CN115984288A - Image segmentation method based on key point detection and asymmetric geodesic growth model - Google Patents

Image segmentation method based on key point detection and asymmetric geodesic growth model Download PDF

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CN115984288A
CN115984288A CN202211532832.9A CN202211532832A CN115984288A CN 115984288 A CN115984288 A CN 115984288A CN 202211532832 A CN202211532832 A CN 202211532832A CN 115984288 A CN115984288 A CN 115984288A
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geodesic
image
curve
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CN115984288B (en
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陈达
孙玉竹
舒明雷
刘丽
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Shandong Institute of Artificial Intelligence
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Abstract

An image segmentation method based on key point detection and an asymmetric geodesic growth model can automatically detect a series of new key points and calculate an optimal connection curve between two adjacent key points until a closed contour is detected. Meanwhile, an anisotropic measurement function is adopted in the key point detection process, and a more accurate and more stable segmentation result is generated under different segmentation scenes by the provided direction characteristic which is based on the key point detection and can utilize the image gradient. Compared with a classical key point detection method, the method introduces the anisotropic measurement function, can overcome the problem that the curve is irrelevant to the motion direction, and obtains a more accurate segmentation result.

Description

Image segmentation method based on key point detection and asymmetric geodesic growth model
Technical Field
The invention relates to the field of computer vision, in particular to an image segmentation method based on a key point detection and asymmetric geodesic growth model.
Background
Since the minimum geodesic model was proposed (reference: cohen L D, kimmel R. Global minor for active control modules: A minor path approach [ J ]. International journel of computer vision,1997,24 (1): 57-78.), the energy minimization technique and the partial differential equation theory have been widely applied in the field of computer vision, such as image segmentation and image feature extraction. The geodesic model uses a continuous curve to express the target boundary of an image, and the basic idea is to define a weighted curve length as an energy function, and geodesic lines meeting requirements can be obtained by minimizing the energy function. The minimization of the energy function can be solved by solving a unique viscous solution of the corresponding static hamiltonian-jacobi-bellman equation. Essentially, by designing a measurement function capable of describing target characteristics, the related geodesic lines can accurately describe interested contours in the image, thereby realizing the purpose of image segmentation. Image features are a common way to delineate the boundaries of image regions. In the application of image segmentation based on geodesic lines, a geodesic line measurement function is often constructed by utilizing image gradient characteristics, so that the geodesic line energy function has a smaller value at a position with stronger image gradient, and therefore, the corresponding geodesic line can depict the image boundary. The minimum geodesic model can obtain the global minimum of the energy function, and can resist the negative effects of high noise and target area boundary fracture. Meanwhile, the global optimum characteristic also easily causes the geodesic line short cut problem, that is, the calculated geodesic line does not pass through the boundary of the target area. A geodesic growth model was proposed in the paper (Benmansour F, cohen L D. Fast object segmentation by growing minor patches from a single point on 2D or 3 Dimaps J. Journal of physical Imaging and Vision,2009,33 (2): 209-221) to address this drawback. Initialization of the model requires the user to provide a point on the boundary of the target region and use that point as the initial key point of the model. Meanwhile, the algorithm can automatically detect a series of new key points and calculate the optimal connection curve between two adjacent key points until a closed contour is detected. However, the geodesic growth model uses an isotropic metric function to calculate geodesic lines, i.e. the weighted length of the geodesic lines is independent of the direction of any point on the geodesic line, which may easily lead to erroneous image segmentation results. Meanwhile, the stopping criterion of the model is established on the basis of the isotropic measurement function, and the model is difficult to be applied to a geodesic growth model based on the anisotropic measurement function.
Disclosure of Invention
In order to overcome the defects of the above technologies, the invention provides a method which is based on the detection of key points and can utilize the direction characteristics of the image gradient to generate more accurate and more stable segmentation results under different segmentation scenes. The technical scheme adopted by the invention for overcoming the technical problems is as follows:
an image segmentation method based on a key point detection and asymmetric geodesic growth model comprises the following steps: a) Inputting a gray-scale image I
Figure BDA0003969901680000028
Representing a vector-valued gray image I, in which>
Figure BDA0003969901680000029
Is a real number space and Ω is a defined field of the image, and->
Figure BDA00039699016800000211
Define a field for an image, based on the image>
Figure BDA00039699016800000210
Giving a point z belonging to omega in a foreground region of the gray scale image I and a point p belonging to omega positioned on a target object boundary of the gray scale image I for a two-dimensional real number space; />
b) Calculating to obtain a geodesic distance map U p ；
c) Calculating to obtain a new simple open curve
Figure BDA00039699016800000212
d) Constructing asymmetric quadratic metric function
Figure BDA00039699016800000213
e) Calculating simple open curves
Figure BDA00039699016800000214
The optimal curves of any two adjacent key points are combined with all the mutually disjoint optimal curvesConstitutes a closed contour curve->
Figure BDA00039699016800000217
Contour curve>
Figure BDA00039699016800000216
Image segmentation is done by a given point p and including a point z.
