CN103295218A - Image cutting method and device - Google Patents

Abstract

The invention discloses an image cutting method and device. The image cutting method comprises the following steps that a zero level set outline is initialized; image parameter information and an Nth level set outline of an image to be processed are substituted into a preset partial differential equation, and the difference value of a Nth level set function is calculated, wherein the preset partial differential equation is obtained from an energy equation in a converted mode, and the energy equation comprises image border information, image region information, and internal energy making a zero level set be similar to a signed distance function; when N is equal to 0, the zero level set outline is the initialized zero level set outline; the difference value of the initialized zero level set outline and the Nth level set function is substituted into a preset iterative formula, and a zero level set curve of N+1th iteration is calculated out; whether the zero level set curve calculated out through current iteration is identical to the zero level set curve calculated through last iteration is judged, and if yes, iteration is finished. The image cutting method has the better cutting effect on images with blurry edges and noise images.

Description

A kind of image partition method and device

Technical field

The present invention relates to image processing field, be specifically related to a kind of image partition method and device.

Background technology

It is the vital task that image is handled that image is cut apart, and its objective is that hope separates interested object in the image with remainder in the image, serves in order to handle for high-level diagram picture more.Image Segmentation Technology is to find profile and the border of the part in the image, and or rather, image Segmentation Technology is to distribute a label to each pixel in the image, and the pixel with same label has common visual signature.

Based on the image partition method of dynamic outline, the thinking that this method adopts comprises in the prior art:

The first step: adopt and set up energy equation, following formula (1-1):

$L_R\left(C\right)={\∫}_0^{L\left(C\right)}g\left(\right|\▿I\left[C\left(s\right)\right]\left|\right)\mathrm{ds}---(1-1)$

Wherein, the arc length of L (C) expression closed curve C, L _R(C) be the curve energy functional of weighting arc length, g is the edge indicator function, and g can be chosen for following (1-2):

$g(x,y)=\frac{1}{1+{(\▿I(x,y)/K)}^p},p=\mathrm{1,2}---(1-2)$

Wherein, I is image to be split,

Be gradient, the constant coefficient of K for choosing according to different images.Need to prove that gradient is very big at the edge of image place, the value convergence of corresponding edge indicator function g zero (being g → 0).

Second step: minimization of energy equation (1-1), that is:

$\min L_R\left(C\right)=\min {\∫}_0^{L\left(C\right)}g\left(\right|\▿I\left[C\left(s\right)\right]\left|\right)\mathrm{ds}---(1-3)$

The physical significance of following formula (1-3) is: the weighting arc length at the closed curve C of place, image border is the shortest.

Find the solution the extreme value of following formula (1-3) functional (this functional replaces with E (I) for convenience of explanation) and can obtain the necessary condition of finding the solution the functional extreme value, that is: according to Euler-Lagrange equation (Euler-Lagrange function)

$\frac{\∂F}{\∂I}-\frac{d}{\mathrm{dx}}\left(\frac{\∂F}{\∂\mathrm{Ix}}\right)-\frac{d}{\mathrm{dy}}\left(\frac{\∂F}{\∂\mathrm{Iy}}\right)=0---(1-4)$

The 3rd step: verified for the partial differential equation (PDE, Partial Differential Equation) of following formula (1-4), adopting classical process of iteration for this partial differential equation is the gradient descent method, can get following curve evolvement equation:

$\frac{\∂C}{\∂t}=g\left(C\right)\mathrm{\κN}-(\▿g\·N)N---(1-5)$

K is curvature of curve in the formula (1-5), and N is normal to curve.

The 4th step: according to verified curve evolvement equation and the relation between the level set, the corresponding horizontal collected explanations or commentaries of formula (1-5) is:

$\frac{\∂C}{\∂t}=g\left(C\right)|\▿\mathrm{\φ}|\mathrm{\κ}-(\▿g\·\▿\mathrm{\φ})---(1-6)$

φ is zero level collection curve in the formula (1-6),

The 5th step: the partial differential equation to formula (1-6) is carried out discretize on the room and time, (1-6) is converted into corresponding difference equation with formula, adopt iterative computation to obtain final numerical solution, the meaning of the numerical solution that this is final is: final numerical solution is the closed curve of split image.Therefore, the operation of carrying out in computing machine is to find the solution by formula (1-6) to be converted into corresponding difference equation, specifically comprises:

Step S1: initialization zero level collection profile;

Step S2: according to being converted into the iterative formula that corresponding difference equation is changed out by formula (1-6), carry out iterative computation;

Formula (1-6) is to be obtained by energy equation (1-1) conversion, has only comprised image edge information in energy equation (1-1), and indicator function g represents with the edge.

Step S3: in iterative computation, regularly reinitialize level set function;

Step S4: stop when satisfying the iteration stopping condition, the curve of acquisition is the curve of split image.

