CN102254097A - Method for identifying fissure on lung CT (computed tomography) image - Google Patents

Method for identifying fissure on lung CT (computed tomography) image Download PDF

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CN102254097A
CN102254097A CN2011101907972A CN201110190797A CN102254097A CN 102254097 A CN102254097 A CN 102254097A CN 2011101907972 A CN2011101907972 A CN 2011101907972A CN 201110190797 A CN201110190797 A CN 201110190797A CN 102254097 A CN102254097 A CN 102254097A
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普建涛
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Abstract

The invention provides a method for automatically detecting and cutting a fissure on a lung CT (computed tomography) image efficiently and accurately based on three-dimensional plane fitting. In the method, a CT image is taken as a group of three-dimensional space point clouds; a lung area is divided into small spherical subdivision bodies, and a fissure plane is discovered in the small subdivision bodies by utilizing the three-dimensional plane fitting method, so that the fissure detection with free-form surface characteristics is converted into detection on planes, and the complexity of the problem is remarkably reduced. The method has the advantage of being not sensitive to noise or abnormal values. Furthermore, in a fissure detection process, fissures (oblique fissure in left and right lungs and horizontal fissure) in different types can be automatically identified by a simple clustering method. Compared with other methods, the method provided by the invention has the characteristics of good accuracy, stability, high efficiency and the like.

Description

Lung on the lung CT image splits recognition methods
Technical field
The present invention relates to based on segmentation three-dimensional planar approximating method, from brand-new angle, the lung of discerning efficiently on the chest CT image splits.
Background technology
Lung interlobar fissure (being called for short lung splits) is the important sign that embodies human lung's structure.The integrity degree that lung is split and the full appreciation of structure, pulmonary disease detects in early days, and classification on PD and the treatment of diseases, all has very big value for clinical application.Therefore, the accurate identification split of lung is very important concerning clinical.It's a pity, the high resolution CT examination comprises a large amount of images usually, allow the expert manually one by one picture to go to indicate that lung splits the locus, place very consuming time, and lung splits and shows to such an extent that be not very clear on the CT image usually, often can't guarantee result's accuracy and consistance.
At present, proposed a lot of lungs in the world wide and split recognition methods, wherein most of method comprises two stages, i.e. initial identification and further optimization improvement.In the specific implementation process, initial detecting/identification is generally by determining that region of interest (ROI:region-of-interest) realizes.Such as, general people such as grade [1] handles by a simple thresholding and discerns area-of-interest; People such as Wiemker [2] utilize Hessian matrix and structure tensor filtering to determine the prime area.In addition in document [5-8], the prime area be by lung split and blood vessel, bronchus between relation on dissecting determine.After determining the prime area, next step is exactly to determine that specifically the locus that lung splits, the method for this respect are by determining straight line or realize at three dimensions searching curved surface or plane in two-dimensional space substantially.Two dimension straight line (2D) method has comprised growth curve method [9-10], and the linear feature of Vanderbrug detects [11], rim detection [8] and Gaussian distribution and/or be mean curvature analysis [12].Consider in identification aspect lung splits, three-dimension curved surface or plane (3D) than two-dimentional straight line (2D) more comprehensively, accurately, people such as Ukil [7] have proposed a kind of ridge degree mensuration [13] of the 3D of having graph search function and sought the plane in region of interest; Generally wait people [1] to propose the computational geometry method that a kind of usefulness comprises the level and smooth and expansion Gaussian image (EGI:extended Gaussian image) of Laplce; People such as Rikxoort [3-4] propose to utilize second-order logic to calculate point are combined into the plane; Kuhnigk[6] etc. the people a kind of interactive three-dimensional watershed algorithm has been proposed.Different with these methods, open to wait a people [14-16] to propose a kind of masterplate matching process and seek lung and split based on picture library.
Summary of the invention
The lung interlobar fissure has two characteristics on the CT image, and the firstth, split lung tissue on every side with lung and compare, lung splits relative higher brightness, and this also is why human eye can be seen the reason that lung splits; The secondth, lung splits higher density in the image space based on voxel.In order fully to excavate these two characteristics, this invention has proposed a kind of based on plane fitting, discerns the method that lung splits on the CT image efficiently and accurately.
