Method and apparatus of segmenting an object in a data set and of determination of the volume of segmented object

• US 7,760,941 B2
• Filed: 08/11/2006
• Issued: 07/20/2010
• Est. Priority Date: 09/23/2005
• Status: Active Grant

• Current Assignee: Fraunhofer Gesellschaft Zur Foerderung Der Angewandten Forsching E.V.
• Original Assignee: Mevis Research GmbH
• Inventors: Dicken, Volker, Bornemann, Lars, Kuhnigk, Jan-Martin
• Primary Examiner(s): Alavi; Amir
• Application Number:
  US11/503,337
• Publication Number:
  US 20070217668A1
• Time in Patent Office: 1,439 Days
• Field of Search: 382/128, 382/131, 382/132, 382/154, 382/164, 382/172, 382/173, 382/254, 382/256, 382/257, 382/267, 382/268, 382/270, 382/276, 382/277, 600/407, 600/425, 378/37, 378/62
• US Class Current: 382/173
• CPC Class Codes: G06F 18/00 Pattern recognition
• CPC Class Codes: G06T 7/0012 Biomedical image inspection
• CPC Class Codes: G06V 2201/03 Recognition of patterns in medical or anatomical images

Abstract

The invention relates to a method of segmenting an object in a data set, wherein the object is initially segmented resulting in a first set (N₀) of voxels. An erosion operation is performed on the first set (N₀) of voxels resulting in an eroded set (N₋) of voxels. A dilation operation is performed on the eroded set (N₋) of voxels resulting in a dilated set (N₊) of voxels. The erosion operation depends on a variable erosion threshold (Θ₋), and the dilation operation depends on a variable dilation threshold (Θ₊).

Claims

1. A method of segmenting an object in a data set, said method comprising:

a) initial segmenting of the object, resulting in a first set (N₀) of voxels,

b) performing an erosion operation on the first set (N₀) of voxels resulting in an eroded set (N₋

) of voxels,

c) performing a dilation operation on the eroded set (N₋

) of voxels resulting in a dilated set (N₊) of voxels, and

wherein the erosion operation depends on a variable erosion threshold (Θ

₋

) and

wherein the dilation operation depends on a variable dilation threshold (Θ

₊).

2. The method according to claim 1, wherein the first set (N₀) of voxels comprises only connected voxels.

3. The method according to claim 1, wherein the erosion threshold (Θ

₋

) and the dilation threshold (Θ

₊) depend on the first set (N₀) of voxels.

4. The method according to claim 1, wherein the first set (N₀) of voxels is modified, before performing the erosion operation, by:

i) determining a complement of the first set (N₀) of voxels,

ii) performing a connected component analysis on the complement of the first set (N₀) of voxels resulting in the largest connected non-segmented area (P), and

iii) subtracting the largest connected non-segmented area (P) from the data set (V) resulting in a modified first set (N₁) of voxels.

5. The method according to claim 4, wherein, before the erosion operation and after subtracting the largest connected non-segmented area (P) from the data set (V), the method further includes:

performing a convex hull operation on the largest connected non-segmented area (P) resulting in a convex set of voxels, and

modifying the first set of voxels by intersecting the first set of voxels with the convex set of voxels wherein the intersection is the modified first set (N₂) of voxels.

6. The method according to claim 1,

wherein the erosion threshold (Θ

₋

) is determined depending on a first minimal distance (E(v)) of each of at least some voxels of the data set (V), in particular for the voxels of the first set (N₀;

N₁;

N₂), wherein the first minimal distance (E(v)) of each of at least some voxels of the data set (V) is the distance of the respective voxel of the at least some voxels of the data set (V) to a voxel outside of the first set (N₀;

N₁;

N₂) having the shortest distance to the respective voxel of the at least some voxels of the data set (V), and

wherein the dilation threshold (Θ

₊) is determined depending on a second minimal distance (D(v)) of each of at least some voxels of the data set (V), wherein the second minimal distance (D(v)) of each of the at least some voxels of the data set (V) is the distance of each of the at least some voxels of the data set (V) to a voxel of the eroded set (N₋

) of voxels having the shortest distance to the respective voxel of the at least some voxels of the data set (V).

