CN106875365B - Spill image partition method based on GSA - Google Patents
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Abstract
The invention discloses a kind of then the spill image partition method based on GSA is completed the convergence of initial snake element using GSA model, the final convergence of snake element is completed finally by greedy algorithm first to original image progress gray proces；Image is normalized in method of the invention, balanced continuous force, bending force and image force, under the premise of guaranteeing snake element original series, allow snake element into being rapidly and uniformly fitted to around objective contour, it is especially fitted in the concave regions of image, while remaining GSA model high efficiency calculating advantage, the precision of contours extract is improved, the method especially proposed has handled spill contour extraction of objects problem well.
Description
Technical field
The present invention relates to a kind of spill image partition method based on GSA
Background technique
In the research of computer vision, traditional target detection mainly passes through a bottom-up process to image
It is split and edge detection.Feature possessed by the less consideration target of this process itself, therefore the deficient validity.Snake mould
Type is also known as active contour model, proposes that this method is in the fields such as image segmentation, detection, identification by Kass et al. earliest
It is widely used.Different from traditional images dividing method, Snake model takes full advantage of the speciality of target image itself, figure
The information such as size, position, the shape of picture are combined with features such as the gray scale of image, gradients.Currently, Snake model has become figure
As the most commonly used method of target detection.
There are some problems for traditional Snake model, as external force catching range is smaller, topology difficult into sunk area
It is constant etc..Especially when handling spill figure, basic Snake model can not usually converge to sunk area.It is above-mentioned to make up
Deficiency, some innovatory algorithms are proposed in succession, wherein being more successfully that Xu et al. proposes GVF model, are had been applied to very much
The practical problem of spill image segmentation, but the model, for some biggish spill figures of invagination curvature, effect is still undesirable.This
Outside, GVF model is to improve to obtain by basic Snake model, the energy function of basic Snake model need with compared with
More first derivation, second order derivation and integral operationes, therefore there is a problem of that computationally intensive, computational efficiency is not high, GVF model
Equally exist this respect problem.
Greedy snake algorithm (Greedy Snake Algorithm, GSA) is that a kind of improvement is larger and more successful
Snake model.GSA algorithm has used for reference the external force of Snake model, internal force comprehensive function in the basic thought of snake vegetarian refreshments, but uses
Different from the energy function of traditional Snake model, the especially energy function of GSA without completing a large amount of derivation and integral fortune
It calculates, therefore computational efficiency with higher.In traditional GSA algorithm, the value range of image force is excessive in energy function, in turn
So that resultant force is almost influenced by image force, the deficiency of GSA model is that the profile of spill image can not be extracted.
Summary of the invention
The technical problem to be solved by the present invention is, processing spill image effect low for Snake model computational efficiency is paid no attention to
The problem of thinking designs a kind of spill image partition method based on GSA, and image is normalized in this method, and equilibrium is even
Continuous power, bending force and image force allow snake element into being rapidly and uniformly fitted to target under the premise of guaranteeing snake element original series
Around profile, especially it is fitted in the concave regions of image.
The technical solution that the present invention solves technical problem is: carrying out gray proces to original image first, then uses one
The improved GSA model of kind completes the convergence of initial snake element, and the final convergence of snake element is completed finally by a kind of greedy algorithm；Including
Following specific steps:
Step 1: gray scale pretreatment is carried out to image；
Step 2: determining that object boundary is initial profile point in the picture, i.e. snake element；
Step 3: it is deformed by external force and internal force using to the curve being formed by connecting by snake element by GSA algorithm,
The sum of all snake element energy are minimized, initial snake element is made to be finally displaced into objective contour marginal position, and are ensured between snake element
It orderly and is uniformly distributed, completes the initial convergence of snake element；
Step 4: the final convergence of snake element is completed using greedy strategy, all snake elements are locked to image target to be split
On boundary, the especially sunk area of image；
Step 5: sequential connection snake element forms objective contour, completes image segmentation.
More specifically, carrying out gray scale pretreatment to image according to following calculating process in the step 1:
The formula of gray scale pretreatment are as follows:
Gray(v(i),j)=(Δ1R(v(i),j)+Δ2G(v(i),j)+Δ3B(v(i),j)) > > k
In above formula, Gray(v (i), j)Indicate that the gray value of some pixel v (i), j are i snake element neighborhood GpiJ-th interior of picture
Element, formula R(v (i), j)、G(v (i), j)、B(v (i), j)Respectively indicate red, green, blue channel value, △1、△2、△3As weight system
Number, k indicate displacement coefficient, △1=38, △2=75, △3=15, k=7.