Consider that three-dimensional free surface can accurately approach with a lot of little planes, we propose three-dimensional lung areas is subdivided into a lot of little spheries segmentation bodies (overlapping mutually between these segmentation bodies), and the identification problem split of lung just is converted to a series of plane problems of searching in each spheroid like this.This method has comprised five basic steps (as Fig. 1 to Fig. 5): (1) lung areas is cut apart (Fig. 1), (2) lung areas space segmentation (Fig. 2), (3) medium filtering (Fig. 3), (4) lung of discerning in each segmentation body with planar fit method splits (Fig. 4), and (5) lung splits classification (Fig. 5).Filtration is to have utilized higher relatively lung to split contrast, and plane fitting has utilized lung to split the characteristics of density higher relatively in the voxel space.
In this method, the CT image is counted as one group of three dimensional point cloud, and lung areas is subdivided into many little spheroids, is called the segmentation body, and the identification that lung splits is by seek corresponding plane by plane fitting in each segmentation spheroid.
The present invention has a lot of characteristics: at first, this method is very general, both can discern the straight line in the 2D space, also can discern the plane in the 3d space.
The second, aspect stable, this method is for noise or exceptional value and insensitive.
The 3rd, on counting yield, whole lung splits identifying only needs about 8 minutes, and the method [1] of the general invention of mentioning before such as the people of grade probably needs 20 minutes, and needs about 90 minutes by the method [17] of people such as van Rikxoort invention.
The 4th, on accuracy, neoteric method has higher accuracy.
The 5th, the implementation procedure of this method is very succinct, as long as planar fit method is directly applied to segmentation body in lung areas.In addition, dissimilar lungs split can finish simultaneously by a simple clustering method when being identified in lung and splitting testing process.As far as we know, now also there is not any method can carry out identification and the classification that lung splits simultaneously.
Description of drawings
Concrete embodiment will be described in detail by following accompanying drawing.
Fig. 1 to Fig. 5 is the basic step that lung splits dividing method:
Fig. 1 lung areas is cut apart;
The segmentation of Fig. 2 lung areas;
Fig. 3 medium filtering;
Fig. 4 splits with plane fitting analytic approach identification lung;
The dissimilar lungs of Fig. 5 split classification.
Fig. 6 to Figure 11 is by using the performance of two and three dimensions example illustrated planar approximating method:
Fig. 6 and Fig. 7 have shown the match of the straight line that is assembled by point in the two-dimension picture.The result that the green line representative is drawn by least squares approach, and red line has been represented the result who is drawn by the density approximating method of describing among the present invention;
Fig. 8 shows the three-dimensional point cloud atlas of the spheroid that a pair is segmented out from chest CT;
The point cloud of Fig. 9 among visual Fig. 8 of inner product (formula (6) just) of vector sum normal vector;
Figure 10 splits testing result (representing with redness) by using the resulting lung of the present invention;
Figure 11 shows the function of three-dimensional point cloud in the corresponding diagram 8
Figure 12 to Figure 14 is clear, and the lung of having represented splits identification and sorting result:
Figure 12 one secondary CT image;
Figure 13 is through identification, and the lung of classification splits (with different color showings);
Figure 14 is that the final lung that obtains after having removed among Figure 13 the non-lung split plot represented by arrow splits that image is cut apart and classification chart.
Figure 15 to Figure 17 shows that by example institute's inventive method is in the performance of identification lung aspect splitting.
Figure 18 to Figure 20 is the example of splitting at the lung that is recognized in the case that serious bronchiectasis (cyst cystic fibrosis) arranged.
Figure 21 to Figure 23 is that this inventive method identification lung splits example, and the lung in this example splits on image very fuzzy.
Embodiment
Planar fit method is this neoteric key component, below we with clear description.
The first step is the selection of objective function.
