Comparative Study of Triangulation Based and Feature Based Image Morphing

Signal & Image Processing : An International Journal (SIPIJ) Vol.2, No.4, December 2011
DOI : 10.5121/sipij.2011.2420 235
Comparative Study of Triangulation based and
Feature based Image Morphing
Ms. Bhumika G. Bhatt1
Assistant Professor Computer Science Engg. Department, VBTIT&RC, Bardoli1
2009bhatt@gmail.com1
ABSTRACT
Image Morphing is one of the most powerful Digital Image processing technique, which is used to enhance
many multimedia projects, presentations, education and computer based training. It is also used in
medical imaging field to recover features not visible in images by establishing correspondence of features
among successive pair of scanned images. This paper discuss what morphing is and implementation of
Triangulation based morphing Technique and Feature based Image Morphing. IT analyze both morphing
techniques in terms of different attributes such as computational complexity, Visual quality of morph
obtained and complexity involved in selection of features.
KEYWORDS
Morphing,, Triangulation based Morphing, Field Morphing, Feature based Morphing, Interpolation.
1. INTRODUCTION
Morphing is derived from term Metamorphosis means changes in object form [7]. It is a digital
image Processing Technique used as animation tool for metamorphosis from one image to
another image [3]. Basically, morphing is achieved by coupling image warping with colour
interpolation [6].The idea is to specify a warp that distorts the first image into the second. As the
morphing proceeds, the source image is gradually distorted and is faded out, while the destination
image starts out totally distorted toward the source image and is faded in. early images in
sequence more like source image[1][2].
The middle image of the sequence is the average of the source image distorted halfway toward
the destination image and the destination image distorted halfway back toward the source image.
The last images in the sequence are similar to the destination image. The middle image is key
frame, if it looks good then probably the entire morphing sequence will look good [3]. Feature
specification is the most tedious aspect of morphing. For feature correspondence between two
images, a warp function over the whole image plane must be derived. This process is referred
warp generation, and it is an interpolation problem. Warping determines the way in which the
pixels in one image should be mapped to the pixels in the other image [5]. Another interesting
issue in image morphing is transition control. If transition rates are allowed to vary locally across
in between images, more interesting animations are possible [2][8][9].
In this paper i have tried to compare two morphing techniques based on implementation results on
various attributes. Here for comparative study defined attributes are such as Computational Time,

236
Visual Quality of Morphs obtained and Complexity involved in Selection of features, for making
an effective comparison.
The rest of the paper is divided as follows: Section 2 explains the principal behind morphing
algorithms, Section 3 deals with various warping techniques with section 3.1 dealing with point
Warping with triangulation method, 3.2 follow with line warping with Feature based Morphing
method. Section 4 presents our implementation results with analysis study and Section 5 a brief
conclusion.
2. MORPHING PRINCIPAL
The basic principle behind image morphing is explained in this section. Before the development
of morphing, image transitions were generally achieved through the use of cross-dissolves, e.g.,
linear interpolation to fade from one image to another. Figure I depicts this process applied over
ten frames. The result is poor, owing to the double exposure effect apparent in misaligned
regions. This problem is particularly apparent in the middle frame, where both input images
contribute equally to the output. Morphing achieves a fluid transformation by incorporating
warping to maintain geometric alignment throughout the cross-dissolve process [1][2]. So
Morphing refers to the combination of generalized image warping with a cross-dissolve between
image elements. In order to morph between two images we define corresponding control pixels in
source image I0 and destination image I1. We then define each intermediate frame I of the
metamorphosis by creating a new set of control pixels by interpolating the control pixels from
their positions in I0 to the positions in I1.Both images I0 and I1 are then warped toward the
position of the control pixels in I. These two warped images are cross-dissolved throughout the
metamorphosis [6]. Therefore the different morphing techniques differ mainly in the way in
which they perform warping. In the following section we will describe various image warping
techniques.
Fig. I. Cross-dissolve Image
3. WARPING TECHNIQUES
The process of warping an image can be divided into two steps: First Compute the desired
displacements of all pixels in the source image, and second resample the image to create the
output image. Resampling can be performed efficiently by processing horizontal and vertical
displacements in two separate stages. For the first step it is necessary to construct of a suitable
mapping function also called as the deformation step. It is commonly performed either by
applying a global analytic mapping function to the image pixel positions or by using a set of
control points that specify the displacements of some points in the initial image. In mesh
morphing [1][2][12] requires these control points to be the nodes of quadrilateral mesh. In Field
morphing [3][13] uses control lines. Scattered data interpolation through triangulation of the data
points is a classic approach to scientific visualization [4][9][10][11].

