Method for characterizing the development of pathologies involving changes in volumes of bodies, notably tumors
View Patent ↗A method for quantifying the development of pathologies involving changes in volume of a body represented via an imaging technique, including normalizing gray levels by a midway technique for two images I 1 and I 2 representing the same scene, resulting in two normalized images I′ 1 and I′ 2 ; calculating a map of signed differences between the two normalized images I′ 1 and I′ 2 ; and performing one or more statistical tests based on the assumption of a Gaussian distribution of the gray levels for healthy tissues in the normalized images I′ 1 and I′ 2 and/or in the calculated difference map. Advantageously, results of two or more of the tests can be combined for a more specific characterization of the development.
1. A computer-implemented method for characterizing a development of pathologies involving changes in volume of a body, the method comprising:
receiving, from a magnetic resonance imaging device, two images I 1 and I 2 representing the same anatomical part of the body at two successive times;
determining, using a computer, a midway cumulative histogram of gray levels common to the two images I 1 and I 2 , wherein said midway cumulative histogram is equal to an inverse of a geometric mean of inverses of cumulative histograms of gray levels for the two images I 1 and I 2 ;
normalizing, using the computer, gray levels by applying the midway cumulative histogram to the two images I 1 and I 2 resulting in two normalized images I′ 1 and I′ 2 , respectively;
calculating, using the computer, a map of signed differences between the two normalized images I′ 1 and I′ 2 ;
performing, using the computer, one or more statistical tests, including a first test based on an assumption of a Gaussian distribution of gray levels for healthy tissues of the anatomical part of the body in the normalized images I′ 1 and I′ 2 or in the calculated difference map; and
characterizing, using the computer, the development of pathologies based on said performed one or more statistical tests.
2. The computer-implemented method of claim 1 , wherein performing the first test comprises comparing, using the computer, a generalized likelihood ratio defined by the equation:
G
L
R
T
=
p
(
I
1
′
(
x
)
/
μ
1
,
σ
1
)
p
(
I
2
′
(
x
)
/
μ
2
,
σ
2
)
p
(
I
1
′
(
x
)
/
μ
1
-
2
,
σ
1
-
2
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p
(
I
2
′
(
x
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/
μ
1
-
2
,
σ
1
-
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,
and a confidence threshold T 1 of a given value,
wherein p(I′ i (x)/μ i σ i ) is a probability density function for a gray level I′ i (x) of a pixel of a normalized image I′ 1 , calculated with a Gaussian function of mean μ i and standard deviation σ i , to exhibit an observed gray level, the index 1-2 being applicable to combined values of the normalized images I′ 1 and I′ 2 , and
wherein statistics for a given pixel are determined over an area extending around the pixel over a given number of pixels.
3. The computer-implemented method of claim 2 , wherein comparing of the first test is established by the following equation:
ln
(
p
(
I
1
′
(
x
)
/
μ
1
,
σ
1
)
p
(
I
2
′
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x
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/
μ
2
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σ
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p
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σ
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>
ln
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T
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.
4. The computer-implemented method of claim 3 , wherein the confidence threshold T 1 is equal to 2.
5. The computer-implemented method of claim 1 , wherein performing the first test comprises comparing, using the computer, a probability density function p(I′ 2 (x)−I′ 1 (x)/μ 2 −μ 1 , √{square root over (σ 1 2 +σ 2 2 ))} and a confidence threshold T 2 of a given value.
6. The computer-implemented method of claim 5 , wherein comparing of the first test is established by the following equation:
p ( I′ 2 ( x )− I′ 1 ( x )|μ 2 −μ 1 ,√{square root over (σ 1 2 +σ 2 2 )})< T 2 .
7. The computer-implemented method of claim 6 , wherein the confidence threshold T 2 is equal to
ⅇ
-
α
2
πσ
n
2
,
α being a variable non-zero positive real number, and σ n representing a standard deviation of noise in the calculated difference map.
8. The computer-implemented method of claim 1 , wherein performing the first test comprises comparing, using the computer, a probability value F(|I′ 2 (x)−I′ 1 (x)|, 0, √{square root over (σ 1 2 −σ 2 2 ))} and a confidence threshold T 3 of a given value, the function F denoting integral
F
(
t
,
μ
,
σ
)
=
1
-
∫
-
t
t
ⅇ
-
(
s
-
μ
)
2
2
σ
2
2
π
σ
ⅆ
s
,
where t is an input variable equal to |I 2 ′(x)-I 1 ′(x)|.
