Hama, Hiromitsu

Sein, Myint Myint

Osaka City University Repository

Mem. Fac. Eng., Osaka City Univ., Vol. 38, pp.159-163 (1997)
Estimating the Motion Parameters of a Moving Camera
from Perspective Image Sequences
Myint Myint SEIN* and Hiromitsu HAMA#
(Received September 30, 1997)
Synopsis
This paper describes the results of some experiments on estimating the motion
parameters of a moving camera from two or more consecutive image frames. Our method is
based on the image sequences of a scene taken from different positions and orientations
using a digital still camera in static environment. We extract the motion information about
the scene and camera from two image sequences of a scene by perspective transformation.
Experimental results with real images are presented.
Keywords: moving camera, perspective transformation, motion parameters.
1. Introduction
The problem of estimating the motion parameters of a moving camera from a
sequence of images is important for the application of image processing and computer
vision in mobile robots and so on. Most methods for the detection of motion in image
sequences involve the subtraction of successive frames [1], [3]. We estimate the motion
parameters from two image sequences by perspective transformation. First, we find
the corresponding points in two image frames of a given scene taken from different
positions and orientations by manually moving a camera. Particularly, we detect the
rotational motion parameters and translation parameters of the camera.
In Section 2, we review the mapping of a three-dimensional scene into a two
dimensional picture from the process of optical imaging. In 2.2, we define our camera
coordinate system and derive the linear equations for camera motion. Then, using this
set of linear equations, we computed the camera motion parameters and experimental
results with real images are presented in Section 3. Our experiment is based on two
images taken from a digital camera. The image, in this experiment, contains
1528 x 1146 pixels.
* Doctor-Course Student, Dept. of Information and Communication Engineering.
** Professor, Dept. of Information and Communication Engineering.
159
160
2. Basic Model and Equations
2.1 Imaging Transformation
Let P(X, Y, Z) denote the Cartesian coordinates of a scene point with respect to the
camera, as shown in Fig. 1, and let p(x,y) denote the corresponding coordinates in the
image plane. The image plane is located at the focal length Z = Ie. It can be
normalized to 1 without loss of generality. The perspective projection of a 3D-point
P(X,Y,Z) to a point p(x,y) on the image plane is express by:
x
X=-
Z
y
y=-
Z
z
(1)
2.2 Camera Motion
Fig. 1 Coordinate system of camera and image plane.
In this section, we present a notation for describing the motion of a camera through
an environment containing reference object (see Fig. 2). Due to the camera motion the
3D scene point (X, Y, Z) appears to be motion relative to the camera with rotation n
and translation T and therefore observed at new world coordinates (X',Y',Z')
express by:
X' X
Y' =Rn Y +T ............... (2)
Z' Z
Object in 3-D scene
161
Frame 1
Frame-2
Rotation an ranslation
Fig. 2 Camera motion system.
Where T = (Tx ' Ty,Tz) and 0 = (0x' Oy, Qz) represent the relative translation and
rotation of the camera in the scene. The rotation matrix Rn can be approximated,
assuming a small field of view and small values of the rotation parameters.[2]
1 -Oz Oy
Oz 1 -Ox
Oy Ox 1
...........(3)
If (x,y) and (x',y') are the image coordinates corresponding to the points (X,Y,Z)
and (X',Y',Z') , respectively, then
, X' x-Ozy+Oy+Tx/Z
x =- =------..;~----..;;.-........;;..;;--
Z' -Oyx+Oxy+l+Tz /Z
................(4)
Y',
y = Z'
Qzx+y-Ox+Ty/Z
- Qyx + Q x y + 1+ Tz / Z
................(5)
All points (X,Y,Z) of a planer surface in the 3D scene satisfy a plane equation
Z = AX + BY + C , which can be expressed in terms of image coordinates by using
equation (1) as:
1
-=a.x+ P.Y+r =u
Z
................(6)
A
where a =--
C
1
,r =-. Substituting (6) in (4) and (5), we get:
C
162
(x'y)Qx - (1 + xx')Qy + (y)Oz -uTx -(x'u)Tz =
(1+ W')Qx - (xy')Qy -(x)Qz -uTy + (y'u)Tz =
,
x-X)
,y-y }. ..... (7)
We can get the coefficients of T and n from two image sequences.
3. Computing Camera Motion Parameters and Experimental Results
First, we take the two image frames using a moving camera from different positions
and orientations. We extract any three-feature points, which are projected from a
planer surface in the three dimensional scene, in the first frame and their
corresponding points in the second frame, as shown in Table 1. So any three pairs of
image coordinates can be obtained from two pictures and substitute in (7), which is the
set of linear equations in six unknowns. Each pair of image coordinates gives us two
equations in these parameters, these three pairs of image coordinates yield a total of
six equations in the six independent parameters. Solving these equations system we
can obtain the translation parameters T =(Tx ' Ty,Tz) and rotation parameters
Q = (Qx,Qy,nz )·
The camera motion parameters between two frames in Fig. 3 are,
T = (Tx ,Ty,Tz) = (24.2cm,3cm,O.35cm) ' Q = (Qx,Qy,nz) = (-5° ,150 ,5°).
Ones computed by equation (7) are (Tx ,Ty , Tz ) =(25 em ,2.9em ,0.5em)
(Qx,Qy,Qz ) =(-2°,17°,3°). We can confirm the effectiveness of our method
through this result.
Table-} Three pairs of image coordinates in two frames
x Y X' y'
933.745 758.951 851.487 767.99
635.585 768.836 541.804 769.02
631.983 571.319 539.480 573.25
4. Conclusion
In this paper we detected the camera motion from two image sequences in static
scenes and we demonstrate for the real images. In the next step, we should take into
consideration of the reconstruction of a 3D scene from two dimension images based on
this approach.
(a)
(b)
Fig. 3 Two image frames, (a) frame-! and (b) frame-2 are taken from different positions and orientations.
References
[1] G.Adiv, "Determining Three Dimensional Motion and Structure from Optimal Flow
Generated by Several Moving Objects," IEEE Trans. Pattern Analysis and Machine
Intelligence, vol. 7, no. 4, pp. 384-401, July 1985.
[2] Y.Yasumoto, "Robust Estimation of Three Dimensional Motion Parameters from a
Sequences of Image Frames Using Regularization," IEEE Trans. Pattern Analysis and
Machine Intelligence, vol. PAMI-8, no. 4, pp. 464-471, July 1986.
[3] M.lrani, B.Rousso and S.Peleg, "Recovery of Ego-Motion Using Region Alignment,"
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 3, pp. 268-272, March 1997.
163


Estimating the Motion Parameters of a Moving Camera from Perspective Image Sequences

http://dlisv03.media.osaka-cu.ac.jp/infolib/user_contents/kiyo/DB00010286.pdf

Estimating the Motion Parameters of a Moving Camera from Perspective Image Sequences

Abstract

Similar works

Full text

Available Versions

Osaka City University Repository