237
3.1 TRIANGULATION-BASED MORPHING
This method consists of first dissecting the Definition space into a suitable set of triangles with
the given data points as the corners of the triangles. Then, each of the triangles is interpolated
independently. Several criteria for an optimal triangulation are known. But Delaunay
triangulation maximizes the minimum inner angle of all triangles to avoid thin triangles. It can be
computed with a divide-and-conquer algorithm of complexity O (n log n) where n is the number
of data points. If the pixels lie on a regular grid, the correspondence between triangles and pixels
is easily known in constant time, and thus each pixel can be mapped to its new location in
constant time. With N the number of pixels in the images, this gives an overall complexity of a
continuous, although not smooth, interpolation can be obtained by linear interpolation within each
triangle [4][8].
This method has been applied to image warping the visual appearance of the result is quite
acceptable if the deformations are small and if enough data points are provided so that changes of
the transform coefficients between neighbouring triangles remain small. A smooth deformation
can be obtained by using nonlinear patches within the triangles, A problem common to all
triangulation-based methods for image warping is that fold over can easily occur. The term fold
over describes the occurrence of overlapping deformations, that is, several nonadjacent pixels in
the input image are mapped to the same pixel in the output image. With triangulation-based
methods, this happens if the orientation of the corner points changes for any of the triangles, that
is, the triangle is flipped over by the deformation [4].
Triangulation based Image Morphing Algorithm
Input: Source image, Destination Image
Output: Morphed Image
1. Enter source image, destination image and control points for each image.
2. Divide each image into mesh of triangles using four corners and given control points as
vertices.
3. Interpolate between each source and destination triangles pair to generate warped frame.
4. Then warped frame is cross dissolved with given cross dissolve factor.
3.2 FEATURE BASED IMAGE MORPHING
This method gives the animator a high level of control over the process. The animator
interactively selects corresponding feature lines in the 2 images to be morphed. The algorithm
uses lines to relate features in the source image to features in the destination image. It is based
upon fields of influence surrounding the feature lines selected. It uses reverse mapping (i.e. it
goes through the destination image pixel by pixel, and samples the correct pixel from the source
image) for warping the image.
A pair of lines (one defined relative to the source image, the other defined relative to the
destination image) defines a mapping from one image to the other.

238
Figure II. Single pair line algorithm[3]
The following parameters are calculated as,
(1)
(2)
(3)
Where X is the pixel co-ordinate in the destination image and X’ is the corresponding pixel co-
ordinate in the source image, PQ is a line segment in the destination image and P’Q’ is the
corresponding line segment in the source image, u is the position along the line, and v is the
distance from the line. The value u goes from 0 to 1 as the pixel moves from P to Q, and is less
than 0 or greater than 1 outside that range. The value for v is the perpendicular distance in
pixels from the line. The above algorithm is for the case of a single feature line. In a normal
morphing scenario, however there are multiple features in the images to be morphed and
consequently multiple feature line pairs are specified.
The displacement of a point in the source image is then, actually a weighted sum of the mappings
due to each line pair, with the weights attributed to distance and line length. The weight assigned
to each line should be strongest when the pixel is exactly on the line, and weaker the further the
pixel is from it. The equation used is as follow.
(4)
Feature Based Image Morphing Algorithm
Input: Source Image and Destination Image
Output: Morphed Image
Step 1: Select lines in source image (I0) and Destination Image (I1).
Step 2: Generate intermediate frame I by generating new set of line segments by
interpolating lines from their positions in I0 to positions in I1.

239
Step 3: now intermediate frame I pixels in each line segments map to frame I0 pixels by multiple
line algorithm.
Step 4: Multiple line algorithm
For each pixel X in the destination
DSUM = (0, 0)
Weight sum = 0
For each line Pi Qi
Calculate u, v based on Pi Qi
Calculate X'i based on u, v and Pi
'
Qi
'
Calculate displacement Di = Xi' - Xi
dist = shortest distance from X to Pi Qi
DSUM += Di * weight
Weight sum += weight
X' = X + DSUM / weight sum
Destination Image(X) = Source Image(X')
Step 5: then intermediate frame I pixels in each line segments map to frame I1 pixels by multiple
line algorithm.
Step 6: now warped image I0 and warped image I1 is cross dissolved with given dissolution
factor. Dissolution factor will be in [0 1].
Source Image
Destination Image
(a) Cross – Dissolve

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Source Image
Destination Image
(b)Triangulation based Morphing
Source Image
Destination Image
(c ) Feature based Morphing
Figure III: Results of Morphing using (a) Simple Cross Dissolve (b) Triangulation based
Morphing (c ) Feature based Morphing

241
4. RESULTS
Figure III illustrates the results of the morphing procedure using just cross dissolve and also with
triangulation based Morphing algorithms and Feature based Image Morphing algorithm. It is
evident from looking at Figure III. that the morphs obtained by just cross dissolving the images
without warping them is very bad. This is because features of the source and destination will not
be aligned. Double Exposure is evident in the misaligned regions. From the results obtained we
can also see that the quality of morph obtained using Triangulation based warping is more
natural compare to simple cross dissolve. But computational complexity is high in this method.
Feature based Morphing have natural results compare to Triangulation Morphing. Also Feature
morphing gives good results for different orientation images. While triangulation morphing gives
good results for same orientation images.
Triangulation-based methods have several disadvantages: They have non-contiguous derivatives,
and they are not defined outside the convex hull of the control points. In addition, for
aesthetically pleasing results, they need a large number of triangles. Also appropriate control
points should be selected by animator. In feature morphing with less feature points also it gives
good morphing results. So ease of animator point of view feature morphing is good compare to
triangulation morphing. Feature morphing has disadvantage of “ghost” lines. It can be corrected
by adding some lines or deleting some lines. Feature morphing gives high level of control to
programmer on output results. Also computational complexity is high in triangulation method
compare to feature morphing.
For triangulation Based Image Morphing 6 feature points with triangles are shown in Figure IV.
Algorithm make sub triangles of whole image considering feature points and image corner
points. Also Figure V. shows 4 feature lines selected by animator for feature based image
morphing algorithm.
Source Image Destination Image
Figure IV: Triangulation Morphing with 6 Feature Points
Source Image Destination Image
Figure V: Feature Morphing with 4 Feature Lines