9. The computer-implemented method of claim 8 , wherein comparing of the first test is established by the following equation:
F (|I′ 2 ( x )− I′ 1 ( x )|,0,√{square root over (σ 1 2 +σ 2 2 )})< T 3 ,
the confidence threshold T 3 being a non-zero positive real number less than 1.
10. The computer-implemented method of claim 1 , wherein the one or more statistical tests are performed for all pixels composing the normalized images I′ 1 and I′ 2 or the calculated difference map.
11. The computer-implemented method of claim 1 , wherein the one or more statistical tests are performed based on local means based on pluralities of pixels from the normalized images I′ 1 and I′ 2 or from the calculated difference map forming a plurality of areas covering the normalized images I′ 1 and I′ 2 or the calculated difference map.
12. The computer-implemented method of claim 1 ,
wherein the one or more statistical tests are selected from the group consisting of:
a statistical test performing a comparison between a generalized likelihood ratio defined by the equation:
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L
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T
=
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I
1
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μ
1
,
σ
1
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p
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p
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,
and a first confidence threshold T 1 of a given value, p(I′ i (x)/μ 1 , σ i ) being a probability density function for a gray level I′ i (x) of a pixel of a normalized image I′ i , calculated with a Gaussian function of mean μ i and standard deviation σ i , to exhibit an observed gray level, the index 1-2 being applicable to combined values of the normalized images I′ 1 and I′ 2 ;
a statistical test performing a comparison between a probability density function p(I′ 2 (x)−I′ 1 (x)/μ 2 −μ 1 ,√{square root over (σ 1 2 +σ 2 2 ))} and a second confidence threshold T 2 of a given value; and
a statistical test performing a comparison between a probability value F(|I′ 2 (x)−I′ 1 (x)|,0, √{square root over (σ 1 2 +σ 2 2 ))} and a third confidence threshold T 3 of a given value, the function F denoting the integral
F
(
t
,
μ
,
σ
)
=
1
-
∫
-
t
t
ⅇ
-
(
s
-
μ
)
2
2
σ
2
2
π
σ
ⅆ
s
;
and
wherein the method further comprises combining results of the one or more statistical tests.
13. The computer-implemented method of claim 1 , wherein said pathology is a brain tumor.
14. A computer configured to implement a method for characterizing a development of pathologies involving changes in volume of a body, the computer being programmed to:
receive, from a magnetic resonance imaging device, two images I 1 and I 2 representing the same anatomical part of the body at two successive times;
determine a midway cumulative histogram of gray levels common to the two images I 1 and I 2 , wherein said midway cumulative histogram is equal to an inverse of a geometric mean of inverses of cumulative histograms of gray levels for the two images I 1 and I 2 ;
normalize gray levels by applying the midway cumulative histogram to the two images I 1 and I 2 resulting in two normalized images I′ 1 and I′ 2 , respectively;
calculate a map of signed differences between the two normalized images I′ 1 and I′ 2 ;
perform one or more statistical tests, including a first test, based on an assumption of a Gaussian distribution of gray levels for healthy tissues of the anatomical part of the body in the normalized images I′ 1 and I′ 2 or in the calculated difference map; and
characterize the development of pathologies based on said performed one or more statistical tests.
15. The computer of claim 14 , wherein the computer is programmed to perform the first test by comparing a generalized likelihood ratio defined by the equation:
G
L
R
T
=
p
(
I
1
′
(
x
)
/
μ
1
,
σ
1
)
p
(
I
2
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(
x
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/
μ
2
,
σ
2
)
p
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/
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1
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2
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σ
1
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p
(
I
2
′
(
x
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/
μ
1
-
2
,
σ
1
-
2
)
,
and a confidence threshold T 1 of a given value,
wherein p(I′ i (x)/μ i ,σ i ) is a probability density function for a gray level I′ i (x) of a pixel of a normalized image I′ i , calculated with a Gaussian function of mean μ i and standard deviation σ i , to exhibit an observed gray level, the index 1-2 being applicable to combined values of the normalized images I′ 1 and I′ 2 , and
wherein statistics for a given pixel are determined over an area extending around the pixel over a given number of pixels.
16. The computer of claim 15 , wherein the computer is programmed to compare the first test by the following equation:
ln
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>
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.