THREE-DIMENSIONAL SHAPE RECOVERY BASED ON SINGLE HISTORICAL IMAGE
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#1
16-11-2010, 09:30 PM


INTRODUCTION
Image Reconstruction
As name implies it is the process of reconstructing the three dimensional
shape of a single frame image.
principle
The principle of 3D-reconstruction is that, the object's three dimensions
are acquired by the conversion from the shade of gray to the depth of the
information of the image.

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The basic design concept
The object surface shadeof gray can be expressed as
E(x,y) = I(x,y)cos
Where
I(x,y) = Light intensity of the optical source.
 = Object surface re
ectivity.
 = Included angle between optical source and object surface vertical
vector
The value of cos on the basis of inner product space is
cos  = p ppi+qqi+1
p2+q2+1
p
p2
i +q2
i +1

The direction of the surface vertical vector of the brightest point of the
image is calculated as
Ei = I  cos i
Emax = I coss
Where
s = Source tilt angle
i = Source tilt angle at point i
Suppose any part of the image is sphere
The coordinate of any point i on the surface is (xi ; yi ; zi )
Where
xi = x0 + r sin i cos(i
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seminarsense
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Posts: 53
Joined: Nov 2010
#2
16-11-2010, 09:43 PM

Three-Dimensional Shape Recovery Based On
Single Historical Image
Priyaraj P.R
M1 AEI
November 25, 2009
COLLEGE OF ENGINEERING, TRIVANDRUM



.pdf   Three-Dimensional Shape Recovery Based On.pdf (Size: 171.21 KB / Downloads: 48)

Abstract
To recover 3D shape of precious historical images, conventional methods
are not used. This is because of we are not able to establish the geometrical
relationship of coordinates. In this seminar and presentation we discus about a new method of 3D
shape recovery based on single frame historical images. According to the change
of the shade of gray of each pixel, the tilt angle and slant angle of the surface
vertical vector of each object's pixel in the image is analyzed, then the depth of
each pixel is calculated in response to the tilt angle and slant angle. Then the
3D digitized data of the image or object can be obtained by simulating human
being's vision system and the process of thinking of brain makes the process of
man's 3D comprehension of single image. This 3D digitized data can be used
for the 3D recovery of historical images.

Chapter 1
Principle of 3D shape recovery based on
single frame image

It may be regarded as that the change of the shade of gray of the image
is caused by the change of the object shape [1] [2], because the light intensity
of source, the distance between object and imaging, and surface re
ectivity
is usually xed in the image establishment. In the imaging process, though
the incident light is the same, the information received by image processing
equipment generate the di erence of the shade of gray, for the re
ected light
from the object parts with various shape is di erent. The basic design concept
of this paper is to nd the clue of the object surface shape from the shade of
gray. The object surface shade of gray can be expressed as:
E(x; y) = I(x; y) cos  (1.1)
Where I(x,y) is the light intensity of optical source,  is the object
surface re
ectivity and  is the included angle between optical source and the
object surface vertical vector. The included angle between optical source and
the object surface vertical vector can be shown as formula (1.2) on the basis of
the nature of inner product space
cos  =
ppi + qqi + 1 p
p2 + q2 + 1
p
p2
i + q2
i + 1
(1.2)
Put formula (1.2) into (1.1), then the shade of gray can be calculated as formula
(1.3)
E(x; y) = I(x; y)
ppi + qqi + 1 p
p2 + q2 + 1
p
p2
i + q2
i + 1
(1.3)
According to this, we got important information: the direction of the sur-
face vertical vector of the brightest point of the image is the same as the source
direction. As the source vector direction xed, the direction of the surface ver-
tical vector of the brightest point of the image is con rmed soon afterwards.
From formula (1.2), it is calculated as:
Ei = I cos i (1.4)
1
Emax = I cos s (1.5)
Where Ei is the brightness of the random point i of the image. Express-
ing the object surface shape needs to convert the shade of gray to the quantity
relative to the object geometrical information. At the present time, the 4 ways
are often employed in the expression of the forms of a surface. When the source
direction is used as the z axis to establish the axis system, the source tilt angle
s is 0, put s into formula (1.4), then the formula form is changed as:
Ei
Emax
= cos i (1.6)
Suppose any part of the object is a sphere, and the radius of the sphere
is r, and the center of the sphere is (x0; y0; z0). If the coordinate of any point
i on the surface is (xi; yi; zi), and the tilt and slant of the point i is i and i,
then the relationship can be seen as formula (1.7, 1.8, 1.9):
xi = x0 + r sin i cos i
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