More specifically, completing the initial convergence of snake element according to following calculating process in the step 3；Assuming that snake prime sequences
It is made of N number of snake vegetarian refreshments, comprehensive force functionIt is as follows:
V (i) indicates that i-th of snake element, j are i snake element neighborhood GpiJ-th interior of pixel, the value of j and a step of snake element are moved
Dynamic distance δ is related；One moved further calculation method are as follows: j=i ± δ, δ ∈ { 0,1,2 ... }, δ indicate one moved further of snake vegetarian refreshments away from
From；EcontIndicate continuous force, EcurvIndicate bending force, EimageIndicate image force；α, β, γ are that warp parameter is used to control each group
At the weight relationship of part；The calculating target of entire GSA is: in the neighborhood Gp of snake vegetarian refreshments iiIn calculate a pixel make it is comprehensive
Resultant force E (v (i), j) value minimizes, and as the snake vegetarian refreshments of next moved further；
EcontThe calculation method of continuous force is as follows:
Wherein, dV (i, j)-v (i+1)Indicate i-th of snake element neighborhood GpiIn j-th pixel and i+1 snake element straight line away from
From；davrIndicate the average distance between all snake vegetarian refreshments, calculation method isContinuously
Power EcontCalculating aims at: discovery GpiIn with i+1 snake element distance closest to a pixel of average distance, effect is
Control uniform distribution of forces of the snake vegetarian refreshments in profile space；D after each round iterationavrIt needs to recalculate；
Bending force EcurvEnergy function it is as follows:
In above formula, | v (i-1) -2v (i, j)+v (i+1) | it indicates to i-1, i+1 snake elements and GpiIn pixel j carry out and
Vector calculates；Bending force EcurvCalculating aim at: discovery GpiIn with former and later two snake vegetarian refreshments constitute vector angle it is the smallest
Pixel, effect are the smoothness of snake vegetarian refreshments；
The specific energy function E of image forceimageIt is as follows:
Wherein I (v (i), j) indicates GpiIn j-th of pixel gradient value；Min (v (i), j) indicates GpiThe picture for being included
The minimal gradient value of element；Image force EimageCalculating aim at: discovery GpiMiddle gradient value maximum pixel point.
More specifically, the final convergence of snake element is completed by greedy algorithm according to following calculating process in the step 4:
Step (4.1): initial profile is regarded as the side a N shape, then the center of the side the N shape is registered as reference point p(x, y)；
If reference point in contour area, gos to step (4.4)；If reference point, outside contour area, sequence executes step
(4.2)；
Step (4.2): with reference point p(x,y)For endpoint, N ray L (i) is constructed by each snake element v (i), i=1,
2,…,N；
Step (4.3): the ray L intersected for every with profilep, p=1,2,3 ... n, find its intersecting point coordinate and
It successively records, then this N number of data point is expressed as p(xi,yi)(i=1,2,3 ..., n), and calculate on every ray snake vegetarian refreshments with
The midpoint coordinates M of profile intersection point(xi,yi)(i=1,2,3 ..., n)；
The midpoint coordinates M being made of this N/2(xi,yi)(i=1,2,3 ..., n) calculate last reference point are as follows:
Step (4.4): with reference point p(x,y)As this current snakelike model energy function EimageCenter, construct n item
Ray Lj(j=1,2 ..., n), from current reference point p(x,y)Contour edge after being issued to this iteration i times；At this point, two adjacent
The angle of straight line is 2 π/n；
Step (4.5): with reference point p(x,y)As this current snakelike model energy function EimageCenter, construct n item
Ray Lj(j=1,2 ..., n), from current reference point p(x,y)Contour edge after being issued to this iteration i times；At this point, two adjacent
The angle of straight line is 2 π/n；
Step (4.6): for every straight line Lj(j=1,2 ..., n), we define Pv(i,j)It is this straight line LjOn i-th
Point calculates the gradient G of each pointv(i,j), choose maximum of gradients max { G on this linev(i,j)Be used as convergent maximal end point, i.e.,
The final position of snake element.