The prior art of above-mentioned explanation is difficult to detect edge of image under the ill-defined situation, causes ill-defined image segmentation effect not good.

Summary of the invention

The embodiment of the invention provides a kind of image partition method and device, has overcome for the not good defective of ill-defined image segmentation effect.

The embodiment of the invention provides a kind of image partition method, and described method comprises:

Initialization zero level collection profile;

With image parameter information and the N sub-level collection profile of pending image, the partial differential equation that substitution is preset is calculated the difference of N sub-level set function; Wherein, the described partial differential equation that presets is obtained by the energy equation conversion that has comprised image edge information and image area information; N is zero-based integer, and the zero level collection profile when the N value is 0 is initialized zero level collection profile;

With the difference of initialization zero level collection profile and described N sub-level set function, the iterative formula that substitution is preset calculates the zero level collection curve of iteration the N+1 time;

Regularly zero level collection curve and the symbolic distance function that calculates according to current iteration reinitializes level set function;

With image parameter information and the described level set function that reinitializes of pending image, the described partial differential equation of substitution is calculated the difference of M sub-level set function; M is zero-based integer, and the level set function when the M value is 0 is initialized level set function again;

With the described difference that reinitializes level set function and described M sub-level set function, the iterative formula that substitution is preset calculates the zero level collection curve of iteration the M+1 time;

Judge whether the zero level collection curve that current iteration calculates is identical with the zero level collection curve that last iterative computation goes out, if identical, iteration finishes.

The invention process also example provides a kind of image partition method, and described method comprises:

Initialization zero level collection profile;

With image parameter information and the N sub-level collection profile of pending image, the partial differential equation that substitution is preset is calculated the difference of N sub-level set function; Wherein, the described partial differential equation that presets is by having comprised image edge information, and the energy equation conversion of the internal energy of image area information and maintenance zero level set function and symbolic distance functional similarity obtains; N is zero-based integer, and the zero level collection profile when the N value is 0 is initialized zero level collection profile;

With the difference of initialization zero level collection profile and described N sub-level set function, the iterative formula that substitution is preset calculates the zero level collection curve of iteration the N+1 time;

Judge whether the zero level collection curve that current iteration calculates is identical with the zero level collection curve that last iterative computation goes out, if identical, iteration finishes.

The embodiment of the invention also provides a kind of image segmenting device, and described device comprises:

First initialization unit, first computing unit, second computing unit reinitializes unit and first judging unit;

Described first initialization unit is used for initialization zero level collection profile;

Described first computing unit is used for image parameter information and N sub-level collection profile with pending image, and the partial differential equation that substitution is preset is calculated the difference of N sub-level set function; Wherein, the described partial differential equation that presets is obtained by the energy equation conversion that has comprised image edge information and image area information; N is zero-based integer, and the zero level collection profile when the N value is 0 is initialized zero level collection profile;

Described second computing unit is used for the difference with initialization zero level collection profile and described N sub-level set function, and the iterative formula that substitution is preset calculates the zero level collection curve of iteration the N+1 time;

The described unit that reinitializes is used for timing according to zero level collection curve and symbolic distance function that current iteration calculates, reinitializes level set function; Then, described first computing unit also is used for image parameter information and the described level set function that reinitializes with pending image, and the described partial differential equation of substitution is calculated the difference of M sub-level set function; M is zero-based integer, and the level set function when the M value is 0 is initialized level set function again; Described second computing unit also is used for the described difference that reinitializes level set function and described M sub-level set function, and the iterative formula that substitution is preset calculates the zero level collection curve of iteration the M+1 time;

Described first judging unit, for judging whether the zero level collection curve that current iteration calculates is identical with the zero level collection curve that last iterative computation goes out, if identical, iteration finishes.

The embodiment of the invention also provides a kind of image segmenting device, and described device comprises:

Second initialization unit, the 3rd computing unit, the 4th calculates single and second judging unit;

Described second initialization unit is used for initialization zero level collection profile;

Described the 3rd computing unit is used for image parameter information and N sub-level collection profile with pending image, and the partial differential equation that substitution is preset is calculated the difference of N sub-level set function; Wherein, the described partial differential equation that presets is by having comprised image edge information, and the energy equation conversion of the internal energy of image area information and maintenance zero level set function and symbolic distance functional similarity obtains; N is zero-based integer, and the zero level collection profile when the N value is 0 is initialized zero level collection profile;

The described the 4th calculates singly, is used for the difference with initialization zero level collection profile and described N sub-level set function, and the iterative formula that substitution is preset calculates the zero level collection curve of iteration the N+1 time;

Described second judging unit, for judging whether the zero level collection curve that current iteration calculates is identical with the zero level collection curve that last iterative computation goes out, if identical, iteration finishes.

As can be seen from the above technical solutions, the image partition method of embodiment of the invention explanation is not only considered image edge information, also consider the area information of image, these information are represented by energy functional, by finding the solution minimizing of energy functional, thereby acquire the closed curve of split image, this image partition method comprises that for ill-defined image noisy image has more excellent segmentation effect.