Further, step b) comprises the following steps:
b-1) by the formula
Figure BDA0003969901680000021
Definition of [0,1 ] with respect to the Ripisces continuous curve gamma]Weighted curve length → Ω>
Figure BDA0003969901680000022
In formula (II)>
Figure BDA0003969901680000023
Is a scalar function, <' > based on>
Figure BDA0003969901680000024
A scalar function ^ is a set of all positive real numbers>
Figure BDA0003969901680000025
Is defined as->
Figure BDA0003969901680000026
γ (t) is a Ripisces continuous curve from point p in the grayscale image I to point x in the grayscale image I, t is [0,1 ]]One parameter of (a), γ' (t) is the first derivative of the Ripises continuous curve γ, (= d γ/dt), (| |. I | | |, is the modulus, α is a constant, 1 < α ≦ 5, exp (·) is an exponential function with e as the base,
Figure BDA0003969901680000027
is the gradient vector of the image at point x, <' >>
Figure BDA0003969901680000031
For the image at point yA gradient vector of (a);
b-2) geodesic distance diagram U p Is defined as
Figure BDA0003969901680000032
Is the set of all non-negative real numbers,
Figure BDA0003969901680000033
inf is the infimum of the function, lip ([ 0, 1)]Omega) is a continuous curve gamma: [0,1 ] containing all the Ripisces]Set of → Ω. Further, a geodesic distance map U p The following nonlinear partial differential equation is satisfied:
Figure BDA0003969901680000034
in the formula>
Figure BDA0003969901680000035
For the difference between the field of definition Ω of the image and the point p on the boundary of the target object, <' > H>
Figure BDA0003969901680000036
Is a gradient operator.
Further, step c) comprises the following steps:
c-1) extracting a boundary located in the gray image I
Figure BDA0003969901680000037
Point b,. Sup., is greater than>
Figure BDA0003969901680000038
argmin is such that U p (x) The value of the variable when the minimum value is reached;
c-2) calculating the geodesic
Figure BDA0003969901680000039
And geodetic line->
Figure BDA00039699016800000310
Geodetic wire>
Figure BDA00039699016800000311
Is connected point p to point b, geodetic line->
Figure BDA00039699016800000312
From point z to point b;
c-3) measuring the earth wire
Figure BDA00039699016800000313
And geodetic line->
Figure BDA00039699016800000314
Connected in series to give a new simple opening curve->
Figure BDA00039699016800000315
Novel simple opening curve->
Figure BDA00039699016800000316
Is defined as->
Figure BDA00039699016800000317
Figure BDA00039699016800000318
In the formula>
Figure BDA00039699016800000319
Connecting operators for curves; c-4) when t =0.5>
Figure BDA00039699016800000320
By means of the formula>
Figure BDA00039699016800000321
A direction is calculated which is in point p->
Figure BDA00039699016800000322
Wherein delta is a positive number, and delta is more than 0 and less than 0.01.