The invention has the following advantages that
(1) in some image segmentation problems, often there is the problems such as coarse spot, noise interference in original image；The present invention
Gray scale pretreatment make the feature of original image more obvious, gray proces make image border be strengthened, and denoise, sharpen
Degree also correspondingly improves.
(2) during entire energy function carries out minimization, continuous force energy function is uniformly distributed in snake element to work as
Preceding objective contour, bending force energy function keep its profile as smooth as possible, and image force makes snake element rest on high gradient as much as possible
Pixel；Three power act on simultaneously, and snake element is constantly moved to true specific profile under the effect of external force, and internal force is being protected
Hold snake element topological it is preferable while constantly vary with the movement of snake vegetarian refreshments, final internal force and external force mutually restrict to be formed
One preferable initial profile.
(3) calculation formula of original GSA algorithm synthesis power is that the plus-minus of three power mixes calculating, passes through and improves Eimage's
Calculation method, so that EimageThe value range of power (0,1], three power are added so that Econt、EcurvAnd EimageThree power are more
Balance, such variation keep comprehensive force function controllability more preferable.
(4) greedy algorithm considers reference point in the inner and outer two kinds of situations of initial profile, according to the gradient of image itself
Feature makes snake element finally converge to recessed profile zone.
(5) present invention makes improvement, and introduces greedy algorithm, gray proces etc. on the basis of original GSA model
Strategy, the method proposed improves the precision of contours extract while remaining GSA model high efficiency calculating advantage, special
It is not that proposed method handles spill contour extraction of objects problem well.
Detailed description of the invention
Fig. 1 is overall algorithm process of the invention；
Fig. 2 is the neighborhood of snake element；
Fig. 3 is the overall procedure of greedy algorithm；
Fig. 4 is that non-recessed image reference point is chosen；
Fig. 5 is that spill image reference point is chosen.
Specific embodiment
With reference to the accompanying drawings and examples, technical solution of the present invention is described in detail, but should not be understood as
Limitation to technical solution.In the following description, a large amount of concrete details are given in order to provide more thorough to the present invention
Understanding.However, to those skilled in the art, the present invention may not need one or more of these details and be able to reality
It applies.In other examples, in order to avoid confusion with the present invention, some technical characteristics well known in the art are not carried out
Description.
Fig. 1 gives the overall procedure of multiple target point path planning method of the invention；Referring to Figure 1, here is other side
The detailed description of each step in method:
Step S101: gray scale pretreatment is carried out to whole image, it is therefore an objective to so that the feature of original image is more obvious；
The formula of gray scale pretreatment are as follows:
Gray(v(i),j)=(Δ1R(v(i),j)+Δ2G(v(i),j)+Δ3B(v(i),j)) > > k (1)
In above formula, Gray(v(i),j)Indicate that the gray value of some pixel v (i), j are i snake element neighborhood GpiJ-th interior of picture
Element, formula R(v(i),j)、G(v(i),j)、B(v(i),j)Respectively indicate red, green, blue channel value, △1、△2、△3As weight system
Number, k indicate displacement coefficient；△1=38, △2=75, △3=15, k=7 compare by test of many times, and display above-mentioned parameter is matched
It is higher to set efficiency；
Step S102: setting snake element scale as N, and determines the initial position of each snake element, total iteration time of set algorithm
Number M, and current iteration number is recorded with the number of iterations accumulator m, m is initialized as 1；
Step S103: setting the value of snake element counter i as 1, indicate since number be 1 snake element calculate；
Step S104: as shown in Fig. 2, obtaining 200 (Gp of neighborhood according to the position of i snake element 100i), 9 pictures are shared in neighborhood
Element 300, calculates continuous force, bending force and the image force of each pixel 300, and then calculate the resultant force of each pixel；
EcontThe calculation method of continuous force is as follows:
Wherein, dv(i,j)-v(i+1)Indicate i-th of snake element neighborhood GpiIn j-th pixel and i+1 snake element straight line away from
From；davrIndicate the average distance between all snake vegetarian refreshments, calculation method isContinuous force
EcontMain calculate aims at: discovery GpiIn with i+1 snake element distance closest to a pixel of average distance, act on
In uniform distribution of forces of the snake vegetarian refreshments in profile space；D after each round iterationavrIt needs to recalculate；
Bending force EcurvEnergy function it is as follows:
In above formula, | v (i-1) -2v (i, j)+v (i+1) | it indicates to i-1, i+1 snake elements and GpiIn pixel j carry out and
Vector calculates；Bending force EcurvCalculating aim at: discovery GpiIn with former and later two snake vegetarian refreshments constitute vector angle it is the smallest
Pixel, effect are the smoothness of snake vegetarian refreshments；
The specific energy function E of image forceimageIt is as follows:
Wherein I (v (i), j) indicates GpiIn j-th of pixel gradient value；Min (v (i), j) indicates GpiThe picture for being included
The minimal gradient value of element；Image force EimageCalculating aim at: discovery GpiMiddle gradient value maximum pixel point；
Comprehensive force functionIt is as follows:
Step S105: the selection the smallest pixel of resultant force replaces current i snake element 100；
Step S106: snake element counter adds one, indicates that algorithm sequentially calculates next snake element；
Step S107: if i≤N, algorithm jumps to S104；Otherwise, algorithm executes S108, at this time from snake element 1 to snake
Plain N is calculated one time；
Step S108: the number of iterations accumulator m adds 1；
Step S109: if the number of iterations does not reach total the number of iterations, go to step S103；Otherwise, step is executed
Rapid S110；
Step S110: the final convergence of snake element is completed according to greedy strategy；
Step S111: snake element is sequentially connected, and forms final image object profile.