Description of drawings

In order to be illustrated more clearly in the embodiment of the invention or technical scheme of the prior art, to do to introduce simply to the accompanying drawing of required use in embodiment or the description of the Prior Art below, apparently, accompanying drawing in describing below only is some embodiments of the present invention, for those of ordinary skills, under the prerequisite of not paying creative work, can also obtain other accompanying drawing according to these accompanying drawings.

Fig. 1 is a kind of image partition method flow process simplified schematic diagram that the embodiment of the invention one provides;

Fig. 2 is the concise and to the point schematic flow sheet of thinking that general dotted line evolutionary model realization is cut apart image;

Fig. 3 is a kind of image partition method flow process simplified schematic diagram that the embodiment of the invention two provides;

Fig. 4 is a kind of image partition method flow process simplified schematic diagram that the embodiment of the invention three provides;

Fig. 5 is a kind of image partition method flow process simplified schematic diagram that the embodiment of the invention four provides;

Fig. 6 is the image segmentation effect comparison diagram to a plurality of objects;

Fig. 7 is to the image segmentation effect comparison diagram of noise is arranged;

Fig. 8 is to ill-defined image segmentation effect comparison diagram;

Fig. 9 is a kind of image segmenting device simplified schematic diagram that the embodiment of the invention five provides;

Figure 10 is a kind of image segmenting device simplified schematic diagram that the embodiment of the invention six provides.

Embodiment

Embodiment one

The embodiment of the invention provides a kind of image partition method, and as shown in Figure 1, this method comprises:

Step 101: initialization zero level collection profile;

Wherein, initialization zero level collection profile can be the closed curve of choosing at random.

Step 102: with image parameter information and the N sub-level collection profile of pending image, the partial differential equation that substitution is preset is calculated the difference of N sub-level set function; Wherein, the partial differential equation that presets is obtained by the energy equation conversion that has comprised image edge information and image area information; Zero level collection profile when the N value is 0 is initialized zero level collection profile;

It will be appreciated that equipment can specifically comprise in the operation of the difference of carrying out the calculated level set function: after finishing the difference of a calculated level set function, begin the difference of calculated level set function next time again.

For the ease of understanding present embodiment, general dotted line evolutionary model is realized thinking brief description that image is cut apart herein.As shown in Figure 2, the curve evolvement model can comprise:

The first step: be that energy function (as E (u)) is asked minimization problem, i.e. minE (u) with curve evolvement;

Second step: adopt the variational method, the energy function minimization problem is converted to corresponding Euler-Lagrange equation

The problem of finding the solution;

The 3rd step: find the solution equation in second step by the gradient descent method, obtain the curve evolvement equation that t in time develops;

The 4th step: introduce the Level Set Method of curve, obtain the level set EVOLUTION EQUATION of curve;

The 5th step: the level set equation carry out numerical discretizationization, carry out iteration according to corresponding difference equation and obtain the final curve of cutting apart.In the realization operation of computing machine, calculate all and in the 5th step, carry out.

By above five operations, to the thinking of curve evolvement by basic understanding.From the angle that computing machine is carried out, step 101 to step 105 all is the specific operation process to the 5th step in the curve evolvement thinking among this embodiment.Difference with the prior art is, in embodiments of the present invention, consider in the energy equation to have comprised image edge information and image area information, make computing machine in execution in step 101 to step 105, to ill-defined image better segmentation effect can be arranged.

Step 103: with the difference of initialization zero level collection profile and N sub-level set function, the iterative formula that substitution is preset calculates the zero level collection curve of iteration the N+1 time;

Step 104: timing reinitializes level set function according to zero level collection curve and symbolic distance function that current iteration calculates; With image parameter information and the described level set function that reinitializes of pending image, the partial differential equation that substitution is preset is calculated the difference of M sub-level set function; Level set function when the M value is 0 is initialized level set function again; With the described difference that reinitializes level set function and described M sub-level set function, the iterative formula that substitution is preset calculates the zero level collection curve of iteration the M+1 time;

It will be appreciated that in the calculating of step 103, level set function can be undergone mutation, in order to remedy the sudden change in the level set function evolutionary process, need periodically level set function to be reinitialized to the symbolic distance function.Timing initialization zero level collection profile in the step 104 is not picked at random, is according to the symbolic distance function each point on the image that represents level set to be carried out assignment again, thereby obtains the initialization contour curve.

Step 105: judge whether the zero level collection curve that current iteration calculates is identical with the zero level collection curve that last iterative computation goes out, if iteration finishes, if not, execution in step 104.

Wherein, the zero level collection curve that iteration finishes to obtain in the step 105 is the curve of split image.

Image partition method by embodiment of the invention explanation, this method is not only considered image edge information, also consider the area information of image, these information are represented by energy functional, by finding the solution minimizing of energy functional, thereby acquire the closed curve of split image, this image partition method comprises that for ill-defined image noisy image has more excellent segmentation effect.