Further, the step c-2) comprises the following steps:
c-2.1) by the formula
Figure BDA0003969901680000041
The geodetic line counter-propagating from point b to point p is calculated>
Figure BDA0003969901680000042
Wherein s is [0,1 ]]Is measured in a time-domain measurement system, and,
Figure BDA0003969901680000043
geodesic route
Figure BDA0003969901680000044
Meets the boundary condition of being->
Figure BDA0003969901680000045
For the geodetic line->
Figure BDA0003969901680000046
Carrying out reparameterization operation calculation to obtain the geodetic line->
Figure BDA00039699016800000424
c-2.2) by the formula
Figure BDA0003969901680000047
The geodetic line counter-propagating from point p to point z is calculated>
Figure BDA0003969901680000048
Figure BDA0003969901680000049
Geodesic route
Figure BDA00039699016800000410
Meets a boundary condition of>
Figure BDA00039699016800000411
For the geodetic line->
Figure BDA00039699016800000412
Carrying out reparameterization operation calculation to obtain the geodetic line->
Figure BDA00039699016800000413
Further, step d) comprises the following steps:
d-1) asymmetric quadratic metric function
Figure BDA00039699016800000414
Is defined as->
Figure BDA00039699016800000415
Figure BDA00039699016800000416
In formula (II)>
Figure BDA00039699016800000417
For any vector>
Figure BDA00039699016800000418
ω (x) is a vector field, based on>
Figure BDA00039699016800000419
Lambda and epsilon are both constant, are present>
Figure BDA00039699016800000420
Is a rotation matrix of a rotation angle pi/2, which is multiplied by the number>
Figure BDA00039699016800000421
Representing a scalar quantity
Figure BDA00039699016800000422
Is transposed, g (x) is a scalar function, and->
Figure BDA00039699016800000423
Beta is a constant. />
Preferably, the steps0 < λ.ltoreq.10 in step d-1), ε =1 -4 ，0＜β≤5。
Further, step e) comprises the steps of:
e-1) building a set comprising n ordered keypoints
Figure BDA00039699016800000521
n is not less than 3, wherein p i For a new simple opening curve>
Figure BDA0003969901680000051
The ith point of (i = {1, ·, n }, p = {1, · 1 Is a new simple opening curve->
Figure BDA0003969901680000052
Left end point of (a), p n For a new simple opening curve>
Figure BDA0003969901680000053
Right-hand end point of (1), point p ∈ [ p ] 1 ,p n ]Product of quantity
Figure BDA0003969901680000054
Is->
Figure BDA0003969901680000055
The first derivative of (a);
e-2) geodesic distance map
Figure BDA0003969901680000056
Is defined as->
Figure BDA0003969901680000057
Figure BDA0003969901680000058
By the formula
Figure BDA0003969901680000059
Calculating a region->
Figure BDA00039699016800000522
Mu is a threshold value, and tau is a threshold value; e-3) based on an asymmetric quadratic metric function >>
Figure BDA00039699016800000519
In a region->
Figure BDA00039699016800000523
Upper calculation geodesic distance->
Figure BDA00039699016800000510
Figure BDA00039699016800000511
The geodetic distance->
Figure BDA00039699016800000512
The following partial differential equation is satisfied: />
Figure BDA00039699016800000513
Wherein->
Figure BDA00039699016800000514
Is an arbitrary vector, is selected>
Figure BDA00039699016800000515
Product of quantity
Figure BDA00039699016800000516
Representing a scalar ω (x) T />
Figure BDA00039699016800000517
A positive component of (a);
e-4) constructing the latest key point p i Neighborhood of (2)
Figure BDA00039699016800000518
i = {1,. N-1}, utilizing an asymmetric quadratic metric function->
Figure BDA0003969901680000061
In a region->
Figure BDA00039699016800000620
Up-to-date computation of the keypoint p i Is measured by the geodesic distance->
Figure BDA0003969901680000062
Figure BDA0003969901680000063
The geodetic distance->
Figure BDA0003969901680000064
The following partial differential equation is satisfied: />
Figure BDA0003969901680000065
Figure BDA0003969901680000066
Is boundary->
Figure BDA0003969901680000067
At any point on
Figure BDA0003969901680000068
By solving the equation->
Figure BDA0003969901680000069
Calculate a connection point x to the latest keypoint p i Is measured on the ground line->
Figure BDA00039699016800000610
Is->
Figure BDA00039699016800000611
The first derivative of (a) is,
Figure BDA00039699016800000612
Figure BDA00039699016800000613
is a vector field, is>
Figure BDA00039699016800000614
Figure BDA00039699016800000615
In-situ geodesic for images
Figure BDA00039699016800000616
Is greater than or equal to>
Figure BDA00039699016800000617
Is a function of a scalar quantity,
Figure BDA00039699016800000618
Figure BDA00039699016800000619
by means of the formula>
Figure BDA0003969901680000071
The boundary->
Figure BDA0003969901680000072
The Euclidean length l (x) of the geodesic line corresponding to the upper point;
e-5) merging the target key points p * Is defined as p i+1 ，
Figure BDA0003969901680000073
Order to
Figure BDA0003969901680000074
By means of the formula>
Figure BDA0003969901680000075
Calculating a connection point p * To the latest key point p i Is measured on the ground line->
Figure BDA0003969901680000076
Is->
Figure BDA0003969901680000077
Is first derivative of->
Figure BDA0003969901680000078
Figure BDA0003969901680000079
Is a vector field, is>
Figure BDA00039699016800000710
For an image at a geodetic point->
Figure BDA00039699016800000711
In a gradient vector of (a), is combined with a gradient vector of (b)>
Figure BDA00039699016800000712
In the form of a function of a scalar quantity,
Figure BDA00039699016800000713
Figure BDA00039699016800000714
e-6) updating the set of keypoints
Figure BDA00039699016800000715
And target keypoint p * ＝p i+1 ；
e-7) repeating steps e-2) to e-6) until the geodesic distance
Figure BDA0003969901680000081
Wherein
Figure BDA0003969901680000082
Preferably, in step e-2) 8. Ltoreq. Mu. Ltoreq.15, τ =2 or τ =2.5.