Fig. 3 gives the overall procedure of step S110 greedy algorithm；Fig. 3 is referred to, here is to step each in algorithm
Detailed description；
Step S201: as shown in figure 4, initial profile is regarded as the side a N shape, then the center of the side the N shape, which is referred to as, refers to
Point 400, record are as follows: p(x,y)；
Step S202: the S206 if reference point in contour area, gos to step；If reference point outside contour area,
Then sequence executes step S203；
Step S203: as shown in figure 5, being endpoint with reference point 400, N ray is constructed by each snake element v (i)
500, record are as follows: L (i), i=1,2 ..., N；
Step S204: the ray L intersected for every with profilep, p=1,2,3 ... n, find its intersecting point coordinate and according to
Secondary record, then this N number of data point is expressed as p(xi,yi)(i=1,2,3 ..., n), and calculate snake element and profile on every ray
The midpoint coordinates 600 of intersection point, record are as follows: M(xi,yi)(i=1,2,3 ..., n)；
Step S205: the midpoint coordinates M being made of this N/2(xi,yi)(i=1,2,3 ..., n) calculate last reference point
Are as follows:
S206: with reference point p(x,y)As this current snakelike model energy function EimageCenter, construct n ray Lj
(j=1,2 ..., n), from current reference point p(x,y)Contour edge after being issued to this iteration i times；At this point, two adjacent straight lines
Angle is 2 π/n；
S207: for every straight line Lj(j=1,2 ..., n), we define Pv(i,j)It is this straight line LjOn i-th point, meter
Calculate the gradient G of each pointv(i,j), choose maximum of gradients max { G on this linev(i,j)Be used as convergent maximal end point, i.e., snake element
Final position.
Claims (6)
1. then the spill image partition method based on GSA uses it is characterized in that: carrying out gray proces to original image first
A kind of improved GSA model completes the convergence of initial snake element, and the final convergence of snake element is completed finally by a kind of greedy algorithm；It
Include the following steps:
Step 1: gray scale pretreatment is carried out to image；
Step 2: determining that object boundary is initial profile point in the picture, i.e. snake element；
Step 3: being deformed using to the curve being formed by connecting by snake element by external force and internal force by GSA algorithm, make institute
There is the sum of snake element energy minimum, initial snake element is made to be finally displaced into objective contour marginal position, and ensures between snake element orderly
And be uniformly distributed, complete the initial convergence of snake element；
Step 4: the final convergence of snake element is completed using greedy strategy, all snake elements are locked to the boundary of image target to be split
On；
Step 5: sequential connection snake element forms objective contour, completes image segmentation.
2. the spill image partition method according to claim 1 based on GSA, it is characterized in that: in the step 1, according to
Following calculating process carry out gray scale pretreatment to image:
The formula of gray scale pretreatment are as follows:
Gray(v(i),j)=(Δ1R(v(i),j)+Δ2G(v(i),j)+Δ3B(v(i),j)) > > k
In above formula, Gray(v(i),j)Indicate that the gray value of some pixel v (i), j are i snake element neighborhood GpiJ-th interior of pixel,
Formula R(v(i),j)、G(v(i),j)、B(v(i),j)Respectively indicate red, green, blue channel value, △1、△2、△3As weight coefficient,
K indicates displacement coefficient, △1=38, △2=75, △3=15, k=7.