Embodiment two

The embodiment of the invention provides a kind of image partition method, this method is similar to embodiment one, difference is: the energy equation that is used for obtaining to preset partial differential equation in the present embodiment, not only comprised image edge information and the image area information identical with embodiment one, also comprised and make zero level set function φ and symbolic distance function keep similar internal energy P.By in energy equation, increasing this internal energy P, can keep zero level set function φ and symbolic distance functional similarity, thereby needn't reinitialize, simplify the computing machine carries out image and cut apart middle calculating.

As shown in Figure 3, the embodiment of the invention provides a kind of image partition method, comprising:

Step 201: initialization zero level collection profile;

Wherein, initialization zero level collection profile can be the closed curve of choosing at random.

Step 202: with image parameter information and the N sub-level collection profile of pending image, the partial differential equation that substitution is preset is calculated the difference of N sub-level set function; Wherein, the described partial differential equation that presets is by having comprised image edge information, and the energy equation conversion of the internal energy of image area information and maintenance zero level set function and symbolic distance functional similarity obtains; Zero level collection profile when the N value is 0 is initialized zero level collection profile;

It will be appreciated that equipment can specifically comprise in the operation of the difference of carrying out the calculated level set function: after finishing the difference of a calculated level set function, begin the difference of calculated level set function next time again.

Step 203: with the difference of initialization zero level collection profile and described N sub-level set function, the iterative formula that substitution is preset calculates the zero level collection curve of iteration the N+1 time;

Step 204: judge whether the zero level collection curve that current iteration calculates is identical with the zero level collection curve that last iterative computation goes out, if iteration finishes, if not, execution in step 203.

Image partition method by embodiment of the invention explanation, this method is not only considered image edge information, also consider the area information of image, and make zero level set function φ and symbolic distance function keep similar internal energy P, these information are represented by energy functional, by finding the solution minimizing of energy functional, thereby acquire the closed curve of split image, this image partition method is for ill-defined image, comprise that noisy image has more excellent segmentation effect, and need not initialization, reduced the complexity of calculating.

Embodiment three

The embodiment of the invention provides a kind of image partition method, and this image partition method is considered the area information of image edge information and image, makes that the image segmentation effect is better.

The image partition method of only having considered image edge information has been described in background technology, and the thinking of this method comprises:

The first step: adopt and set up energy equation, following formula (2-1):

$L_R\left(C\right)={\∫}_0^{L\left(C\right)}g\left(\right|\▿I\left[C\left(s\right)\right]\left|\right)\mathrm{ds}---(2-1)$

Wherein, the arc length of L (C) expression closed curve C, L _R(C) be the curve energy functional of weighting arc length, g is the edge indicator function, and g can be chosen for following (2-2):

$g(x,y)=\frac{1}{1+{(\▿I(x,y)/K)}^p},p=\mathrm{1,2}---(2-2)$

Wherein, I is image to be split, Be gradient, K is selected constant.Need to prove that gradient is very big at the edge of image place, the value convergence of corresponding edge indicator function g zero (being g → 0).

Second step: minimization of energy equation (1-1), that is:

$\min L_R\left(C\right)=\min {\∫}_0^{L\left(C\right)}g\left(\right|\▿I\left[C\left(s\right)\right]\left|\right)\mathrm{ds}---(2-3)$

The physical significance of following formula (1-3) is: the weighting arc length at the closed curve C of place, image border is the shortest.

Find the solution the extreme value of following formula (1-3) functional (this functional replaces with E (I) for convenience of explanation) and can obtain the necessary condition of finding the solution the functional extreme value, that is: according to Euler-Lagrange equation (Euler-Lagrange function)

$\frac{\∂F}{\∂I}-\frac{d}{\mathrm{dx}}\left(\frac{\∂F}{\∂\mathrm{Ix}}\right)-\frac{d}{\mathrm{dy}}\left(\frac{\∂F}{\∂\mathrm{Iy}}\right)=0---(2-4)$

The 3rd step: verified for the partial differential equation (PDE, Partial Differential Equation) of following formula (2-4), adopting classical process of iteration for this partial differential equation is the gradient descent method, can get following curve evolvement equation:

$\frac{\∂C}{\∂t}=g\left(C\right)\mathrm{\κN}-(\▿g\·N)N---(2-5)$

K is curvature of curve in the formula (2-5), and N is normal to curve.

What need to describe in detail is that the physical significance of formula (2-5) comprising: at the image flat site, because g is close to 1, and

Be similar to zero, so formula (2-5) has only first on the right to work, this is simple contour curvature evolution equation; At the image border annex, because gradient is much larger than parameter K, so at this moment g has only back one to work close to zero.