In Euclidean three dimensions, set N point
Figure 280680DEST_PATH_IMAGE002
, our target is to find a plane
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, come to minimize on the energy following objective function:
Figure 808930DEST_PATH_IMAGE004
(1)。
Wherein,
Figure 595806DEST_PATH_IMAGE006
Be a little p i To the plane FDistance,
Figure 412453DEST_PATH_IMAGE007
(equaling 1 in this research) is specified point p i Weight (equal 1, just will somewhat same weighting in this research).From formula 1, can release distance function
Figure 211781DEST_PATH_IMAGE006
In minimizing, play a crucial role.It should be noted that in this research, with the point that disperses p i Be positioned at (in the segmentation body) in the predefined spheroid.The restriction of this employing encirclement ball can not influence the versatility of algorithm, because for one group of known point in the space, has one ' encirclement ball ' forever.In Euclidean three dimensions, the degree of freedom on plane is 3, and this plane can be decided by three parameters.The plane FMay be defined as
Figure 817991DEST_PATH_IMAGE008
(2)。
Wherein,
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It is the definition plane FThree parameters.Though just can directly solve formula (1) with least squares approach, wherein
Figure 286199DEST_PATH_IMAGE010
Although, the efficient height, the result who is solved by least squares approach but is easy to be subjected to the interference of noise or exceptional value (as Fig. 6-Fig. 7).For this reason, we select to use the distance function by formula (3) definition D, it has relatively accurate solution, and to exceptional value insensitive [18-19]:
Figure 889218DEST_PATH_IMAGE011
, (3)。
Wherein, uIt is scalar.In this research, uSplit thickness with lung and be closely connected, will uBe made as described lung and split the only about half of value of thickness (for example from 1.0 to 1.5 millimeters).Here, we can be formulated as formula (1) again
Figure 595006DEST_PATH_IMAGE012
(4)。
Bring formula (1) and formula (3) into formula (4), by finding one group of parameters optimization (just
Figure 992489DEST_PATH_IMAGE013
) after, the plane fitting process is from energy minimization
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(formula (1) just) is converted into the energy maximization (formula (5) just).
(5)。
From formula (5), as can be seen, has only the point of working as to the plane FDistance less than uThe time, these points can have influence on objective function E'Since in the space density of point be used for discerning lung in the segmentation body split the plane (if any), doing, we advise using the function of formula (5) E' Divided by plane F
Figure 991221DEST_PATH_IMAGE013
Cross sectional area S.Like this, the problem that will solve based on the plane fitting of density is to find parameters optimization by maximization formula (6)
Figure 272686DEST_PATH_IMAGE013
,
Figure 217508DEST_PATH_IMAGE017
(6)。
Wherein ". " represents inner product,
Figure 632309DEST_PATH_IMAGE018
Be with respect to spheroid midplane F
Figure 637174DEST_PATH_IMAGE013
Cross sectional area, oWith rCenter and the radius of representing spheroid respectively.With
Figure 137425DEST_PATH_IMAGE019
Divided by S is in order to ensure objective function
Figure 620359DEST_PATH_IMAGE020
Be independent of outside the S, so objective function Can only be to determine by near the dot density the plane.
Because target function type (6) is not a convex function, therefore can not come parameters optimization with the gradient descent method.Though exhaustive search also is feasible, computation complexity is quite high.Such as for grid system
Figure 65433DEST_PATH_IMAGE021
, temporal computation complexity is
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, in practical operation, be difficult to be accepted.Therefore, need an effective optimization algorithm.
Next be to come parameters optimization with the method for integration ρ
Suppose parameter
Figure 274359DEST_PATH_IMAGE023
Fix, allow
Figure 663752DEST_PATH_IMAGE024
The expression plane FNorm
(7)。
Bring formula (7) into formula (6),
Figure 485263DEST_PATH_IMAGE026
Can be written as again
Figure 247683DEST_PATH_IMAGE027
(8)。
If variable mWith a vector of unit length n, when
Figure 491582DEST_PATH_IMAGE028
,
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, it is in the spheroid of radius that point exists with r
(9)。
Wherein,
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=2r/
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,
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It is the compartment distance of discrete ρ.Here, we will
Figure 776644DEST_PATH_IMAGE032
Be made as a little value (for example, 0.1 millimeter), A, B, C are a in the formula (10), b, the integration of c
Figure 943183DEST_PATH_IMAGE033
(10)。
ρ (
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), calculating target function formula (8) is:
Figure 21046DEST_PATH_IMAGE035
, (11)。
Wherein,
Figure 629882DEST_PATH_IMAGE036
,
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Here ρ – mWith uBe
Figure 938689DEST_PATH_IMAGE032
Integral multiple; Therefore, lWith kIt is integer.With the method for integration, the parameter that we can be optimized ρ,And can with computation complexity from Reduce to