7. The method according to claim 6, wherein the erosion threshold (Θ

₋

) is determined by

performing a first distance transformation to determine for each of at least some voxels of the data set (V) the first minimal distance (E(v)) resulting in a first distance map,

determining a seed point (S′

) in the first set (N₀;

N₁;

N₂) of voxels being the position of a maximum, in particular a local maximum, in the first distance map, and

determining the erosion threshold by performing a variable threshold region growing on the first distance map starting from the determined seed point (S′

) wherein the erosion threshold is equal to or larger than the highest threshold sufficient to reach the boundaries of the data set (V).

8. The method according to claim 6, wherein the erosion operation is performed such that the eroded set (N₋

) of voxels comprises all voxels of the first set (N₀;

N₁;

N₂) of voxels whose first minimal distance (E(v)) is greater than or equal to the erosion threshold (Θ

₋

).

9. The method according to claim 6, wherein, if the eroded set (N₋

) of voxels comprises different voxel sets, which are separated from each other, one of these different voxel sets is selected by connected component analysis as the eroded set (N₋

) of voxels.

10. The method according to claim 6, wherein the dilation operation comprises:

performing a second distance transformation to determine for each of at least some voxels of the data set (V) the second minimal distance (D(v)) resulting in a second distance map, and

performing the dilation procedure such that the dilated set (N₊) of voxels includes all voxels whose second minimal distance (D(v)) to voxels of the eroded set (N₋

) of voxels is smaller than the dilation threshold (Θ

₊).

11. The method according to claim 1, wherein the dilation threshold (Θ

₊) is determined such that the dilated set (N₊) of voxels comprises the same or more voxels than the first set (N₀;

N₁;

N₂) of voxels and/or that the dilation threshold (Θ

₊) is equal to or larger than the erosion threshold (Θ

₋

).

12. The method according to claim 1, wherein, after the dilation operation, the method further includes:

determining the intersection of the boundary of the dilated set (N₊) of voxels with the first set (N₀;

N₁;

N₂) of voxels resulting in an intersected set of voxels,

dilating the intersection by a tolerance summand (δ

) resulting in a dilated intersected set (I_δ

) of voxels, and

subtracting the dilated intersected set (I_δ

) of voxels from the dilated set (N₊) of voxels.

13. The method according to claim 12, wherein, if the dilation threshold (Θ

₊) is larger than the erosion threshold (Θ

₋

), the tolerance summand (δ

) is equal to the difference between the dilation threshold (Θ

₊) and the erosion threshold (Θ

₋

).

14. The method according to claim 1, wherein, if the dilated set of voxels is surrounded by a rim of voxels, wherein the absolute difference between voxel values of the rim of voxels and voxel values of voxels of the dilated set of voxels located in the vicinity of the rim of voxels is larger than a predetermined difference value, the voxel values of the rim are set to a value having a absolute difference to the voxel values of the dilated set of voxels located in the vicinity of the rim of the voxels which is smaller than the predetermined difference value.

15. The method according to claim 1, wherein the initial segmenting of the object resulting in a first set (N₀) of voxels comprises:

providing a volume of interest inside the data set,

determining an object value from values in the center of the volume of interest,

determining a non-object value from the value of the volume of interest or providing a predetermined non-object value,

determining lower and upper thresholds depending on a relation between the object value and the non-object value, and

performing a region growing procedure starting from a predetermined seed point with the determined lower and upper thresholds resulting in a first set of voxels.

16. The method according to claim 15, wherein the object value is an average value of values located in the center.

17. The method according to claim 15, wherein the non-object value is determined as the value within the volume of interest comprising the largest frequency of occurrence.

18. The method according to claim 15, wherein the lower and upper thresholds are determined such that,

the lower threshold is the smallest voxel value within the volume of interest and the upper threshold is the average of the object value and the non-object value, if the object value is smaller than all values within a predetermined interval surrounding the non-object value,

the lower threshold is the average of the object value and the non-object value and the upper threshold is the largest voxel value within the volume of interest, if the object value is larger than all values within a predetermined interval surrounding the non-object value, and

the lower threshold and the upper threshold within a margin around the non-object value, wherein the margin is determined such that less than a predetermined fraction of the volume of interest is located within the margin, if the object value is located within the predetermined interval surrounding the non-object value.

