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“3D Structure Estimation Using Evolutionary
Algorithms Based on Similarity Transform”
Authors
K. Punnam Chandar &
Dr. T. Satya Savithri
Eighth Asia International Conference on Mathematical
Modeling and Computer Simulation (AMS-2014).
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AMS-2014 Sep-25; Kuala Lumpur -
Malaysia

Outline:---
• Introduction: 3D Model Acquisition
• Koo and Lam Algorithm - SFM
• 3D to 2D Projection Model
• Objective function
• Optimization using GA
• Differential Evolution and other EA
• Results: Pose and Depth Estimation
• Conclusion
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Introduction
• 3D Models of face are gaining importance in the fields of face
recognition, face Tracking, 3D Virtual Worlds & Games, 3D
Simulation due to their superior performance over 2D
Models.
• Currently there are two main streams of creating the 3D face
models, one approach is to use specialized 3D Depth sensing
cameras and the other is reconstructing the 3D face model
from 2D images.
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3D Face
Source:
3D Face Home
Page

• The high cost of 3D depth sensing cameras limit their deployment
in Security Applications.
• The alternative is to develop algorithms to reconstruct the 3D face
model from 2D images such as video sequences and multi-view
photographs.
• The goal of the reconstruction algorithm is to derive the 3D shape
information of the face from N-2D images (N≥2), one frontal view
and others non-frontal view images.
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• During the past decade 3D reconstruction algorithms based
on 2D images have been developed to estimate the 3D
Structure.
• Representative algorithms can be categorized into four groups
 Shape-from-X (ref.1)
 3D Morphable Model (ref.2)
 Learning (ref.3)
 Structure from motion (ref.4)
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• Notable difference among the mentioned four techniques is that
different information is utilized to perform the task of 3D
reconstruction.
• Among various structure from motion techniques spatial
transformation approach is one important branch.
• The beauty of the spatial transformation model is that they are
sparse in nature and extract the depth information of only
important features.
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• Koo and lam (ref.5) proposed a 3D reconstruction
algorithm(SFM) based on Similarity Transform Measurements.
• The algorithm utilizes group of face images to reconstruct the
sparse 3D structure.
• 3D to 2D projection model is formulated using the 2D point sets.
• The solution vector minimizing the model is searched using the
Genetic Algorithm
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Five Sample Poses of person (myself) :
Different Pan Angles
Front (0,15,0) (0,30,0) (0,-15,0)
3a 3b 3c 3d 3e
(0,-30,0)
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Four Sample Poses of person 5 of Head Pose Database:
Different Tilt and Pan Angles
Front (-15,0,0) (-15,15,0) (15,0,0)
4a 4b 4c 4d
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3D to 2D Projection Model
• The projection of the 3D face model to the
corresponding 2D face via given rotation matrix and scale
is given by 3D to 2D transformation under orthographic
projection is performed using the transformation:
pi = si * Ri2x3 * C + Ti for i = 1,2,3,4,5…N.
where N is the number of non-frontal-view 2D face images, si, Ti and Ri
denote the scaling factor, the translation Matrix and the rotation matrix
between the frontal view image and the ith non-frontal-view face image, C:
2D coordinates with Candie Depths, respectively.
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11 12 13
21 22 23
1 2 3 4
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1 2 3 4
12
1 2 3 4
1 2 3 4
i i i
i i i
c c c c
X X X X
r r r tx x x x
Y Y Y Y
ty y y y r r r
Z Z Z Z
 
             
         