3. the spill image partition method according to claim 1 based on GSA, it is characterized in that: in the step 3, under
State the initial convergence that calculating process completes snake element；Assuming that snake prime sequences are made of N number of snake vegetarian refreshments, comprehensive force function
It is as follows:
V (i) indicates that i-th of snake element, j are i snake element neighborhood GpiJ-th interior of pixel, the value of j and a moved further distance of snake element
δ is related；One moved further calculation method are as follows: j=i ± δ, δ ∈ 0,1,2 ... }, δ indicates one moved further distance of snake vegetarian refreshments；Econt
For continuous force, EcurvFor bending force, EimageFor image force；α, β, γ are the weight passes that warp parameter is used to control each component part
System；The calculating target of entire GSA is: in the neighborhood Gp of snake vegetarian refreshments iiIn calculate a pixel and make resultant force E (v (i), j)
Value minimizes, and as the snake vegetarian refreshments of next moved further；
Continuous force EcontCalculation method it is as follows:
Wherein, dv(i,j)-v(i+1)Indicate i-th of snake element neighborhood GpiIn j-th pixel and i+1 snake element linear distance；
davrIndicate the average distance between all snake vegetarian refreshments, calculation method isContinuous force
EcontCalculating aims at: discovery GpiIn with i+1 snake element distance closest to a pixel of average distance, effect is to control
Uniform distribution of forces of the snake vegetarian refreshments processed in profile space；D after each round iterationavrIt needs to recalculate；
Bending force EcurvCalculation method it is as follows:
In above formula, | v (i-1) -2v (i, j)+v (i+1) | it indicates to i-1, i+1 snake elements and GpiIn pixel j carry out and vector
It calculates；Bending force EcurvCalculating aim at: discovery GpiIn with former and later two snake vegetarian refreshments constitute the smallest pixel of vector angle
Point, effect are the smoothness of snake vegetarian refreshments；
EimageCalculation method it is as follows:
Wherein I (v (i), j) indicates GpiIn j-th of pixel gradient value；Min (v (i), j) indicates GpiThe pixel for being included
Minimal gradient value；Image force EimageCalculating aim at: discovery GpiMiddle gradient value maximum pixel point.
4. the spill image partition method according to claim 1 based on GSA, it is characterized in that: in the step 4, according to
Following calculating process complete the final convergence of snake element by greedy algorithm:
Step (4.1): initial profile is regarded as the side a N shape, then the center of the side the N shape is registered as reference point p(x,y)；If ginseng
Examination point is in contour area, and go to step (4.4)；If reference point, outside contour area, sequence executes step (4.2)；
Step (4.2): with reference point p(x,y)For endpoint, N ray L (i) is constructed by each snake element v (i), i=1,2 ...,
N；
Step (4.3): the ray L intersected for every with profilep, p=1,2,3 ... n find its intersecting point coordinate and successively remember
Record, then this N number of data point is expressed as p(xi,yi)(i=1,2,3 ..., n), and calculate the midpoint of every ray Yu profile intersection point
Coordinate M(xi,yi)(i=1,2,3 ..., n)；
The midpoint coordinates M being made of this N/2(xi,yi)(i=1,2,3 ..., n) calculate last reference point are as follows:
Step (4.4): with reference point p(x,y)As the center of current outline, n ray L is constructedj(j=1,2 ..., n), from
Current reference point p(x,y)Contour edge after being issued to this iteration i times；At this point, the angle of two adjacent rays is 2 π/n；
Step (4.5): for every ray Lj(j=1,2 ..., n), we define Pv(i,j)It is this ray LjOn i-th point,
Calculate the gradient G of each pointv(i,j), choose maximum of gradients max { G on this linev(i,j)It is used as convergent maximal end point, i.e. snake element
Final position.