19. The method according to claim 1, wherein, before performing an initial segmentation of the object as set forth in element (a) above,

an initial segmentation of the object is performed, resulting in an initial set of voxels,

a first neighboring set of voxels is defined, wherein the voxels of the initial set of voxels are located within a first predetermined voxel distance from the initial set of voxels,

a second neighboring set of voxels is defined, wherein the voxels of the second neighboring set of voxels are located within a second predetermined voxel distance from the first neighboring set of voxels, and

if the difference between a first average of the voxels of the first neighboring set of voxels and an second average of the second neighboring set of voxels is larger than a predetermined first fraction of the first average and if the first average is larger than a third average of the initial set of voxels and if the first average is larger than the second average, to each of the voxels of the initial set of voxels a value is assigned such that a predetermined second fraction of voxel values of the first neighboring set of voxels is smaller than the assigned value of the voxels of the first set of voxels, wherein the values within the volume of interest are modified.

20. The method according to claim 1, wherein performing an erosion operation on the first set (N₀) of voxels and performing a dilation operation on the eroded set (N₃₁ ) of voxels are performed several times with different predetermined erosion thresholds (Θ

₋

).

21. The method according to claim 1, wherein the erosion operation is performed using a predetermined erosion threshold (Θ

₋

) and the dilation operation is performed according to claim 11 or 10.

22. An apparatus for segmenting an object in a data set for carrying out the method according to claim 1, said apparatus comprising:

initial segmenting means for initial segmenting of the object, resulting in a first set (N₀;

N₁;

N₂) of voxels,

erosion means for performing an erosion operation on the first set (N₀;

N₁;

N₂) of voxels resulting in an eroded set (N₋

) of voxels, and

dilation means for performing a dilation operation on the eroded set (N₋

) of voxels resulting in a dilated set (N₊) of voxels, and

wherein the erosion operation depends on a variable erosion threshold (Θ

₋

) and wherein the dilation operation depends on a variable dilation threshold (Θ

₊).

23. An apparatus for segmenting an object in a data set and of determination of the volume of a segmented object, wherein the apparatus comprises an apparatus of segmenting an object according to claim 22 and an apparatus of determination of the volume of a segmented object comprising:

defining means,

for defining an inner set (NC) of voxels comprising voxels arranged inside the segmented object and having a distance from a boundary of the segmented object which is larger than a predetermined minimum distance, wherein, if such voxels do not exist, the inner set (NC) of voxels is a zero set of voxels,

for defining an outer set (PC) of voxels comprising voxels arranged outside the segmented object and having a distance from the boundary of the segmented object which is larger than the predetermined minimum distance, and

for defining a middle set (PV) of voxels comprising voxels which are not included in the inner (NC) or outer set (PC) of voxels;

assigning means

for assigning to each voxel of the inner set (NC) of voxels the same weighting factor (w(v)), in particular one, and

for assigning to each voxel of the middle set (PV) of voxels a weighting factor (w(v)) which depends on the position and/or the value of the respective voxel within the middle set (PV) of voxels and/or the values of the voxels in the inner voxel and outer set (PC) of voxels; and

determining means for determining the volume of the segmented object, wherein the determining means is adapted to add the weighting factors assigned to the voxels of the middle set (PV) of voxels and, if the inner set (NC) of voxel is not a zero set of voxels, of the inner set (NC) of voxels.

24. A computer program embodied on a non-transitory computer-readable medium for segmenting an object in a data set for carrying out the method of claim 1, when the computer program is run on a computer, comprising:

first program code for initial segmenting of the object, resulting in a first set (N₀;

N₁;

N₂) of voxels,

second program code for performing an erosion operation on the first set (N₀) of voxels resulting in an eroded set (N₋

) of voxels, and

third program code for performing an dilation operation on the eroded set (N₋

) of voxels resulting in a dilated set (N₊) of voxels, and

wherein the erosion operation depends on a variable erosion threshold (Θ

₋

) and wherein the dilation operation depends on a variable dilation threshold (Θ

₊).