Figure 124481DEST_PATH_IMAGE039
Final step is to optimize with refinement strategy progressively
Figure 570506DEST_PATH_IMAGE023
Allow
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Expression
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, it is right to draw parameters optimization by the formula of solving (12)
Figure 610509DEST_PATH_IMAGE041
Figure 922542DEST_PATH_IMAGE042
. (12)。
Though objective function
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Be not with
Figure 279891DEST_PATH_IMAGE023
Relevant convex function, but right at optimized parameter Near zone (
Figure 528656DEST_PATH_IMAGE043
) functional value with (describing among Figure 11) zone functional value big equally.Utilize this characteristics, it is right that we propose to search for optimized parameter effectively with refinement strategy progressively
Figure 433682DEST_PATH_IMAGE023
We at first use a relatively large error
Figure 976659DEST_PATH_IMAGE044
(search spacing just,
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Arrive
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) Near-optimization parameter in the search type in the space (12) is right
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Then, use the less error of predefine again
Figure 766630DEST_PATH_IMAGE048
(for example
Figure 224156DEST_PATH_IMAGE049
) by It is right to search for the final optimization pass parameter in the segmentation space of definition Consider the characteristics that lung splits, for fear of limited in local minimum, for initial ranging
Figure 249728DEST_PATH_IMAGE044
=0.1 is just enough.Such as, at Fig. 8-11, the sphere segmentation body that the some cloud that takes out from chest CT is checked constitutes,
Figure 245366DEST_PATH_IMAGE051
Figure 11 shows the three-dimensional point cloud objective function in the corresponding diagram 8
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, wherein,
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Utilize progressively refinement strategy, search Time from
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Reduce to
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Such as,
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With
Figure 967706DEST_PATH_IMAGE049
,
Figure 573655DEST_PATH_IMAGE023
The actual search time by original general 10 5Drop to 10 3
In order to raise the efficiency and guarantee desired accuracy, homogenize on the half unit spherome surface (just unified sampling) correspondence Candidate's normal vector
Figure 614609DEST_PATH_IMAGE024
Otherwise, when θValue hour (for example, θ=0, even establish
Figure 140269DEST_PATH_IMAGE045
Be different values,
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Also be identical.), will there be many similarity direction search to be repeated.In the present invention, for each self-generating
Figure 107274DEST_PATH_IMAGE023
To with normal vector n, specify θ=0:
Figure 675658DEST_PATH_IMAGE044
: π and α=0:
Figure 954193DEST_PATH_IMAGE044
/ sin (θ): π, the search parameters optimization is right
Figure 836698DEST_PATH_IMAGE023
Time by
Figure 334324DEST_PATH_IMAGE054
Drop to
Fig. 6-Figure 11 has verified the performance of fitting algorithm by the example of two and three dimensions.Although there are many exceptional values to disturb, line in the picture and surface (plane) come out by accurate recognition.Fig. 6 and Fig. 7 have shown the fitting a straight line of two-dimension picture mid point set.The result that the green line representative is drawn by least squares approach, and red line has been represented the result who is drawn by the density approximating method of being invented.Fig. 8 shows the three-dimensional point cloud atlas of the spheroid that a pair extracts from chest CT.The point cloud of Fig. 9 among visual Fig. 8 of inner product (formula (6) just) of vector sum normal vector.Figure 10 has shown fit Plane (representing with redness) by the method for using the present invention.Figure 11 shows the function of three-dimensional point cloud in the corresponding diagram 8
Lung splits the basic step of cutting apart: extremely shown in Figure 5 as Fig. 1.
Lung segmentation: it is to dwindle the search volume that lung splits identification that lung areas is cut apart (as Fig. 2) fundamental purpose, thereby improves counting yield, has eliminated and produce the possibility that lung splits identification error (false positive) beyond lung areas.
Lung areas segmentation: the lung areas of cutting apart is further segmented.At first, be that lung areas among each CT is created one and segmented grid system with axle alignment bounding box AABB, each cell size is 5 *5 *5 cubic millimeters.The center of segmentation spheroid is located at the summit of case system, is radius (as Fig. 3) with r.Because lung splits and generally has relatively low curvature, we are located at 10 millimeters with the r value.Why we be because the rotational invariance of spheroid and can efficient calculation spheroid cross sectional area in any direction with spheroid rather than cube.If compartment is divided into 5mm, in Euclidean three dimensions, any point GTo nearest summit ODistance (d)Less than
Figure 322374DEST_PATH_IMAGE058
The millimeter or 4.4 millimeters.