Because

Direction always point to the direction that g increases, so no matter in interior of articles or outside,

Always point to the direction of leaving the edge.Supposition curve C (t) has moved near the edge of object now, and the method direction N of C (t) always points to the inside of curve in accordance with regulations.So, if the position of current curves is the outside that is in the border, so N will with Direction is opposite, namely

For negative, thereby

Consistent with N, visible second effect at this moment is to make curve C (t) from the outside, border, to the direction motion on more close border.

In like manner, if the position of current curves is the inside that is in the border, so N will with

Direction is identical, namely

For on the occasion of, thereby

Opposite with N, visible second effect at this moment is to make C (t) from inside, border, to the direction motion on more close border.

By above reasoning as can be known, second behavior is the local maximum of curve C (t) being pushed to image gradient on the right of in the formula (2-5).

The 4th step: according to verified curve evolvement equation and the relation between the level set, the corresponding horizontal collected explanations or commentaries of formula (2-5) is:

$\frac{\∂C}{\∂t}=g\left(C\right)|\▿\mathrm{\φ}|\mathrm{\κ}-(\▿g\·\▿\mathrm{\φ})---(2-6)$

φ is zero level collection curve in the formula (2-6).

The 5th step: the partial differential equation shown in the formula (2-6) is carried out discretize on the room and time, ((2-6) is converted into corresponding difference equation with formula, adopt iterative computation to obtain final numerical solution, the meaning of the numerical solution that this is final is: final numerical solution is the closed curve of split image.

Also need to illustrate the image partition method of only having considered image area information in the present embodiment, also claim the Chan-Vese Image Segmentation Model, the basic ideas of this method only consider that to above-mentioned the image partition method of image edge information is similar, and its key distinction is the energy function difference that arranges.Describe in detail with reference to as follows:

Suppose that C is the evolution curve, Ω is image-region, ω represent the to develop interior zone (inside (C)) of curve C, then the perimeter of curve C (outside (C)) be Ω ω (" " difference set of two set of symbology).For the characteristics of this model are described, lift a simple example: suppose image u ₀In only have two homogeneous regions, the zone in gray-scale value be respectively

With

Further the hypothesis gray-scale value is

The zone be zone to be detected, its border is C ₀Can obtain examined object border C by above-mentioned hypothesis ₀Inside, namely examined object inside has

C ₀The outside has

Therefore, can suppose that energy equation is as follows:

F ₁(C)+F ₂(C)＝

∫ _inside(C)|u ₀(x，y)-c ₁| ²dxdy+∫ _outside(C)|u ₀(x，y)-c ₂| ²dxdy

(2-7)

Wherein, C represents the arbitrary curve in the evolutionary process, C ₁Be the average gray of all pixels of C inside, C ₂Average gray for all pixels of C outside.

Can be drawn by (2-7), when curve C develops to object boundary C ₀The time, F ₁(C)+F ₂(C) can obtain minimum value.That is:

Min{F ₁(C)+F ₂(C)}≈0≈F ₁(C ₀)+F ₂(C ₀) (2-8)

The total energy equation of Chan-Vese Image Segmentation Model not only comprises the energy term in (2-7), also comprises some relevant informations of evolution curve C, as the length of curve C, and the interior zone area of curve C.Therefore, the energy equation of Chan-Vese Image Segmentation Model is defined as follows:

F(c ₁，c ₂，C)＝μLength(C)+vArea(inside(C))

+λ ₁∫ _inside(C)|u ₀(x，y)-c ₁| ²dxdy (2-9)

+λ ₂∫ _outside(C)|u ₀(x，y)-c ₂| ²dxdy

Wherein, μ, v, λ ₁, λ is positive weight coefficient μ 〉=0 of each energy term, v 〉=0, λ ₁＞0, λ ₂＞0, and be fixing parameter.In numerical solution, can get λ ₁=λ ₂=0, v=0.General μ, v, λ ₁, λ ₂Value the experience data are arranged.

In order to find the solution the energy functional shown in the formula (2-9), introduced Level Set Method.

If (x is interior just outer negative symbolic distance function y) to φ, and zero level collection curve is represented curve C, that is:

$\left\{\begin{array}{c}C=\&PartialD;\mathrm{\&omega;}=(x,y)\&Element;\mathrm{\&Omega;}:\mathrm{\&phi;}(x,y)=0,\\ \mathrm{inside}\left(C\right)=\mathrm{\&omega;}=(x,y)\&Element;\mathrm{\&Omega;}:\mathrm{\&phi;}(x,y)>0,\\ \mathrm{outside}\left(C\right)=\mathrm{\&Omega;}\backslash \mathrm{\&omega;}=(x,y)\&Element;\mathrm{\&Omega;}:\mathrm{\&phi;}(x,y)<0\end{array}\right.---(2-10)$

Introduce Heaviside function and a Di Lake function δ, they are defined as follows:

