Data processing: measuring – calibrating – or testing – Measurement system – Statistical measurement
Reexamination Certificate
2003-02-07
2004-04-20
Barlow, John (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system
Statistical measurement
C702S014000, C703S010000
Reexamination Certificate
active
06725174
ABSTRACT:
PRIORITY CLAIM
The present application claims priority on European Patent Application 00306780.8, filed on Aug. 9, 2000.
BACKGROUND OF THE INVENTION
The present invention relates to a method of processing an image, for example a seismic image, applying a diffusion process. Such methods are known, see for example the thesis J. Weickert, ‘Anisotropic Diffusion in Image Processing’, Ph.D. Thesis, University of Kaiserslautem, Germany, January 1996, pages 41-44.
Known is a diffusion method that comprises the steps of
(a) obtaining an n-dimensional initial image data set, wherein each element u(m=0) of the data set is the initial image intensity of a point of the image, and wherein n=2 or n=3;
(b) calculating for each point the partial derivatives of u(m) in n directions to obtain n derivative data sets of the partial derivatives u
xi
;
(c) calculating for each point a symmetric n×n structural matrix S, wherein the elements s
pq
equal u
xp
.u
xq
;
(d) calculating for each point an n×n diffusion matrix D, wherein the elements d
ij
are a function of the elements s
pq
;
(e) calculating for each point u(m+1) from u(m) using the following equation u(m+1)=u(m)+div(Dgrad(u(m))); and
(f) repeating steps (b) through (e) M times to obtain the processed image.
Unless otherwise specified, the following holds throughout the specification and the claims:
i, j, p, q=
1, . . . ,
n ;
u
xi
=∂u/∂x
i
.
An element of the image data set is also referred to as a point of the image.
In the known method an initial image is processed to obtain successive images, wherein each image is obtained from the previous one by a diffusion process. The diffusion method can as well be described by the
diffusion
equation
∂
u
∂
t
=
div
(
D
·
∇
u
)
.
There are four types of diffusion methods. At first there is the isotropic diffusion in which the diffusivity D is a scalar and the anisotropic diffusion in which D is a matrix. Then for each of these two types, the diffusion can be linear, in which D is not a function of u or the diffusion can be non linear in which D is a function of u.
This method can as well be applied to processing a seismic image, in that case the image intensity is the amplitude of the seismic signal.
An advantage of the diffusion method is that noise is suppressed. A further advantage, which is particularly relevant to processing a seismic image is that after a few cycles the geological structure is highlighted more clearly. However, a problem with this method is preserving edges.
Edge preservation is of great interest in the interpretation of seismic images, which play an important role in the study of underground formations, and in particular in the study of underground formations that contain hydrocarbons. Moreover there is a great interest in edge preserving techniques, which allow highlighting of faults while removing noise from the seismic data.
SUMMARY OF THE INVENTION
For edge preservation in combination with isotropic diffusion processing is proposed a method based on the Perona-Malik model (see the thesis of Weickert, page 10) of which the diffusion equation is
∂
u
∂
t
=
div
(
g
(
&LeftBracketingBar;
∇
u
&RightBracketingBar;
2
)
∇
u
)
,
wherein the non-linear diffusivity is g(|∇u|
2
)=(1+|∇u|
2
/&lgr;
2
)
−1
, the scalar &lgr; being a pre-determined edge preservation parameter.
Applicant proposes a simple addition to the known method that has proved to be an effective way of preserving edges while capable of removing noise. Moreover Applicant proposes such a method that is applicable to anisotropic diffusion.
To this end the method of processing an image according to the present invention comprises the steps of
(a) obtaining an n-dimensional initial image data set, wherein each element u(m=0) of the data set is the initial image intensity of a point of the image, and wherein n=2 or n=3;
(b) calculating for each point the partial derivatives of u(m) in n directions to obtain n derivative data sets of the partial derivatives u
xi
;
(c) calculating for each point a symmetric n×n structural matrix S, wherein the elements s
pq
equal u
xp
.u
xq
;
(d) calculating for each point an n×n diffusion matrix D, wherein the elements d
ij
are a function of the elements s
pq
;
(e) calculating for each point u(m+1) from u(m) using the following equation u(m+1)=u(m)+c.div(&egr;.Dgrad(u(m))), wherein c is a predetermined constant, 0≦c≦1, and wherein &egr; is a scalar, 0≦&egr;≦1, wherein &egr; is close to zero when near an edge and close to 1 when far away from an edge; and
(f) repeating steps (b) through (e) M times to obtain the processed image.
In this way edge preservation is introduced in anisotropic, non-linear diffusion.
Suitably step (c) comprises calculating for each point a symmetric n×n structural precursor matrix S
0
, wherein the elements s
0
pq
equal u
xp
.u
xq
; creating (½)n(n+1) data sets, wherein the elements of the first data set are s
0
11
pertaining to each point, the elements of the second data set are s
0
12
and so on; and filtering each of these data sets by convolution with a suitable kernel to obtain the elements s
pq
of the n×n structural matrix S.
Alternatively step (c) comprises filtering for each point the partial derivatives u
xi
by convolution with a suitable kernel to obtain regularized partial derivatives u
r
xi
; calculating for each point a symmetric n×n structural precursor matrix S
0
, wherein the elements s
0
pq
equal u
r
xp
.u
r
xq
; creating (½)n(n+1) data sets, wherein the elements of the first data set are s
0
11
pertaining to each point, the elements of the second data set are s
0
12
and so on; and filtering each of these data sets by convolution with a suitable kernel to obtain the elements s
pq
of the n×n structural matrix S.
The above described alternatives for step (c), wherein a precursor matrix is calculated allows defining the edge preservation parameter as follows: &egr;=trace(S
0
S)/(trace(S
0
).trace(S)). In this way the edge preservation parameter is calculated for each point.
The present invention also relates to a method of processing an image in order to display the edge preservation parameter. This method comprises the steps of
(a) obtaining an n-dimensional initial image data set, wherein each element u(m0) of the data set is the initial image intensity of a point of the image, and wherein n=2 or n=3;
(b) calculating for each point the partial derivatives of u(m) in n directions to obtain n derivative data sets of the partial derivatives u
xi
;
(c) calculating for each point a symmetric n×n structural matrix S
0
, wherein the elements s
0
pq
equal u
xp
.u
xq
; creating (½)n(n+1) data sets, wherein the elements of the first data set are s
0
11
pertaining to each point, the elements of the second data set are s
0
12
and so on; and filtering each of these data sets by convolution with a suitable kernel to obtain the elements s
pq
of the n×n structural matrix S; and
(d) calculating for each point &egr;=trace(S
0
S)/(trace(S
0
).trace(S)) and attributing the calculated value of &egr; to each point to obtain an image in which faults are highlighted.
Alternatively, the method of processing an image comprises the steps of
(a) obtaining an n-dimensional initial image data set, wherein each element u(m=0) of the data set is the initial image intensity of a point of the image, and wherein n=2 or n=3;
(b) calculating for each point the partial derivatives of u(m) in n directions to obtain n derivative data sets of the partial derivatives u
xi
;
(c) filtering for each point the partial derivatives u
xi
by convolution with a suitable kernel to obtain regularized partial derivatives
Bouts Erik
Fehmers Gijsbert Christiaan
Kalitzin Stiliyan Nikolov
Barlow John
Shell Oil Company
Taylor Victor J.
LandOfFree
Edge-preserving enhancement of seismic images by nonlinear... does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Edge-preserving enhancement of seismic images by nonlinear..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Edge-preserving enhancement of seismic images by nonlinear... will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-3241480