25. A method of segmenting an object in a data set, said method comprising:

a) initial segmenting of the object, resulting in a first set (N₀) of voxels,

b) modifying the first set (N₀) of voxels by;

determining a complement of the first set (N₀) of voxels,

performing a connected component analysis on the complement of the first set (N₀) of voxels resulting in the largest connected non-segmented area (P), and

subtracting the largest connected non-segmented area (P) from the data set (V) resulting in a modified first set (N₁) of voxels,

c) performing a first distance transformation to determine for each of at least some voxels of the data set (V) the first minimal distance (E(v)) resulting in a first distance map, wherein the first minimal distance of each of at least some voxels of the data set (V) is the distance of the respective voxel of the at least some voxels of the data set (V) to a voxel outside of the first set (N₁) having the shortest distance to the respective voxel of the at least some voxels of the data set (V),

d) determining a seed point (S′

) in the first set (N₁) of voxels being the position of a maximum, in particular of a local maximum, in the first distance map,

e) determining an erosion threshold (Θ

₋

) by performing a variable threshold region growing on the first distance map starting from the determined seed point (S′

) wherein the erosion threshold (Θ

₋

) is equal to or larger than the highest threshold sufficient to reach the boundaries of the data set (V),

f) performing an erosion operation on the first set (N₁) of voxels resulting in an eroded set (N₋

) of voxels, wherein the erosion operation is performed such that the eroded set (N₋

) of voxels comprises all voxels of the first set (N₁) of voxels whose first minimal distance is smaller than or equal to the erosion threshold (Θ

₋

),

g) performing a second distance transformation to determine for each of at least some voxels of the data set (V) the second minimal distance (D(v)), wherein the second minimal distance (D(v)) of each of the at least some voxels of the data set (V) is the distance of each of the at least some voxels of the data set (V) to a voxel of the eroded set (N₋

) of voxels having the shortest distance to the respective voxel of the at least some voxels of the data set (V), and

h) performing a dilation operation on the eroded set (N₋

) of voxels resulting in a dilated set (N₊) of voxels such that the dilated set (N₊) of voxels includes all voxels whose second minimal distance (D(v)) to voxels of the eroded set (N₋

) of voxels is smaller than the dilation threshold (Θ

₊), wherein the dilation threshold (Θ

₊) is defined such that the dilated set (N₊) of voxels comprises the same or more voxels than the first set (N₁) of voxels and/or that the dilation threshold (Θ

₊) is equal to or larger than the erosion threshold (Θ

₋

).

26. The method according to claim 25, wherein, after the dilation operation, the method further comprises:

determining the intersection of the boundary of the dilated set (N₊) of voxels with the first set (N₁) of voxels resulting in an intersected set of voxels,

dilating the intersection by a tolerance summand resulting in a dilated intersected set of voxels, and

subtracting the dilated intersected set of voxels from the dilated set (N₊) of voxels.

27. The method according to claim 26, wherein, if the dilation threshold (Θ

₊is larger than the erosion threshold (Θ

₋

), the tolerance summand is equal to the difference between the dilation threshold (Θ

₊) and the erosion threshold (Θ

₋

).

28. A method of segmenting an object in a data set, said method comprising:

a) initial segmenting of the object, resulting in a first set (N₀) of voxels,

b) modifying the first set (N₀) of voxels by;

determining a complement of the first set (N₀) of voxels,

performing a connected component analysis on the complement of the first set (N₀) of voxels resulting in the largest connected non-segmented area (P), and

subtracting the largest connected non-segmented area (P) from the data set (V) resulting in a modified first set (N₁) of voxels,

c) performing a convex hull operation on the largest connected non-segmented area (P) resulting in a convex set of voxels,

d) modifying the first set of voxels by intersecting the first set of voxels with the convex set of voxels wherein the intersection is the modified first set (N₂) of voxels,

e) performing a first distance transformation to determine for each of at least some voxels of the data set (V) the first minimal distance (E(v)) resulting in a first distance map, wherein the first minimal distance (E(v)) of each of at least some voxels of the data set (V) is the distance of the respective voxel of the at least some voxels of the data set (V) to a voxel outside of the first set (N₂) having the shortest distance to the respective voxel of the at least some voxels of the data set (V),

f) determining a seed point (S′

) in the first set (N₂) of voxels being the position of the maximum in the first distance map,

g) determining an erosion threshold (Θ

₋

) by performing a variable threshold region growing on the first distance map starting from the determined seed point (S′