The invention has the beneficial effects that: the image segmentation method based on the key point detection and the asymmetric geodesic growth model can automatically detect a series of new key points and calculate the optimal connection curve between two adjacent key points until a closed contour is detected. Meanwhile, an anisotropic measurement function is adopted in the key point detection process, and a more accurate and more stable segmentation result is generated under different segmentation scenes by using the direction characteristic of the image gradient based on the key point detection.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention is further illustrated with reference to fig. 1.
An image segmentation method based on key point detection and an asymmetric geodesic growth model comprises the following steps: a) Inputting a gray-scale image I
Figure BDA0003969901680000083
Represents a vector-valued gray-scale image I, in which->
Figure BDA0003969901680000084
Is a space of real numbers Ω is a defined field of the image, R>
Figure BDA0003969901680000085
Defining a field for an image>
Figure BDA0003969901680000086
And for a two-dimensional real number space, giving a point z E omega positioned in a foreground region of the gray scale image I, and giving a point p E omega positioned on the boundary of a target object of the gray scale image I.
b) Calculating to obtain a geodesic distance map U p 。
c) Calculating to obtain a new simple open curve
Figure BDA0003969901680000087
d) Constructing asymmetric quadratic metric function
Figure BDA0003969901680000089
/>
e) Calculating simple open curves
Figure BDA0003969901680000088
The optimal curves of any two adjacent key points are combined into a closed contour curve->
Figure BDA00039699016800000810
Contour curve->
Figure BDA00039699016800000812
Image segmentation is done by a given point p and including a point z.
This initialization of the keypoint-based detection and asymmetric geodesic growth model requires the user to provide a point on the boundary of the target area and to use this point as the initial keypoint of the model. Meanwhile, the algorithm can automatically detect a series of new key points and calculate the optimal connection curve between two adjacent key points until a closed contour is detected. Meanwhile, an anisotropic measurement function is adopted in the key point detection process, and a more accurate and more stable segmentation result is generated under different segmentation scenes by using the direction characteristic of the image gradient based on the key point detection. Compared with a classical key point detection method, the method introduces the anisotropic measurement function, can overcome the problem that the curve is irrelevant to the motion direction, and obtains a more accurate segmentation result.
The step b) comprises the following steps:
b-1) by the formula
Figure BDA0003969901680000091
Definition of [0,1 ] for Riposis continuous Curve γ]Weighted curve length → Ω>
Figure BDA0003969901680000092
In the formula>
Figure BDA0003969901680000093
Is a scalar function, is greater than or equal to>
Figure BDA0003969901680000094
A scalar function ^ is a set of all positive real numbers>
Figure BDA0003969901680000095
Is defined as->
Figure BDA0003969901680000096
γ (t) is a Ripisces continuous curve from point p in the grayscale image I to point x in the grayscale image I, t is [0,1 ]]One parameter of (a), γ '(t) is the first derivative of the Ripises continuous curve γ, γ' (t) = d γ/dt, | | | | | | is the modulus, α is a constant, 1 < α ≦ 5, exp (·) is an exponential function with e as the base,
Figure BDA0003969901680000097
for a gradient vector of an image at point x>
Figure BDA0003969901680000098
Is the gradient vector of the image at point y.
b-2) geodesic distance diagram U p Is defined as U p (x)，
Figure BDA0003969901680000099
Is the set of all non-negative real numbers,
Figure BDA00039699016800000910
inf is the infimum of the function, lip ([ 0, 1)]Omega) is a continuous curve gamma: [0,1 ] containing all the Ripisces]Set of → omega. Further, a geodesic distance map U p The following nonlinear partial differential equation is satisfied:
Figure BDA00039699016800000911
in the formula>
Figure BDA00039699016800000912
For the difference between the field of definition Ω of the image and the point p on the boundary of the target object, <' > H>
Figure BDA00039699016800000913
Is a gradient operator. The numerical solution of the partial differential equation can be derived from the classical fast marching algorithm (reference: sethian J A. Fast marching methods [ J.)]SIAM review,1999,41 (2): 199-235).
