixel X in the destinationDSUM=0

weightsum = 0

For each line PiQi

calculate u, v based on PiQi

calculate Xi based on u, v and PiQi

calculate displacement Di=Xi-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


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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

Advantages Disadvantages

The only positions that are used in the algorithm are

ones the animator explicitly created. Everything that is

specified is moved exactly as the animator wants them

moved, and everything else is blended smoothly based

on those positions.

Speed problems: All line segments need to

be referenced for every pixel. The runtime

is proportional to the number of lines

times the number of pixels in the image.Control: Between the lines, sometimes

unexpected interpolations are generated.


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