Image analysis – Applications – Motion or velocity measuring
Reexamination Certificate
1998-05-21
2004-09-07
Au, Amelia M. (Department: 2721)
Image analysis
Applications
Motion or velocity measuring
C382S284000
Reexamination Certificate
active
06788802
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to an optical flow estimation method, an image synthesis method, an image synthesizer, a recording medium on which an image synthesis program is recorded, a digital camera, and a printer.
2. Description of the Prior Art
A technique for calculating optical flow from two images, and registering the two images on the basis of the obtained optical flow has been known. Description is now made of a conventional method of calculating optical flow.
(1) Lucas-Kanade Method
A large number of methods of calculating apparent optical flow of a moving object in a moving image have been conventionally proposed. The Lucas-Kanade method which is a local gradient method out of the methods is one of the best methods. The reason for this is that the speed of processing is high, implementing is easy, and the result has confidence.
As for the details of the Lucas-Kanade method, see an article: B. Lucas and T. Kanade, “An Iterative Image Registration Technique with an Application to Stereo Vision”, In Seventh International Joint Conference on Artificial Intelligence (IJCAI-81), pp. 674-979, 1981.
The outline of the Lucas-Kanade method will be described.
When a gray scale pattern I(x, y, t) of image coordinates p=(x, y) at time t is moved to coordinates (x+&dgr;x, y+&dgr;y) with its gradation distribution kept constant after a very short time period (&dgr;t), the following optical flow constraint equation (1) holds:
∂
I
∂
x
δ
x
δ
t
+
∂
I
∂
y
δ
y
δ
t
+
∂
I
∂
t
δ
t
=
0
(
1
)
In order to calculate optical flow {v=(&dgr;x/&dgr;t, &dgr;y/&dgr;t)=(u, v)} in a two-dimensional image, the number of unknown parameters is two, so that another constraint equation is required. Lucas and Kanade have assumed that optical flow is constant in a local region of an identical object.
Suppose optical flow is constant within a local region &ohgr; on an image, for example. In this case, a square error E of a gray scale pattern to be minimized can be defined by the following equation (2) when the following substitutions are made:
I
0
(P)=I(x,y,t), I
1
(p+v)=I(x+u,y+v,t+&dgr;t)
E
=
∑
ω
[
I
1
(
p
+
v
)
-
I
0
(
p
)
]
2
(
2
)
When v is very small, the terms of second and higher degrees in Taylor's expansion can be ignored, so that the relationship expressed by the following equation (3) holds:
I
1
(
p+v
)=
I
1
(
p
)+
g
(
p
)
v
(3)
where g(p) is a linear differential of I
1
(p).
The error E is minimized when the derivative of E with respect to v is zero, so that the relationship expressed by the following equation (4) holds:
0
=
∂
∂
v
E
≈
∂
∂
v
∑
ω
[
I
1
(
p
)
+
g
(
p
)
v
-
I
0
(
p
)
]
2
=
∑
ω
2
g
(
p
)
[
I
1
(
p
)
+
g
(
p
)
v
-
I
0
(
p
)
]
(
4
)
Therefore, the optical flow v is found by the following equation (5):
v
≈
∑
ω
g
(
p
)
[
I
0
(
p
)
-
I
1
(
p
)
]
∑
ω
g
(
p
)
2
(
5
)
Furthermore, the optical flow can be found with high precision by Newton-Raphson iteration, as expressed by the following equation (6):
v
k
+
1
=
v
k
+
∑
g
k
[
I
0
-
I
1
k
]
∑
(
g
k
)
2
(
6
)
where I
1
k
=I
1
(P+v
k
), g
k
=g(p+v
k
), I
0
=I
0
(p).
(2) Hierarchical Estimation Method
The largest problem of the gradient methods, including the Lucas-Kanade method, is that they cannot be applied to large motion because a good initial value is required. Therefore, a method of producing images respectively having resolutions which are different at several levels like a pyramid hierarchical structure to solve the problem has been conventionally proposed.
Images having resolutions which are different at several levels are first previously produced from each of two consecutive images. Approximate optical flow is then calculated between the images having the lowest resolution. More precise optical flow is calculated between the images having a resolution which is higher by one level. The processing is successively repeated until optical flow is calculated between the images having the highest resolution.
FIG. 1
d
,
FIG. 1
c
,
FIG. 1
b
, and
FIG. 1
a
respectively illustrate optical flow found from an original image, optical flow found from an image having lower resolution than that of the original image shown in
FIG. 1
d
, optical flow found from an image having lower resolution than that of the image having low resolution shown in
FIG. 1
c
, and optical flow found from an image having lower resolution than that of the image having low resolution shown in
FIG. 1
b
. In
FIGS. 1
a
to
1
d
, S indicates one patch.
The optical flow is gradually found from the image shown in
FIG. 1
a
(an image in a hierarchy 1) the image shown in
FIG. 1
b
(an image in a hierarchy 2), the image shown in
FIG. 1
c
(an image in a hierarchy 3) and the image shown in
FIG. 1
d
(an image in a hierarchy 4) in this order. In
FIGS. 1
a
to
1
d
, an arrow indicates an optical flow vector found for each patch.
However, the problem is that in a real image, there are few regions containing sufficient texture, so that reliable optical flow is not obtained.
A technique for affixing a plurality of images to one another and synthesizing the images to obtain a seamless image having a wide field of view and having high resolution (image mosaicking) has been conventionally actively studied. Classical applications include synthesis of aerial photographs or satellite photographs. In recent years, a method of synthesizing a plurality of digital images to obtain a seamless panoramic image, constructing a virtual reality environment has been paid attention to.
The following two methods have been known as a technique for obtaining a panoramic image by synthesis.
The first method is a method of translating a camera to previously pick up a plurality of images. The plurality of images obtained are simultaneously displayed on a monitor by a personal computer. A user designates corresponding points between the two images, to synthesize the two images.
In the first method, the motion of the camera is restricted to translation. In the first method, the user must designate the corresponding points.
The second method is a method of fixing a camera to a tripod and restricting the motion of the camera to only rotation on a horizontal surface, to pick up a plurality of images. The plurality of images obtained are projected on a cylindrical surface, to synthesize the images (see U.S. Pat. No. 5,396,583).
In the second method, the motion of the camera must be restricted to only rotation on a horizontal surface. Further, the focal length of the camera must be measured.
SUMMARY OF THE INVENTION
An object of the present invention is to provide an optical flow estimation method in which reliable optical flow is obtained even when an image region is hardly textured.
Another object of the present invention is to provide an image synthesis method, an image synthesizer, and a recording medium on which an image synthesis program is recorded, in which a seamless panoramic image can be obtained from a plurality of images, a camera is allowed to freely moving in order to pick up the plurality of images, and the focal length need not be measured.
Still another object of the present invention is to provide a digital camera or a printer having an image synthesis function capable of obtaining a seamless panoramic image from a plurality of images, allowing a camera to freely moving in order to pick up the plurality of images, and eliminating the necessity of me
Chiba Naoki
Kanade Takeo
Kano Hiroshi
Arent Fox PLLC.
Au Amelia M.
Miller Martin
Sanyo Electric Co,. Ltd.
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