) wherein the erosion threshold (Θ

₋

) is equal to or larger than the highest threshold sufficient to reach the boundaries of the data set (V),

h) performing an erosion operation on the first set (N₂) of voxels resulting in an eroded set (N₋

) of voxels, wherein the erosion operation is performed such that the eroded set (N₋

) of voxels comprises all voxels of the first set (N₂) of voxels whose first minimal distance is smaller than or equal to the erosion threshold (Θ

₋

),

i) performing a second distance transformation to determine for each of at least some voxels of the data set (V) the second minimal distance (D(v)) wherein the second minimal distance (D(v)) of each of the at least some voxels of the data set (V) is the distance of each of the at least some voxels of the data set (V) to a voxel of the eroded set (N₋

) of voxels having the shortest distance to the respective voxel of the at least some voxels of the data set (V), and

j) performing an dilation operation on the eroded set (N₋

) of voxels resulting in a dilated set (N₊) of voxels such that the dilated set (N₊) of voxels includes all voxels whose second minimal distance (D(v)) to voxels of the eroded set (N₋

) of voxels is smaller than the dilation threshold (Θ

₊), wherein the dilation threshold (Θ

₊) is defined such that the dilated set (N₊) of voxels comprises the same or more voxels than the first set (N₂) of voxels and/or that the dilation threshold (Θ

₊) is equal to or larger than the erosion threshold (Θ

₋

).

29. The method according to claim 28, wherein, after the dilation operation, the method further comprises:

determining the intersection (I) of the boundary of the dilated set (N₊) of voxels with the first set (N₂) of voxels resulting in an intersected set of voxels,

dilating the intersection (I) by a tolerance summand (δ

) resulting in a dilated intersected set (I_δ

) of voxels, and

subtracting the dilated intersected (I) set of voxels from the dilated set (N₊) of voxels.

30. The method according to claim 28 or claim 29, wherein, if the dilation threshold (Θ

₊) is larger than the erosion threshold (Θ

₋

), the tolerance summand (δ

) is equal to the difference between the dilation threshold (Θ

₊) and the erosion threshold (Θ

₋

).

31. A method for determination of the volume of a segmented object, in particular a lesion, in a data set, said method comprising:

defining an inner set (NC) of voxels comprising voxels arranged inside the segmented object and having a distance from the boundary of the segmented object which is larger than a predetermined minimum distance, wherein, if such voxels do not exist, the inner set (NC) of voxels is a zero set of voxels,

defining an outer set (PC) of voxels comprising voxels arranged outside the segmented object and having a distance from the boundary of the segmented object which is larger than the predetermined minimum distance,

defining a middle set (PV) of voxels comprising voxels which are not included in the inner (NC) or outer set (PC) of voxels,

assigning to each voxel of the inner set (NC) of voxels the same weighting factor, in particular one, if the inner set (NC) of voxels is not a zero set of voxels,

assigning to each voxel of the middle set (PV) of voxels a weighting factor (w(v)) which depends on the position and/or the value of the respective voxel within the middle set (PV) of voxels and/or the values of the voxels in the inner (NC) and outer set (PC) of voxels, and

determining the volume of the segmented object, wherein the weighting factors (w(v)) assigned to the voxels of the middle set (PV) of voxels and, if the inner set (NC) of voxels is not a zero set of voxels, of the inner set (NC) of voxels are added.

32. The method according to claim 31, wherein an inner average voxel value (μ

_NC)is determined for the inner set (NC) of voxels, if the inner set (NC) of voxels is not a zero set of voxels, wherein an outer average voxel value (μ

_PC) is determined for the outer set (PC) of voxels and wherein the weighting factors assigned to the voxels of the middle set (PV) of voxels depend on the ratio of the difference between the voxel value of the respective voxel of the middle set (PV) of voxels and the outer average voxel (μ

_PC) value to the difference between the inner average voxel value (μ

_NC) and the outer average voxel value (μ

_PC).