The step c) comprises the following steps:
c-1) extracting a boundary located in the gray image I
Figure BDA0003969901680000101
Point b, & ltR & gt>
Figure BDA0003969901680000102
argmin is such that U p (x) The value of the variable when the minimum value is reached.
c-2) calculating geodesic lines
Figure BDA0003969901680000103
And geodetic line->
Figure BDA0003969901680000104
Geodetic wire>
Figure BDA0003969901680000105
Is connected point p to point b, geodetic line->
Figure BDA0003969901680000106
Connecting point z to point b. />
c-3) measuring the earth wire
Figure BDA0003969901680000107
And geodesic line>
Figure BDA0003969901680000108
In series a new simple opening curve>
Figure BDA0003969901680000109
Novel simple opening curve>
Figure BDA00039699016800001010
Is defined as->
Figure BDA00039699016800001011
Figure BDA00039699016800001012
In the formula>
Figure BDA00039699016800001013
The operators are connected for the curves. c-4) when t =0.5, is selected>
Figure BDA00039699016800001014
By the formula
Figure BDA00039699016800001015
Calculating a direction ^ at point p>
Figure BDA00039699016800001016
Wherein delta is a positive number, and delta is more than 0 and less than 0.01.
The step c-2) comprises the following steps:
c-2.1) by the formula
Figure BDA00039699016800001017
The geodetic line counter-propagating from point b to point p is calculated>
Figure BDA00039699016800001018
Wherein s is [0,1 ]]Is measured in a single measurement unit, and is,
Figure BDA00039699016800001019
geodesic route
Figure BDA00039699016800001020
Meets a boundary condition of>
Figure BDA00039699016800001021
For the geodetic line->
Figure BDA00039699016800001022
Carrying out reparameterization operation calculation to obtain geodesic line>
Figure BDA00039699016800001023
c-2.2) by the formula
Figure BDA00039699016800001024
The geodetic line counter-propagating from point p to point z is calculated>
Figure BDA0003969901680000111
Figure BDA0003969901680000112
Geodetic line path->
Figure BDA0003969901680000113
Meets the boundary condition of being->
Figure BDA0003969901680000114
For geodetic lines &>
Figure BDA0003969901680000115
Carrying out reparameterization operation calculation to obtain the geodetic line->
Figure BDA0003969901680000116
The step d) comprises the following steps:
d-1) asymmetric quadratic metric function
Figure BDA0003969901680000117
Is defined as->
Figure BDA0003969901680000118
Figure BDA0003969901680000119
In formula (II)>
Figure BDA00039699016800001110
Is an arbitrary vector, is->
Figure BDA00039699016800001111
ω (x) is a vector field, and->
Figure BDA00039699016800001112
Lambda and epsilon are both constant, are present in the blood>
Figure BDA00039699016800001113
Is a rotation matrix of a rotation angle pi/2, which is multiplied by the number>
Figure BDA00039699016800001114
Representing a scalar>
Figure BDA00039699016800001115
Is transposed, g (x) is a scalar function, and->
Figure BDA00039699016800001116
Beta is a constant.
In the step d-1), λ is more than 0 and less than or equal to 10, and epsilon =1 -4 ，0＜β≤5。
Step e) comprises the following steps:
e-1) building a set comprising n ordered keypoints
Figure BDA00039699016800001124
n is not less than 3, wherein p i Is a new simple opening curve->
Figure BDA00039699016800001117
The ith point above, i = {1,.., n }, p 1 Is a new simple opening curve->
Figure BDA00039699016800001118
Left end point of p n For a new simple opening curve>
Figure BDA00039699016800001119
Right-hand end point of (1), point p ∈ [ p ] 1 ,p n ]Product of quantity
Figure BDA00039699016800001120
Is->
Figure BDA00039699016800001121
The first derivative of (a).
e-2) geodesic distance map
Figure BDA00039699016800001122
Is defined as>
Figure BDA00039699016800001123
Figure BDA0003969901680000121
This equation can be formulated by classical fast marching algorithms (reference: sethian J A. Fast marching methods [ J.)]SIAM review,1999,41 (2): 199-235). />
Figure BDA0003969901680000122
By the formula
Figure BDA0003969901680000123
Calculating a region->
Figure BDA00039699016800001215
μ is the threshold and τ is the threshold.
e-3) using asymmetric quadratic metric functions
Figure BDA00039699016800001216
In a region->
Figure BDA00039699016800001217
Upper calculation geodesic distance->
Figure BDA0003969901680000124
Figure BDA0003969901680000125
The geodetic distance->
Figure BDA0003969901680000126
The following partial differential equation is satisfied:
Figure BDA0003969901680000127
this equation can be solved by Hamilton fast marching algorithm (ref: mirebeau J M. Riemannian fast-marching on cartesian grids, using voronoi's first reduction of quadratic forms J]SIAM Journal on Numerical Analysis,2019,57 (6): 2608-2655). Wherein->
Figure BDA00039699016800001220
The vector is an arbitrary vector, and the vector is a vector,
Figure BDA0003969901680000128
number and/or greater>
Figure BDA0003969901680000129
Representing a scalar ω (x) T />
Figure BDA00039699016800001210
The positive component of (a).