Point filters: in order to dwindle the search volume that lung splits, we are with two filter process lung areas.At first, because the brightness value that splits of lung (I ( p)) generally be from-900HU(Hausfeld unit) to-300HU, like this, the voxel outside this range of luminance values is disallowable as non-crack voxel.The second, because territory, most of lung split plot has higher brightness than circle zone (voxel) on every side, therefore some can be proposed in the regional area less than the voxel of intermediate intensity value.Regional area size definition interested is the spheroid size in the lung areas segmentation.
Lung splits identification: split by plane fitting identification lung in each segmentation body.Suppose one with o( x 0 , y 0 , z 0) be center, radius rBe 10 millimeters spheroid, through the point set to be selected of remainder in spheroid after the filter operation
Figure 529365DEST_PATH_IMAGE059
The objective function of application formula (6), come match by
Figure 705131DEST_PATH_IMAGE013
Optimal planar after the parametrization FSince represent voxel intensity value that lung splits in different detections with zones of different in identical detection in all very inequality, the weighted value of points all in the formula (6) is made as identical value (just
Figure 692679DEST_PATH_IMAGE060
), just only consider the plane fitting Density Distribution.For the planar structure (being that lung splits) in accurate each segmentation body of identification, only consider spheroid ( o) distance at center is less than 5 millimeters plane
Figure 979303DEST_PATH_IMAGE061
, just
Figure 368696DEST_PATH_IMAGE062
Mm has wherein defined in formula (2) f(o).Guaranteed spheroid like this
Figure 718294DEST_PATH_IMAGE063
In FCross sectional area greater than
Figure 865241DEST_PATH_IMAGE064
Mm 2Any point GThe distance that arrives nearest lattice summit so just has from the ball centre to the point-of-interest less than 5 millimeters (G)Less than 5 millimeters segmentation bodies (center is located at place, nearest summit).Therefore, considered in the fit procedure that lung splits have a few.Suppose that the optimal planar in the spheroid that identifies is
Figure 17874DEST_PATH_IMAGE065
, simultaneously
Figure 199457DEST_PATH_IMAGE066
With
Figure 717026DEST_PATH_IMAGE067
Show normal vector and (circle) transversal section center relevant respectively, if energy function with spherical volume
Figure 679165DEST_PATH_IMAGE068
Greater than predetermined threshold T, the circular cross sections that identifies (plane) is just regarded the part that (supposition is) lung splits as.In this invention, the application self-adapting threshold value T(for example,
Figure 307593DEST_PATH_IMAGE069
).Density basis fitting algorithm is used for all segmentation bodies will be identified lung and split (as Figure 12-shown in Figure 14).Figure 12-Figure 14 has represented that lung splits identification and classification results: Figure 12 one secondary CT image; Figure 13 splits (covering with different color) through the lung of identification, classification, and Figure 14 is that the final lung that obtains after having removed among Figure 13 the non-lung split plot represented by arrow splits that image is cut apart and classification chart.
Lung splits classification: except the identification lung splits, this new invention can be split lung simultaneously and classify.Suppose and in two adjacent spheroids, identify two lung broken face sheets F i With F j , be met as one of following condition, just suppose it two be belong to identical gathering (just ),
(1) F i Be F j 26-be communicated with the neighbour, with
Figure 32152DEST_PATH_IMAGE071
With
Figure 216009DEST_PATH_IMAGE072
;
(2).
Figure 645198DEST_PATH_IMAGE073
Suppose in adjacent spheroid and identify F i With F j Flat blocks, parameter
Figure 863689DEST_PATH_IMAGE074
Be used for controlling F i With F j Between curvature or allow the angle, parameter
Figure 723061DEST_PATH_IMAGE075
Be used for controlling F i With F j Between the continuity of distance.Here, by rule of thumb will
Figure 394214DEST_PATH_IMAGE074
Be made as 0.98 millimeter, similarly will
Figure 364444DEST_PATH_IMAGE075
Be made as 2 millimeters.Split the series arrangement of successively decreasing of quantity between accumulation area by the lung that is comprised in each gathering.In the lung of a left side, first (maximum) gathering is used for representing left oblique segmentation.In the right lung, first and second (maximum) assemble be used for respectively representing right oblique segmentation and laterally lung split (as Figure 12-Figure 14).Other all gathering is removed as non-lung split plot.