33. The method according to claim 31, wherein, if the inner set (NC) of voxels is a zero set of voxels, an outer average voxel value is determined for the outer set (PC) of voxels and wherein the weighting factors assigned to the voxels of the middle set (PV) of voxels depend on the ratio of the difference between the voxel value of the respective voxel of the middle set (PV) of voxels and the outer average voxel (μ

_PC) value to the difference between the predetermined inner average voxel value (μ

_NC) and the outer average voxel value (μ

_PC).

34. The method according to claim 31, wherein the segmented object has been segmented by:

initial segmenting of the object, resulting in a first set (N₀) of voxels,

performing an erosion operation on the first set (N₀) of voxels resulting in an eroded set (N₋

) of voxels,

performing a dilation operation on the eroded set (N₋

) of voxels resulting in a dilated set (N₊) of voxels, and

wherein the erosion operation depends on a variable erosion threshold (Θ

₋

) and the dilation operation depends on a variable dilation threshold (Θ

₊).

35. The method according to claim 31, wherein the segmented object has been segmented by:

initial segmenting of the object, resulting in a first set (N₀) of voxels,

performing an erosion operation on the first set (N₀) of voxels resulting in an eroded set (N₋

) of voxels,

performing a dilation operation on the eroded set (N₋

) of voxels resulting in a dilated set (N₊) of voxels, and

wherein the erosion operation depends on a variable erosion threshold (Θ

₋

) and the dilation operation depends on a variable dilation threshold (Θ

₊); and

wherein, after the dilation operation, the method further includes;

determining the intersection of the boundary of the dilated set (N₊) of voxels with the first set (N₀;

N₁;

N₂) of voxels resulting in an intersected set of voxels,

dilating the intersection by a tolerance summand (δ

) resulting in a dilated intersected set (I_δ

) of voxels, and

subtracting the dilated intersected set (I_δ

) of voxels from the dilated set (N₊) of voxels; and

wherein the inner (NC), middle (PV) and outer set (PC) of voxels do not comprise voxels which are in the dilated intersected set (I_δ

) of voxels.

36. The method according to claim 31, wherein the segmented object has been segmented by:

initial segmenting of the object, resulting in a first set (N₀) of voxels,

performing an erosion operation on the first set (N₀) of voxels resulting in an eroded set (N₋

) of voxels,

performing a dilation operation on the eroded set (N₋

) of voxels resulting in a dilated set (N₊) of voxels, and

wherein the erosion operation depends on a variable erosion threshold (Θ

₋

) and the dilation operation depends on a variable dilation threshold (Θ

₊); and

wherein the first set (N₀) of voxels is modified, before performing the erosion operation, by;

i) determining a complement of the first set (N₀) of voxels,

ii) performing a connected component analysis on the complement of the first set (N₀) of voxels resulting in the largest connected non-segmented area (P), and

iii) subtracting the largest connected non-segmented area (P) from the data set (V) resulting in a modified first set (N₁) of voxels; and

wherein the inner (NC), middle (PV) and outer sets (PC) only comprise voxels located outside the convex set of voxels.

37. A method of segmenting an object in a data set and of determination of the volume of a segmented object, wherein the object is segmented by:

initial segmenting of the object, resulting in a first set (N₀) of voxels,

performing an erosion operation on the first set (N₀) of voxels resulting in an eroded set (N₋

) of voxels,

performing a dilation operation on the eroded set (N₋

) of voxels resulting in a dilated set (N₊) of voxels, and

wherein the erosion operation depends on a variable erosion threshold (Θ

₋

) and the dilation operation depends on a variable dilation threshold (Θ

₊) thereby yielding a segmented object; and

wherein the volume of the segmented object is determined according to claim 31.