e-4) constructing the latest key point p i Neighborhood of (2)
Figure BDA00039699016800001211
i = {1,. N-1}, utilizing an asymmetric quadratic metric function->
Figure BDA00039699016800001218
In a region->
Figure BDA00039699016800001219
Up-to-date computation of the keypoint p i In measuring the distance of the ground line>
Figure BDA00039699016800001212
Figure BDA00039699016800001213
The geodetic distance->
Figure BDA00039699016800001214
The following partial differential equation is satisfied:
Figure BDA0003969901680000131
Figure BDA0003969901680000132
is boundary->
Figure BDA0003969901680000133
At any point on
Figure BDA0003969901680000134
By solving the equation->
Figure BDA0003969901680000135
Calculate a connection point x to the latest keypoint p i Is measured on the ground line->
Figure BDA0003969901680000136
Is->
Figure BDA0003969901680000137
The first derivative of (a) is,
Figure BDA0003969901680000138
Figure BDA0003969901680000139
is a vector field, is>
Figure BDA00039699016800001310
Figure BDA00039699016800001311
In-situ geodesic for images
Figure BDA00039699016800001312
Is greater than or equal to>
Figure BDA00039699016800001313
Is a function of a scalar quantity,
Figure BDA00039699016800001314
Figure BDA00039699016800001315
by means of the formula>
Figure BDA00039699016800001316
The boundary->
Figure BDA00039699016800001317
The upper point corresponds to the euclidean length l (x) of the geodesic.
e-5) merging the target key points p * Is defined as p i+1 ，
Figure BDA0003969901680000141
Make->
Figure BDA0003969901680000142
By means of the formula>
Figure BDA0003969901680000143
Calculating a connection point p * To the latest key point p i Is measured on the ground line->
Figure BDA0003969901680000144
Is->
Figure BDA0003969901680000145
The first derivative of (a) is,
Figure BDA0003969901680000146
Figure BDA0003969901680000147
is a vector field, is>
Figure BDA0003969901680000148
For an image at a geodetic point->
Figure BDA0003969901680000149
Is greater than or equal to>
Figure BDA00039699016800001410
In the form of a function of a scalar quantity,
Figure BDA00039699016800001411
Figure BDA00039699016800001412
e-6) updating the set of keypoints
Figure BDA00039699016800001415
And target keypoint p * ＝p i+1 。
e-7) repeating the steps e-2) to e-6) until the geodesic distance
Figure BDA00039699016800001413
Wherein
Figure BDA00039699016800001414
In step e-2), 8 ≦ μ ≦ 15, τ =2 or τ =2.5.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. An image segmentation method based on a key point detection and asymmetric geodesic growth model is characterized by comprising the following steps:
a) Inputting a gray-scale image I
Figure FDA0003969901670000011
Representing a vector-valued gray image I, in which>
Figure FDA0003969901670000012
Is a real number space and Ω is a defined field of the image, and->
Figure FDA0003969901670000013
Define a field for an image, based on the image>
Figure FDA0003969901670000014
Giving a point z belonging to omega in a foreground region of the gray scale image I and a point p belonging to omega positioned on a target object boundary of the gray scale image I for a two-dimensional real number space;
b) Calculating to obtain a geodesic distance map U p ；
c) Calculating to obtain a new simple open curve
Figure FDA0003969901670000015
d) Constructing asymmetric quadratic metric function
Figure FDA0003969901670000016
e) Calculate simple open curve
Figure FDA0003969901670000017
Forming a closed contour curve based on the optimal curves of any two adjacent key points and all the mutually disjoint optimal curves>
Figure FDA0003969901670000018
Contour curve pick>
Figure FDA0003969901670000019
Image segmentation is accomplished by a given point p and including a point z.
2. The method of image segmentation based on keypoint detection and an asymmetric geodesic growth model according to claim 1, characterized in that step b) comprises the following steps:
b-1) by the formula
Figure FDA00039699016700000110
Definition of [0,1 ] with respect to the Ripisces continuous curve gamma]Weighted curve length → Ω>
Figure FDA00039699016700000111
In the formula>
Figure FDA00039699016700000112
Is a scalar function, is greater than or equal to>
Figure FDA00039699016700000113
A scalar function ^ is a set of all positive real numbers>
Figure FDA00039699016700000114
Is defined as->
Figure FDA00039699016700000115
γ (t) is a Ripisces continuous curve from point p in the grayscale image I to point x in the grayscale image I, t is [0,1 ]]One parameter of (a), γ' (t) is the first derivative of the Ripises continuous curve γ, (= d γ/dt), (| |. I | | |, is the modulus, α is a constant, 1 < α ≦ 5, exp (·) is an exponential function with e as the base,
Figure FDA00039699016700000116
is the gradient vector of the image at point x, <' >>
Figure FDA00039699016700000117
Is shown as a drawingA gradient vector like at point y;
b-2) geodesic distance diagram U p Is defined as U p (x)，
Figure FDA00039699016700000118
Figure FDA00039699016700000119
Is the set of all non-negative real numbers,
Figure FDA0003969901670000021
inf is the infimum of the function, lip ([ 0,1 ]]Omega) is a continuous curve gamma: [0,1 ] containing all the Ripisces]Set of → omega.