$H\left(z\right)=\left\{\begin{array}{cc}1,& \mathrm{if\; z}\&GreaterEqual;0\\ 0,& \mathrm{if\; z}<0\end{array}\right.,---(2-11)$

$\mathrm{\&delta;}\left(z\right)=\frac{d}{\mathrm{dz}}H\left(z\right)---(2-12)$

Then the every of the energy functional shown in the formula (2-9) with level set representations is:

First zero level collection length of curve is:

$\mathrm{Length\&phi;}=0={\&Integral;}_{\mathrm{\&Omega;}}|\&dtri;H(x,y))|\mathrm{dxdy}={\&Integral;}_{\mathrm{\&Omega;}}{\mathrm{\&delta;}}_0\left(\mathrm{\&phi;}(x,y)\right)|\&dtri;\mathrm{\&phi;}(x,y)|\mathrm{dxdy}$

(2-13)

Second zero level collection curve interior zone area is:

Areaφ＝∫ _ΩH(φ(x，y))dxdy≥0 (2-14)

The variance of third and fourth zero level collection curve interior zone and the variance of curve perimeter.

∫ _φ＞0|u ₀(x，y)-c ₁|dxdy＝∫ _Ω|u ₀(x，y)-c ₁| ²H(φ(x，y))dxdy

∫ _φ＞0|u ₀(x，y)-c ₂|dxdy＝∫ _Ω|u ₀(x，y)-c ₂| ²(1-H(φ(x，y)))dxdy

(2-15)

So gross energy equation F (c ₁, c ₂, φ) can be expressed as following form:

$F(c_1,{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000140259140000061.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,\mathrm{\&phi;})=\mathrm{\&mu;}{\&Integral;}_{\mathrm{\&Omega;}}\mathrm{\&delta;}\left(\mathrm{\&phi;}(x,y)\right)|\&dtri;\mathrm{\&phi;}(x,y)|\mathrm{dxdy}$

$+\mathrm{\&nu;}{\&Integral;}_{\mathrm{\&Omega;}}H\left(\mathrm{\&phi;}(x,y)\right)\mathrm{dxdy}$

$+{\mathrm{\&lambda;}}_1{\&Integral;}_{\mathrm{\&Omega;}}{|u_0(x,y)-c_1|}^{2}H\left(\mathrm{\&phi;}(x,y)\right)\mathrm{dxdy}$

$+{\mathrm{\&lambda;}}_2{\&Integral;}_{\mathrm{\&Omega;}}{|u_0(x,y)-{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000140259140000061.png"\; state="\{\{state\}\}">c</figure-callout>}}_2|}^2(1-H\left(\mathrm{\&phi;}(x,y)\right))\mathrm{dxdy}---(2-16)$

c ₁, c ₂Be defined as follows:

$\left\{\begin{array}{c}{c}_1\left(\mathrm{\&phi;}\right)=\mathrm{average}\left(u_0\right)\mathrm{in}\{\mathrm{\&phi;}\&GreaterEqual;0\}\\ c_2\left(\mathrm{\&phi;}\right)=\mathrm{average}\left(u_0\right)\mathrm{in}\{\mathrm{\&phi;}<0\}\end{array}\right.---(2-17)$

In order to calculate the corresponding Eulerian equation of zero level set function, Heaviside function H and Di Lake function δ are adjusted slightly, use H _εAnd δ _εExpression, wherein ε → 0.At this time can be similar to and obtain δ _ε=δ ' _εIn the gross energy equation that is based on ε be:

$F(c_1,{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000140259140000061.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,\mathrm{\&phi;})=\mathrm{\&mu;}{\&Integral;}_{\mathrm{\&Omega;}}{\mathrm{\&delta;}}_{\mathrm{\&epsiv;}}\left(\mathrm{\&phi;}(x,y)\right)|\&dtri;\mathrm{\&phi;}(x,y)|\mathrm{dxdy}$

$+\mathrm{\&nu;}{\&Integral;}_{\mathrm{\&Omega;}}{H}_{\mathrm{\&epsiv;}}\left(\mathrm{\&phi;}(x,y)\right)\mathrm{dxdy}$

$+{\mathrm{\&lambda;}}_1{\&Integral;}_{\mathrm{\&Omega;}}{|u_0(x,y)-c_1|}^2{H}_{\mathrm{\&epsiv;}}\left(\mathrm{\&phi;}(x,y)\right)\mathrm{dxdy}$

$+{\mathrm{\&lambda;}}_2{\&Integral;}_{\mathrm{\&Omega;}}{|u_0(x,y)-{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000140259140000061.png"\; state="\{\{state\}\}">c</figure-callout>}}_2|}^2(1-H_{\mathrm{\&epsiv;}}\left(\mathrm{\&phi;}(x,y)\right))\mathrm{dxdy}---(2-18)$

Keep c in the formula (2-18) ₁, c ₂Immobilize, only adjust φ and make the F minimum.Introduce time step t＞0, then φ (Eulerian equation y) is for t, x:

