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Ординатура / Офтальмология / Английские материалы / Binocular Vision Development, Depth Perception and Disorders_McCoun, Reeves_2010.pdf
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28

Hossein Ebrahimnezhad and Hassan Ghassemian

 

 

f x

 

0

 

 

x 0

 

(Rwc

)1 (Rwc

)1 Tcw

(40)

P =

0

 

f y

 

 

y 0

 

 

0

 

0

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[

x

im

, y

,1

T

P X w

,Y w , Z w ,1 T

(41)

 

 

im

]

 

 

 

 

 

 

Where, Rcw and Tcw are the rotation and translation of the camera coordinate system

to the world coordinate system, respectively. fx and fy are the focal length in x and y direction and x0, y0 are the coordinates of principal point in the camera plane. From Eq.29, we can get:

W(n ) = M

n 1

W(n 1) = M

n 1

 

M

M W(1)

(42)

 

 

 

2

1

 

By multiplying the projection matrix to the motion matrix, a new projection matrix is deduced for any sequence. This matrix defines a calibrated virtual camera for that sequence as:

P(n ) = P (Mn 1 M2 M1 )

(43)

The matrix P(n) , which produces a new silhouette of the object, projects any point in the world coordinate to the image plane of the virtual camera n as:

(n) (n) T

(n)

 

w w w

 

T

(44)

xim , yim ,1 P

 

 

 

 

X

,Y , Z ,1

 

 

In fact, by generating the virtual cameras, the moving object and fixed camera system is substituted by the fixed object and moving camera that moves in the opposite direction.

5.2. Visual Hull Reconstruction from Silhouettes of Multiple Views

In the resent years, shape from silhouette has been used widely to reconstruct three dimensional shape of an object. Each silhouette makes one cone in the space, with the camera center. Using more cameras from different views of object, more cones are constructed. The visual hull is defined as a shared volume between these cones. There are two conventional approach to extract the visual hull: voxel