Test and result: the performance of inventive method in order to assess, we have collected 200 routine chronic obstructive pulmonary disease (COPD) chest CT data, and the lung that detects in these data with this method splits, and the result is compared on same group of data with a kind of method before.Recognition performance is measured with Hausdorff distance and tired knowledge error distance distribution (CEDD).The lung that identifies with these two kinds of methods splits nearly 95% within 2 millimeters distances, between average error probably at 0.6 millimeter, average crack maximum error is 16 millimeters.Computing time the aspect, this new method (being configured to the Duo i3 of Intel, 3.2 hertz of central processing units, the desktop computer of 6.0G internal memory) on Daepori energising brain was split identification general 8 minutes consuming time to the lung on the CT image.
In order to show that visually the new invention method splits performance in the identification at lung, we provide the example as Figure 15-Figure 17.In the example, the crack of identifying black line sign.
The example that Figure 18 to Figure 20 provides has shown that lung splits identification in serious bronchiectasis the is arranged abnormality detection of (cyst cystic fibrosis).
Figure 21 to Figure 23 is example that detection difficulty is bigger in splitting with new invention method identification lung.It is very difficult wanting the clear definite position of seeing that clearing lung-heat is split.And method [1] before is applied in this detection, be complete failure.
Here, described a full automatic lung and split identification and sorting technique, by utilize that lung splits in the image space the characteristics of Density Distribution.This method is the Free Surface of complexity to be discerned be converted into serial plane fitting, has characteristics such as versatility, high efficiency in method.
Though by being described with reference to its concrete enforcement, those of ordinary skill in the art will be appreciated that, can realize a lot of modifications, reinforcement and/or variation under the situation that does not break away from the spirit or scope of the present invention in the present invention.The present invention is intended to be limited by the scope of its claims and equivalent thereof.
List of references
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Claims (9)

1. one kind is the automatic calculating method that basic lung splits identification with the analytical plane approximating method, and the method comprises
The select target function; Parameters optimization ρParameters optimization is right
Figure 37549DEST_PATH_IMAGE001
2. in accordance with the method for claim 1, wherein the selection of objective function comprises:
Be decided to be the plane FFor
Figure 558660DEST_PATH_IMAGE002
Definition is to noise or the insensitive distance function of exceptional value DFor
Figure 808376DEST_PATH_IMAGE003
With
Figure 731332DEST_PATH_IMAGE004
In function
Figure 978774DEST_PATH_IMAGE005
Divided by plane F
Figure 987181DEST_PATH_IMAGE006
Cross sectional area S be in order to ensure objective function
Figure 978271DEST_PATH_IMAGE007
Be independent of outside the S, therefore, objective function
Figure 818051DEST_PATH_IMAGE007
Determine by near the dot density the plane.
3. parameters optimization wherein in accordance with the method for claim 1, ρ,Also comprise: the method with integration is come parameters optimization ρ
4. in accordance with the method for claim 1, wherein parameters optimization is right
Figure 233465DEST_PATH_IMAGE001
, also comprise: with progressively the next effective search parameter of thinning method is right
Figure 463589DEST_PATH_IMAGE001
5. also comprise in accordance with the method for claim 4:
With a relatively large error
Figure 258369DEST_PATH_IMAGE008
(search spacing
Figure 952656DEST_PATH_IMAGE009
Arrive
Figure 541900DEST_PATH_IMAGE010
)
Figure 524900DEST_PATH_IMAGE001
Search near-optimal parameter is right in the space
Figure 857792DEST_PATH_IMAGE011
With the littler error of predefine (for example
Figure 432310DEST_PATH_IMAGE013
) by
Figure 637026DEST_PATH_IMAGE014
It is right to search for the final optimization pass parameter in the segmentation space of definition
Figure 505101DEST_PATH_IMAGE015
6. the divided method of lung areas comprises and uses axle alignment bounding box AABB to build a segmentation system for each CT detects.
7. with the method for two filter process through the lung areas of over-segmentation.
8. in segmentation body to be selected, discern the planar fit method that lung splits.
9. split in the testing process at lung and split clustering method in order to discern different types of lung simultaneously.
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