$\frac{\&PartialD;\mathrm{\&phi;}}{\&PartialD;t}={\mathrm{\&delta;}}_{\mathrm{\&epsiv;}}\left(\mathrm{\&phi;}\right)[\mathrm{\&mu;}\mathrm{div}\left(\frac{\&dtri;\mathrm{\&phi;}}{|\&dtri;\mathrm{\&phi;}|}\right)-\mathrm{\&nu;}-{\mathrm{\&lambda;}}_1{(u_0-c_1)}^2+{\mathrm{\&lambda;}}_2{(u_0-c_2)}^2]$ (2-19)

φ(0，x，y)＝φ ₀(x，y)inΩ

Wherein initialization curve φ (0, x, y)=φ ₀(x, y).

The verified numerical solution for the partial differential equation shown in the formula (2-19) is that (2-19) is converted into corresponding difference equation with formula to formula (2-19) discretize on time and space, adopts iterative computation to obtain final numerical solution.

The image splitting scheme of above-mentioned explanation is the image partition method of considering image area information, i.e. Chan-Vese Image Segmentation Model.When handling ill-defined picture, can access good segmentation effect based on the image splitting scheme of image area information.

The embodiment of the invention provides a kind of image edge information of not only considering, also considers the image splitting scheme of the area information of image, can obtain the better pictures segmentation effect.Following is to describe in detail.

In the explanation about the Chan-Vese Image Segmentation Model, introduced, when considering factors such as arc length and area, total energy equation of supposing such as formula (2-9), first and second physical significance refers on the right of in the formula (2-9): under the identical situation of area, arc length is more short, and the expression curve is more smooth.Third and fourth is in order to guarantee that different zones can be divided into different parts on the right of in the formula (2-9).

In conjunction with the splitting scheme of only considering image edge information of above explanation with only consider the splitting scheme (being the Chan-Vese Image Segmentation Model) of the area information of image, ignore the slickness at edge.Can obtain following energy functional:

$F(c_1,{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000140259140000061.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,\mathrm{\&phi;})=\mathrm{\&lambda;}{\&Integral;}_C\mathrm{gds}$

$+{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_1}{\mathrm{\&lambda;}}_1{|u_0(x,y)-c_1|}^2\mathrm{dxdy}---(2-20)$

$+{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_2}{\mathrm{\&lambda;}}_2{|u_0(x,y)-{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000140259140000061.png"\; state="\{\{state\}\}">c</figure-callout>}}_2|}^2\mathrm{dxdy}$

For in conjunction with Level Set Method, zero level collection curve φ and the curved profile C of above definition are associated, be defined as follows:

$\left\{\begin{array}{c}C=\&PartialD;\mathrm{\&omega;}=(x,y)\&Element;\mathrm{\&Omega;}:\mathrm{\&phi;}(x,y)=0,\\ \mathrm{inside}\left(C\right)=\mathrm{\&omega;}=(x,y)\&Element;\mathrm{\&Omega;}:\mathrm{\&phi;}(x,y)>0,\\ \mathrm{outside}\left(C\right)=\mathrm{\&Omega;}\backslash \mathrm{\&omega;}=(x,y)\&Element;\mathrm{\&Omega;}:\mathrm{\&phi;}(x,y)<0\end{array}\right.---(2-21)$

Introduce Heaviside function and Dirac function δ, they are defined as follows:

$H\left(z\right)=\left\{\begin{array}{cc}1,& \mathrm{if\; z}\&GreaterEqual;0\\ 0,& \mathrm{if\; z}<0\end{array}\right.,$ ${\mathrm{\&delta;}}_0\left(z\right)=\frac{d}{\mathrm{dz}}H\left(z\right)---(2-22)$

To including the function g definition of marginal information, can in the present embodiment g be defined as follows according to design to the g definition:

$g(x,y)=\frac{1}{1+{(\&dtri;I(x,y)/K)}^p},p=\mathrm{1,2}---(2-23)$

Therefore, the expression formula of the energy equation shown in the formula (2-20) is converted to following expression:

$F(c_1,{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000140259140000061.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,\mathrm{\&phi;})=\mathrm{\&lambda;}{\&Integral;}_{\mathrm{\&Omega;}}g\&CenterDot;\mathrm{\&delta;}\left(\mathrm{\&phi;}(x,y)\right)|\&dtri;\mathrm{\&phi;}(x,y)|\mathrm{dxdy}$

$+{\mathrm{\&lambda;}}_1{\&Integral;}_{\mathrm{\&Omega;}}{|u_0(x,y)-c_1|}^{2}H\left(\mathrm{\&phi;}(x,y)\right)\mathrm{dxdy}---(2-24)$

$+{\mathrm{\&lambda;}}_2{\&Integral;}_{\mathrm{\&Omega;}}{|u_0(x,y)-{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000140259140000061.png"\; state="\{\{state\}\}">c</figure-callout>}}_2|}^2(1-H\left(\mathrm{\&phi;}(x,y)\right))\mathrm{dxdy}$