2D Co-ordinates
Non-Frontal View
Rotation
Matrix
2D Coordinates
Frontal View &
Initial Candide
Depths
2D Translation
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Objective Function to be optimized
2 3
2
min 2 3
,
min
i i x
i i i x i
s R
D p s R C T  
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Optimization using Genetic Algorithm
koo and Lam Algorithm
• The GA encounters a heavy computational burden.
• Moreover the GA is time consuming and the accuracy
depends on the control parameter set which requires
adjustment, which presents practical difficult problems for
feasible operation for a chromosome of moderate size and
the situation is difficult if the chromosome size increases.
• To overcome these practical difficulties in finding the solution
vector, Differential Evolution Optimization is employed.
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Differential Evolution
Our Approach
• The method of Differential Evolution functioning is similar to
genetic Algorithm approach.
• DE can be applied to real-valued problems with much more ease
than a GA.
• The ideal behind the method of differential evolution is that the
difference between two vectors yields a difference vector which can
be used with a scaling factor to traverse the search space.
• The Solution vector is known as Genome.
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DE GA PSO SA
Cr = 0.1
F = 0.6
Population Size =120
Iterations = 250
Strategy [1 − 5]
Crossover rate = 80%
Mutation rate =20%
Population Size = 1200
Iterations = 250
Rank Selection
Max. Run Time = 2.6 Sec
c 1 = 0.6
c2 = 1.0
Population Size
= 200
Iterations =
250
T start = 10
T end = 1E − 9
Exponential
Cooling
Schedule:
T k+1 =
0.8 · T k
Parameters Used in Optimization Algorithms
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Fig -
Index
Actual
Pose
DE – S1 GA PSO SA
4c (-15,15,0) (17,-2,-1) (14,8,11) (13,4,3 ) (15,0,-1)
4d (15,0,0) (14,-16,0) (-4,-11,-9) (12,-21,-1) (15,-16,-1)
Table.III
Best Estimated Poses of Person 5 Using DE & other Optimization Algorithms.
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4c: (-15,15,0) 4d: (15,0,0)

Fig -
Index
Actual
Pose
DE – S1 GA PSO SA
3b (0,15,0) (0,13,-1) (7,12,0) (2,19,-4) ( 0,15,-1)
3e (0,-30,0) (0,-31,0) (-3,-29,0) (-3,-29,-1) (0,-30,0)
Table. IV
Best Estimated Poses of Person 1 Using DE & other Optimization Algorithms.
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3b : (0,15,0) 3e: (0,-30,0)

OptAlg 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
DE_S1 6 1 3 0 15 0 21 15 16 6 0 3 0 15 2
GA 6 2 2 1 22 2 31 19 19 8 1 2 1 22 7
PSO 3 1 1 1 14 0 19 12 13 6 0 2 0 13 4
SA 6 0 2 0 15 0 21 14 15 6 0 2 0 15 2
Table : V
Estimated Depth Values of Person 1 (myself)
Note: Depth values obtained are floating point numbers they are rounded to nearest
Integer and mentioned in the paper and here
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OptAlg 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
DE_S1 4 0 2 1 15 1 20 14 14 7 1 3 1 14 3
GA 6 1 2 1 18 0 25 17 17 8 1 3 1 18 4
PSO 5 0 2 0 13 0 18 12 13 4 0 1 0 13 1
SA 6 0 2 0 15 0 21 14 15 6 0 2 0 15 2
Table : VI
Estimated Depth Values of Person 5
Note: Depth values obtained are floating point numbers they are rounded to nearest
Integer and mentioned in the paper and here
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Conclusion
• Differential Evolution Optimization is used to optimize the objective
function.
• Other soft computing techniques are implemented and compared
for this task.
• Experimental results signify that DE outperformed the other
techniques in estimation of DEPTHS of important face feature
points.
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References
1. Zhang, Ruo, et al. "Shape-from-shading: a survey." Pattern Analysis and Machine
Intelligence, IEEE Transactions on 21.8 (1999): 690-706.
2. Romdhani, Sami, and Thomas Vetter. "Efficient, robust and accurate fitting of a 3D
morphable model." Computer Vision, 2003. Proceedings. Ninth IEEE International
Conference on. IEEE, 2003.
3. Castelán, Mario, and Edwin R. Hancock. "A simple coupled statistical model for 3d
face shape recovery." Pattern Recognition, 2006. ICPR 2006. 18th International
Conference on. Vol. 1. IEEE, 2006.
4. Shapiro, Larry S., Andrew Zisserman, and Michael Brady. "3D motion recovery via
affine epipolar geometry." International Journal of Computer Vision 16.2 (1995):
147-182.
5. Koo, Hei-Sheung, and Kin-Man Lam. "Recovering the 3D shape and poses of face
images based on the similarity transform." Pattern Recognition Letters 29.6 (2008):
712-723.
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Queries ?
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3D Face Structure Estimation using Evolutionary Algorithms

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3D Face Structure Estimation using Evolutionary Algorithms