5. the spill image partition method according to claim 1 based on GSA, it is characterized in that it includes following specific step
It is rapid:
Step S101: gray scale pretreatment is carried out to whole image, it is therefore an objective to so that the feature of original image is more obvious；
The formula of gray scale pretreatment are as follows:
Gray(v(i),j)=(Δ1R(v(i),j)+Δ2G(v(i),j)+Δ3B(v(i),j)) > > k (1)
In above formula, Gray(v(i),j)Indicate that the gray value of some pixel v (i), j are i snake element neighborhood GpiJ-th interior of pixel,
Formula R(v(i),j)、G(v(i),j)、B(v(i),j)Respectively indicate red, green, blue channel value, △1、△2、△3As weight coefficient,
K indicates displacement coefficient；△1=38, △2=75, △3=15, k=7；
Step S102: setting snake element scale as N, and the initial position of determining each snake element, total the number of iterations M of set algorithm,
And current iteration number is recorded with the number of iterations accumulator m, m is initialized as 1；
Step S103: setting the value of snake element counter i as 1, indicate since number be 1 snake element calculate；
Step S104: neighborhood Gp is obtained according to the position of i snake element 100i200,9 pixels 300 are shared in neighborhood, are calculated each
Continuous force, bending force and the image force of pixel 300, and then calculate the resultant force of each pixel；
Continuous force EcontCalculation method it is as follows:
Wherein, dv(i,j)-v(i+1)Indicate i-th of snake element neighborhood GpiIn j-th pixel and i+1 snake element linear distance；
davrIndicate the average distance between all snake vegetarian refreshments, calculation method isContinuous force Econt
Calculating aims at: discovery GpiIn with i+1 snake element distance closest to a pixel of average distance, effect is snake element
Uniform distribution of forces of the point in profile space；D after each round iterationavrIt needs to recalculate；
Bending force EcurvCalculation method it is as follows:
In above formula, | v (i-1) -2v (i, j)+v (i+1) | it indicates to i-1, i+1 snake elements and GpiIn pixel j carry out and vector
It calculates；Bending force EcurvCalculating aim at: discovery GpiIn with former and later two snake vegetarian refreshments constitute the smallest pixel of vector angle
Point, effect are the smoothness of snake vegetarian refreshments；
Image force EimageCalculation method it is as follows:
Wherein I (v (i), j) indicates GpiIn j-th of pixel gradient value；Min (v (i), j) indicates GpiThe pixel for being included
Minimal gradient value；Image force EimageCalculating aim at: discovery GpiMiddle gradient value maximum pixel point；
Comprehensive force functionIt is as follows:
Step S105: the selection the smallest pixel of resultant force replaces current i snake element 100；
Step S106: snake element counter adds one, indicates that algorithm sequentially calculates next snake element；
Step S107: if i≤N, algorithm jumps to S104；Otherwise, algorithm executes S108, at this time from snake element 1 to snake element N quilt
It calculates one time；
Step S108: the number of iterations accumulator m adds 1；
Step S109: if the number of iterations does not reach total the number of iterations, go to step S103；Otherwise, step is executed
S110；
Step S110: the final convergence of snake element is completed according to greedy strategy；
Step S111: snake element is sequentially connected, and forms final image object profile.
6. the spill image partition method according to claim 5 based on GSA, it is characterized in that: step S110 greedy algorithm
Overall procedure in each steps are as follows:
Step S201: being regarded as the side a N shape for initial profile, then the center of the side the N shape is referred to as reference point 400, record are as follows:
p(x,y)；
Step S202: the S206 if reference point in contour area, gos to step；If reference point is outside contour area, suitable
Sequence executes step S203；
Step S203: being endpoint with reference point 400, constructs N ray 500 by each snake element v (i), record are as follows: L (i), i
=1,2 ..., N；
Step S204: the ray L intersected for every with profilep, p=1,2,3 ... n find its intersecting point coordinate and successively remember
Record, then this N number of data point is expressed as p(xi,yi)(i=1,2,3 ..., n), and calculate snake element and profile intersection point on every ray
Midpoint coordinates 600, record are as follows: M(xi,yi)(i=1,2,3 ..., n)；
Step S205: the midpoint coordinates M being made of this N/2(xi,yi)(i=1,2,3 ..., n) calculate last reference point are as follows:
S206: with reference point p(x,y)As the center of current outline, n ray L is constructedj(j=1,2 ..., n), from current ginseng
Examination point p(x,y)Contour edge after being issued to this iteration i times；At this point, the angle of two adjacent rays is 2 π/n；
S207: for every ray Lj(j=1,2 ..., n), we define Pv(i,j)It is this ray LjOn i-th point, calculate every
The gradient G of a pointv(i,j), choose maximum of gradients max { G on this linev(i,j)Being used as convergent maximal end point, i.e., snake element is final
Position.
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