3. The method of claim 2, wherein the geodesic distance map U is a geodesic distance map p The following nonlinear partial differential equation is satisfied:
Figure FDA0003969901670000022
in the formula>
Figure FDA0003969901670000023
For the difference between a field of definition Ω of the image and a point p on the boundary of the target object, based on the difference>
Figure FDA0003969901670000024
Is a gradient operator.
4. The method of image segmentation based on keypoint detection and asymmetric geodesic growth models according to claim 2, characterized in that step c) comprises the following steps:
c-1) extracting a boundary located in the gray image I
Figure FDA0003969901670000025
Point b,. Sup., is greater than>
Figure FDA0003969901670000026
argmin is such that U p (x) The value of the variable when the minimum value is reached;
c-2) calculating the geodesic
Figure FDA0003969901670000027
And geodetic line->
Figure FDA0003969901670000028
Figure FDA0003969901670000029
Geodetic wire>
Figure FDA00039699016700000210
In order to connect point p to point b, geodesic lines>
Figure FDA00039699016700000211
From point z to point b;
c-3) grounding wire
Figure FDA00039699016700000212
And geodetic line->
Figure FDA00039699016700000213
Connected in series to give a new simple opening curve->
Figure FDA00039699016700000214
New simple open curve
Figure FDA00039699016700000215
Is defined as->
Figure FDA00039699016700000216
Figure FDA00039699016700000217
In the formula
Figure FDA00039699016700000218
Connecting operators for curves; c-4) when t =0.5>
Figure FDA00039699016700000219
By the formula
Figure FDA00039699016700000220
Calculating a direction theta at the point p p In the formula, delta is a positive number, and delta is more than 0 and less than 0.01.
5. The method of image segmentation based on keypoint detection and asymmetric geodesic growth models according to claim 4, characterized in that step c-2) comprises the following steps:
c-2.1) by the formula
Figure FDA0003969901670000031
Calculating to obtain the geodesic line reversely propagated from the point b to the point p
Figure FDA0003969901670000032
Wherein s is [0,1 ]]Is measured in a time-domain measurement system, and,
Figure FDA0003969901670000033
geodetic line path->
Figure FDA0003969901670000034
Meets the boundary condition of being->
Figure FDA0003969901670000035
For the geodetic line->
Figure FDA0003969901670000036
Carrying out reparameterization operation calculation to obtain geodesic line>
Figure FDA0003969901670000037
c-2.2) by the formula
Figure FDA0003969901670000038
Calculating to obtain the geodesic line reversely propagated from the point p to the point z
Figure FDA0003969901670000039
Figure FDA00039699016700000310
Geodetic line path->
Figure FDA00039699016700000311
Meets the boundary condition of being->
Figure FDA00039699016700000312
For geodetic lines &>
Figure FDA00039699016700000313
Carrying out reparameterization operation calculation to obtain the geodetic line->
Figure FDA00039699016700000314
6. The method of claim 2, wherein step d) comprises the steps of:
d-1) asymmetric quadratic metric function
Figure FDA00039699016700000315
Is defined as->
Figure FDA00039699016700000316
Figure FDA00039699016700000317
In formula (II)>
Figure FDA00039699016700000318
Is an arbitrary vector, is->
Figure FDA00039699016700000319
ω (x) is a vector field, and->
Figure FDA00039699016700000320
Lambda and epsilon are both constant, are present>
Figure FDA00039699016700000321
Is a rotation matrix of a rotation angle pi/2, which is multiplied by the number>
Figure FDA00039699016700000322
Representing a scalar quantity
Figure FDA00039699016700000323
Is transposed, g (x) is a scalar function, and->
Figure FDA0003969901670000041
Beta is a constant.