38. A computer program embodied on a non-transitory computer-readable medium for segmenting an object in a data set and of determination of the volume of a segmented object for carrying out the method of claim 37, when the computer program is run on a computer, comprising the computer program code of the computer program of segmenting an object in a data set by first program code for initial segmenting of the object, resulting in a first set (N₀;

N₁;

N₂) of voxels, second program code for performing an erosion operation on the first set (N0) of voxels resulting in an eroded set (N−

) of voxels and third program code for performing a dilation operation on the eroded set (N−

) of voxels resulting in a dilated set (N+) of voxels, and wherein the erosion operation depends on a variable erosion threshold (Θ

₋

) and wherein the dilation operation depends on a variable dilation threshold (Θ

₊) and the computer program code of the computer program of determination of the volume of a segmented object of first program code for defining an inner set (NC) of voxels comprising voxels arranged inside the segmented object and having a distance from the boundary of the segmented object which is larger than a predetermined minimum distance, second program code for defining an outer set (PC) of voxels comprising voxels arranged outside the segmented object and having a distance from the boundary of the segmented object which is larger than the predetermined minimum distance, third program code for defining a middle set (PV) of voxels comprising voxels which are not included in the inner (NC) or outer set (PC) of voxels, fourth program code for assigning to each voxel of the inner set (NC) of voxels the same weighting factor (w(v)), in particular one, if the inner set (PC) of voxels is not a zero set of voxels, fifth program code for assigning to each voxel of the middle set (PV) of voxels a weighting factor (w(v)) which depends on the position and/or the value of the respective voxel within the middle set (PV) of voxels and/or the values of the voxels in the inner (NC) and outer set (PC) of voxels, and sixth program code for determining the volume of the segmented object, wherein the weighting factors (w(v)) assigned to the voxels of the middle set (PV) of voxels and, if the inner set (PC) of voxels is not a zero set of voxels, of the inner set (PC) of voxels are added.

40. A computer program embodied on a non-transitory computer-readable medium for determination of the volume of a segmented object, in particular a lesion, in a data set for carrying out the method of claim 31, when the computer program is run on a computer, comprising:

first program code for defining an inner set (NC) of voxels comprising voxels arranged inside the segmented object and having a distance from the boundary of the segmented object which is larger than a predetermined minimum distance,

second program code for defining an outer set (PC) of voxels comprising voxels arranged outside the segmented object and having a distance from the boundary of the segmented object which is larger than the predetermined minimum distance,

third program code for defining a middle set (PV) of voxels comprising voxels which are not included in the inner (NC) or outer set (PC) of voxels,

fourth program code for assigning to each voxel of the inner set (NC) of voxels the same weighting factor (w(v)), in particular one, if the inner set (PC) of voxels is not a zero set of voxels,

fifth program code for assigning to each voxel of the middle set (PV) of voxels a weighting factor (w(v)) which depends on the position and/or the value of the respective voxel within the middle set (PV) of voxels and/or the values of the voxels in the inner (NC) and outer set (PC) of voxels, and

sixth program code for determining the volume of the segmented object, wherein the weighting factors (w(v)) assigned to the voxels of the middle set (PV) of voxels and, if the inner set (PC) of voxels is not a zero set of voxels, of the inner set (PC) of voxels are added.

39. An apparatus for determination of the volume of a segmented object, in particular a lesion, in a data set, said apparatus comprising:

defining means,

for defining an inner set (NC) of voxels comprising voxels arranged inside the segmented object and having a distance from a boundary of the segmented object which is larger than a predetermined minimum distance, wherein, if such voxels do not exist, the inner set (NC) of voxels is a zero set of voxels,

for defining an outer set (PC) of voxels comprising voxels arranged outside the segmented object and having a distance from the boundary of the segmented object which is larger than the predetermined minimum distance, and

for defining a middle set (PV) of voxels comprising voxels which are not included in the inner (NC) or outer set (PC) of voxels;

assigning means

for assigning to each voxel of the inner set (NC) of voxels the same weighting factor (w(v)), in particular one, and

for assigning to each voxel of the middle set (PV) of voxels a weighting factor (w(v)) which depends on the position and/or the value of the respective voxel within the middle set (PV) of voxels and/or the values of the voxels in the inner voxel and outer set (PC) of voxels; and

determining means for determining the volume of the segmented object, wherein the determining means is adapted to add the weighting factors assigned to the voxels of the middle set (PV) of voxels and, if the inner set (NC) of voxel is not a zero set of voxels, of the inner set (NC) of voxels.