Apparatus, a method and a computer program for image processing
There is provided methods, apparatuses and computer program products for image segmentation in which pixel data of an image and information of a first set of pixels of the image indicative of pixels belonging to a foreground of the image are obtained. A color model of the image is estimated. To obtain a geodesic distance map at least one geodesic distance from a pixel of the first set of pixel to another pixel of the image which is not in the first set of pixels is determined. An energy function is optimized on the basis of the geodesic distance map to obtain a segmentation of the image.
1. A method comprising:
obtaining pixel data of an image;
obtaining information of a first set of pixels of the image indicative of pixels belonging to one of a foreground of the image and a background of the image;
estimating a colour model of the image;
estimating a probability that a pixel of the first set of pixels belongs to one of a foreground of the image and a background of the image based on the colour model;
obtaining a geodesic distance map based on determining at least one geodesic distance from the pixel of the first set of pixels to another pixel of the image which is not in the first set of pixels and the estimated probability; and
optimizing an energy function on the basis of the geodesic distance map to obtain a segmentation of the image.
2. The method according to claim 1 further comprising obtaining information of a second set of pixels of the image indicative of pixels belonging to the other one of the background of the image and the foreground of the image.
3. The method according to claim 1 , wherein the determining at least one geodesic distance comprises obtaining a smallest integral of a weight function over all paths from the pixels of the first set of pixels to the another pixel.
4. The method according to claim 3 further comprising obtaining the geodesic distance map as
G
l
(
x
)
=
D
l
(
x
)
D
F
(
x
)
+
D
B
(
x
)
,
where
D
l
(
x
)
=
min
s
∈
Ω
l
ⅆ
(
s
,
x
)
,
l
∈
{
F
,
B
}
,
ⅆ
(
s
1
,
s
2
)
:=
min
C
s
1
,
s
2
∫
0
1
W
·
C
.
s
1
,
s
2
(
p
)
ⅆ
p
,
W
=
∇
P
l
(
c
)
,
P
l
(
c
)
=
P
(
c
❘
l
)
P
(
c
❘
F
)
+
P
(
c
❘
B
)
,
l
∈
{
F
,
B
}
.
5. The method according to claim 1 , wherein the optimization comprising minimizing a summation of the total relative geodesic distance to the first set of pixels in the region inside a contour and the total relative geodesic distance to the second set of pixels in the region outside the contour.
6. The method according to claim 1 further comprising repeating the optimization of the energy function.
7. An apparatus comprising at least one processor and at least one memory including computer program code, the at least one memory and the computer program code configured to, with the at least one processor, cause the apparatus to perform at least the following:
obtain pixel data of an image;
obtain information of a first set of pixels of the image indicative of pixels belonging to one of a foreground of the image and a background of the image;
estimate a colour model of the image;
estimate a probability that a pixel of the first set of pixels belongs to one of a foreground of the image and a background of the image based on the colour model;
obtain a geodesic distance map based on determining at least one geodesic distance from the pixel of the first set of pixels to another pixel of the image which is not in the first set of pixels and the estimated probability; and
optimize an energy function on the basis of the geodesic distance map to obtain a segmentation of the image.
8. The apparatus according to claim 7 , said at least one memory including computer program code, which with the at least one processor, cause the apparatus to obtain information of a second set of pixels of the image indicative of pixels belonging to the other one of the background of the image and the foreground of the image.
9. The apparatus according to claim 7 , wherein said at least one memory including computer program code, which with the at least one processor, cause the apparatus to determine the at least one geodesic distance by obtaining a smallest integral of a weight function over all paths from the pixels of the first set of pixels to the another pixel.
10. The apparatus according to claim 9 , wherein said at least one memory including computer program code, which with the at least one processor, cause the apparatus to obtain the geodesic distance map as
G
l
(
x
)
=
D
l
(
x
)
D
F
(
x
)
+
D
B
(
x
)
,
where
D
l
(
x
)
=
min
s
∈
Ω
l
ⅆ
(
s
,
x
)
,
l
∈
{
F
,
B
}
,
ⅆ
(
s
1
,
s
2
)
:=
min
C
s
1
,
s
2
∫
0
1
W
·
C
.
s
1
,
s
2
(
p
)
ⅆ
p
,
W
=
∇
P
l
(
c
)
,
P
l
(
c
)
=
P
(
c
❘
l
)
P
(
c
❘
F
)
+
P
(
c
❘
B
)
,
l
∈
{
F
,
B
}
.
11. The apparatus according to claim 7 , wherein said at least one memory including computer program code, which with the at least one processor, further cause the apparatus to perform the optimization by minimizing a summation of the total relative geodesic distance to the first set of pixels in the region inside a contour and the total relative geodesic distance to the second set of pixels in the region outside the contour.
12. The apparatus according to claim 7 , wherein said at least one memory including computer program code, which with the at least one processor, cause the apparatus to repeat the optimization of the energy function.
13. The apparatus according to claim 7 , wherein the apparatus is an element of a mobile phone.
14. The apparatus according to claim 7 , wherein the apparatus is an element of a computing device.
15. A computer program product including one or more sequences of one or more instructions which, when executed by one or more processors, cause an apparatus to perform at least the following:
obtain pixel data of an image;
obtain information of a first set of pixels of the image indicative of pixels belonging to one of a foreground of the image and a background of the image;
estimate a colour model of the image;
estimate a probability that a pixel of the first set of pixels belongs to one of a foreground of the image and a background of the image based on the colour model;
obtain a geodesic distance map based on determining at least one geodesic distance from the pixel of the first set of pixels to another pixel of the image which is not in the first set of pixels and the estimated probability; and
optimize an energy function on the basis of the geodesic distance map to obtain a segmentation of the image.
16. The computer program product according to claim 15 , wherein said at least one memory including computer program code, which with the at least one processor, cause the apparatus to obtain information of a second set of pixels of the image indicative of pixels belonging to the other one of the background of the image and the foreground of the image.
17. The computer program product according to claim 15 , wherein said at least one memory including computer program code, which with the at least one processor, cause the apparatus to determine the at least one geodesic distance by obtaining a smallest integral of a weight function over all paths from the pixels of the first set of pixels to the another pixel.
18. The computer program product according to claim 17 , wherein said at least one memory including computer program code, which with the at least one processor, further cause the apparatus to obtain the geodesic distance map as
G
l
(
x
)
=
D
l
(
x
)
D
F
(
x
)
+
D
B
(
x
)
,
where
D
l
(
x
)
=
min
s
∈
Ω
l
ⅆ
(
s
,
x
)
,
l
∈
{
F
,
B
}
,
ⅆ
(
s
1
,
s
2
)
:=
min
C
s
1
,
s
2
∫
0
1
W
·
C
.
s
1
,
s
2
(
p
)
ⅆ
p
,
W
=
∇
P
l
(
c
)
,
P
l
(
c
)
=
P
(
c
❘
l
)
P
(
c
❘
F
)
+
P
(
c
❘
B
)
,
l
∈
{
F
,
B
}
.
19. The computer program product according to claim 15 , wherein said at least one memory including computer program code, which with the at least one processor, cause the apparatus to perform the optimization by minimizing a summation of the total relative geodesic distance to the first set of pixels in the region inside a contour and the total relative geodesic distance to the second set of pixels in the region outside the contour.
20. The computer program product according to claim 15 , wherein said at least one memory including computer program code, which with the at least one processor, cause the apparatus to repeat the optimization of the energy function.