7. The method of claim 6, wherein the image segmentation based on keypoint detection and an asymmetric geodesic growth model is performed by: in the step d-1), λ is more than 0 and less than or equal to 10, and epsilon =1 -4 ，0＜β≤5。
8. The method of claim 6, wherein step e) comprises the steps of:
e-1) building a set comprising n ordered keypoints
Figure FDA0003969901670000042
Wherein p is i Is a new simple opening curve->
Figure FDA0003969901670000043
The ith point of (i = {1, ·, n }, p = {1, · 1 Is a new simple opening curve->
Figure FDA0003969901670000044
Left end point of p n Is a new simple opening curve->
Figure FDA0003969901670000045
Right end point of (c), point p ∈ [ p ] 1 ,p n ]Product of quantity<p 1 -p n ,θ p >＝0，
Figure FDA0003969901670000046
Figure FDA0003969901670000047
Is->
Figure FDA0003969901670000048
The first derivative of (a);
e-2) geodesic distance map
Figure FDA0003969901670000049
Is defined as>
Figure FDA00039699016700000410
Figure FDA00039699016700000411
Figure FDA00039699016700000412
By means of a formula>
Figure FDA00039699016700000413
Calculating a region->
Figure FDA00039699016700000414
Figure FDA00039699016700000415
Mu is a threshold value, and tau is a threshold value;
e-3) using asymmetric quadratic metric functions
Figure FDA00039699016700000416
In a region->
Figure FDA00039699016700000417
On-counting geodesic distance>
Figure FDA00039699016700000418
Figure FDA00039699016700000419
The geodetic distance->
Figure FDA00039699016700000420
The following partial differential equation is satisfied:
Figure FDA00039699016700000421
wherein->
Figure FDA00039699016700000422
Is a vector of any one of the vectors,
Figure FDA0003969901670000051
number and/or greater>
Figure FDA0003969901670000052
Represents a scalar pick>
Figure FDA0003969901670000053
A positive component of (a);
e-4) constructing the latest key point p i Neighborhood of (2)
Figure FDA0003969901670000054
Utilizing an asymmetric quadratic metric function->
Figure FDA0003969901670000055
In a region->
Figure FDA0003969901670000056
Up-to-date computation of the keypoint p i Is measured by the geodesic distance->
Figure FDA0003969901670000057
Figure FDA0003969901670000058
The geodetic distance->
Figure FDA0003969901670000059
The following partial differential equation is satisfied:
Figure FDA00039699016700000510
Figure FDA00039699016700000511
Figure FDA00039699016700000512
is boundary->
Figure FDA00039699016700000513
At any point on
Figure FDA00039699016700000514
By solving the equation->
Figure FDA00039699016700000515
Computing a join point x to the latest keypoint p i Is measured on the ground line->
Figure FDA00039699016700000516
Figure FDA00039699016700000517
Is->
Figure FDA00039699016700000518
The first derivative of (a) is,
Figure FDA00039699016700000519
Figure FDA00039699016700000520
is a vector field, is>
Figure FDA00039699016700000521
Figure FDA00039699016700000522
On the geodetic line for an image>
Figure FDA00039699016700000523
Is greater than or equal to>
Figure FDA00039699016700000524
Is a function of a scalar quantity,
Figure FDA0003969901670000061
Figure FDA0003969901670000062
by means of the formula>
Figure FDA0003969901670000063
Calculated boundary>
Figure FDA0003969901670000064
The Euclidean length l (x) of the geodesic line corresponding to the upper point; />
e-5) matching the target keypoint p * Is defined as p i+1 ，
Figure FDA0003969901670000065
Make/combine>
Figure FDA0003969901670000066
By means of the formula>
Figure FDA0003969901670000067
Calculating a connection point p * To the latest key point p i Is measured on the ground line->
Figure FDA0003969901670000068
Figure FDA0003969901670000069
Is->
Figure FDA00039699016700000610
The first derivative of (a) is,
Figure FDA00039699016700000611
Figure FDA00039699016700000612
is a vector field, is>
Figure FDA00039699016700000613
Figure FDA00039699016700000614
For an image at a geodetic point->
Figure FDA00039699016700000615
In a gradient vector of (a), is combined with a gradient vector of (b)>
Figure FDA00039699016700000616
Is a scalar function, is greater than or equal to>
Figure FDA00039699016700000617
Figure FDA0003969901670000071
e-6) updating the set of keypoints
Figure FDA0003969901670000072
And target keypoint p * ＝p i+1 ；
e-7) repeating steps e-2) to e-6) until the geodesic distance
Figure FDA0003969901670000073
Wherein
Figure FDA0003969901670000074
9. The method of image segmentation based on keypoint detection and asymmetric geodesic growth models of claim 8, characterized in that: in the step e-2), mu is more than or equal to 8 and less than or equal to 15, and tau =2 or tau =2.5.
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