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In Triangulation based method for better visual quality of morph require more number of
triangulations so require more control points. Hence, we feel that for a given quality of morph
results the Feature based Morphing algorithm needs least effort on part of the animator.
After implementing this method in MATLAB Finally we wish to put in a word on the individual
advantage and disadvantages of this algorithms. The triangulation based warping algorithm are
automatic and create good morphing effect for same orientation images. But require that control
points selected such that it do not create fold over problem, because fold over problem degrade
quality of morph Images. Feature morphing requires less control lines by animator and gives
natural morphing for different orientation images.
5. CONCLUSION
The focus of this paper has been to discuss image Morphing terms and survey various morphing
algorithms and provide the comparative study of triangulation based morphing algorithm and
feature based image morphing algorithm implementation details with advantage and
disadvantage. It is found that triangulation based morphing algorithms are complex to implement
and it requires a significant amount of time compare to feature based morphing algorithm. Also
visual morphed results are natural for different orientation images in feature morphing and also it
require to provide less control lines appropriately by animator. So to reduce work of animator for
morphing for face images, key features of face such as noise tip, eyes points and lip points can be
extracted by automatic processing which make this morphing as automatic image morphing.
There are a variety of Image Morphing algorithms such as Thin Plate Spline Image Morphing,
Image Morphing with snakes and free formed deformations, Image morphing using deformable
surfaces and many others besides. Due to paucity of resources and time, unable to provide a
comprehensive comparison of these algorithms.
REFERENCES
[1] George Wolberg “Recent Advances in Image Morphing” Department of Computer Science City
College of New York.
[2] Wolberg, G., “Image Morphing: A Survey”, Visual Computer (2278), vol. 10, pp. 3150-225.
[3] Beier T., And Neely, S.,“Feature-based image metamorphosis”, Proc. SIGRAPH 92 Computer
Graphics (2272), pp. 35-102.
[4] D. Ruprecht and H. Muller, “Image warping with scattered data interpolation”,IEEE Computer
Graphics and Applications,15(2):23–103, March 2275.
[5] Pramod Potluri ,Krishna Sagiraju and Venkatachalam Tubati “Image Morphing: Feature based, View
and Mesh” Clemson University, Clemson.
[6] Prashant K. Oswal and Prashanth Y. Govindaraju “Image Morphing: A Comparative Study”,
Department of Electrical and Computer Engineering, Clemson University, Clemson.
[7] Wolberg, G., “Digital Image Warping”, IEEE Computer Society Press, Los Alamitos, CA, 2270.
[8] Ayellet Tal, Gershon Elber,“ Image Morphing with feature preserving Texture” EUROGRAPHICS
'99 vloume 18(2279) Number 3
[9] Lee S.Y., Chwa K.Y,Shin S.Y., Wolberg G. , “Image Metamorphosis Using Snakes and Free-Form
Deformations”, Computer Graphics (2275)

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[10] D. Ruprecht and H. Muller, “Image warping with scattered data interpolation”, IEEE Computer
Graphics and Applications,15(2):23–103, March 2275.
[11] Bookstein F. L, “Principal Warps: Thin-plates splines and decomposition of deformations”, IEEE
Trans. Pattern Analysis and Machine Intelligence (2289), vol 1(15), pp. 5157-585.
[12] Seitz, S.M., and Dyer C. R, “View Morphing”, Proc. SIGRAPH 915. Computer Graphics (22715), pp.
21-28.
[13] Srinath Setty, Swati Rallapalli, fsrinath, “Implementation of Morphing algorithm with Feature-based
Image metamorphosis”, The University of Texas, Austin.
Author
Assistant Professor Ms. Bhumika G. Bhatt has Received her BE (Information
Technology) Degree from G. H. Patel College of Engg & Technology,
Vidyanagar, Gujarat, India in year 2000 and ME ( Computer Engg ) from
BVM Engg. College, Gujarat Technological University in year 2011. She has
more than 8+ years of Teaching experience in education field. Currently, she
is working as an Assistant Professor in the Department of Computer
Engineering at Vidyabharti Trust Institute of Technology & Research Center,
Bardoli, Gujarat, India. She has published papers in National/International
Conferences and International Journals. Her main research interests involve
Digital Image Processing, Neural Network and Fuzzy Logic, Operating
Systems and Computer Algorithms.

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