When other parameters fixedly the time, with respect to c ₁, c ₂Minimize following formula, can obtain:

$c_i={\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_i}u(x,y)\mathrm{dxdy}/{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_i}\mathrm{dxdy},i=\mathrm{1,2}---(2-25)$

Work as c ₁, c ₂In the time of fixedly, minimize above-mentioned partial differential equation with respect to φ, can obtain:

$\frac{\&PartialD;\mathrm{\&phi;}}{\&PartialD;t}={\mathrm{\&delta;}}_{\mathrm{\&epsiv;}}[\mathrm{\&lambda;}\mathrm{div}\left(g\frac{\&dtri;\mathrm{\&phi;}}{|\&dtri;\mathrm{\&phi;}|}\right)-{\mathrm{\&lambda;}}_1{(u_0-c_1)}^2+{\mathrm{\&lambda;}}_2{(u_0-c_2)}^2]---(2-26)$

Numerical solution for the partial differential equation shown in the formula (2-26) is to formula (2-26) discretize on time and space, according to pixels be divided into image latticed, to be divided into several time periods Δ t the time, formula (2-26) is converted into corresponding difference equation (as formula (2-28)), adopts iterative computation to obtain final numerical solution.

Wherein, the Dirac function that adopts in real image is cut apart is as follows:

${\mathrm{\&delta;}}_{\mathrm{\&epsiv;}}\left(x\right)=\left\{\begin{array}{cc}0,& \left|x\right|>\mathrm{\&epsiv;}\\ \frac{1}{2\mathrm{\&epsiv;}}[1+\cos \left(\frac{\mathrm{\&pi;x}}{\mathrm{\&epsiv;}}\right)],& \left|x\right|\&le;\mathrm{\&epsiv;}\end{array}\right.---(2-27)$

Wherein, adopt the Di Lake function of ε=1 in the present embodiment.Iterative process only needs simple difference, in the following way estimation:

$\frac{{\mathrm{\&phi;}}_{i,j}^{n+1}-{\mathrm{\&phi;}}_{i,j}^n}{\mathrm{\&Delta;t}}=L\left({\mathrm{\&phi;}}_{i,j}^n\right)---(2-28)$

Wherein,

Representative grid (i j) locates the level set function value of the n time iteration,

Be the value of the n+1 time iteration,

Represent the value on formula (2-26) equal sign right side.

In the usage level diversity method carries out process that image cuts apart, need to calculate each Δ t constantly, each net point in the full images scope is to the distance of current outline line, tries to achieve distance and be zero point

Connect all these then successively and put to regain new preliminary examination contour curve, so iterate to cut apart up to image and finish.

Above-mentioned is that the embodiment of the invention provides a kind of image edge information of not only considering, also considers the image splitting scheme of the area information of image.As shown in Figure 4, this scheme specifically comprises in the implementation of computing machine:

Step 301: initialization zero level collection profile is assumed to be φ ₀

Wherein, initialization zero level collection profile φ ₀It can be the closed curve of picked at random.

Step 302: at each Δ t constantly, the formula on computing formula (2-26) equal sign the right remembers that its value is

Wherein, in the formula (2-26), μ, λ, λ ₁, λ ₂Be the constant coefficient of selecting according to actual conditions, other parameter can be by obtaining pending image calculation in the formula (2-26).Need to prove that also the partial differential equation shown in the formula (2-26) is to be converted to by the energy equation that has comprised image edge information and image area information.Wherein, image edge information in the energy equation is represented by edge indicator function g, image area information in the energy equation is embodied by formula (2-7), can be understood as image area information and represents by the variance of curve interior zone and the variance of curve perimeter.

Step 303: according to formula (2-28), and known initialization zero level collection profile, iterative computation

For example: when initialization zero level collection profile is φ ₀, calculate by step 302

Then

Can obtain easily with reference to following formula (2-29).

Get access to reference to formula (2-29) iteration

Step 304: zero level collection curve and the symbolic distance function that calculates according to current iteration regularly reinitializes level set function, according to the profile that reinitializes with calculate

And formula (2-29), iterative computation zero level collection curve;

It will be appreciated that in the calculating of step 303, level set function can be undergone mutation, in order to remedy the sudden change in the level set function evolutionary process, need periodically level set function be reinitialized to the level set function with the symbolic distance functional similarity.Timing initialization zero level collection profile in the step 304 is not picked at random, is according to the symbolic distance function each point on the image that represents level set to be carried out assignment again, thereby obtains the initialization contour curve.

Step 305: when

With

Value identical (perhaps approximate identical), then iteration finishes, otherwise continues next iteration.

The closed curve that the point that iteration acquires after finishing forms is cut apart image.

Image partition method by embodiment of the invention explanation, this method is not only considered image edge information, also consider the area information of image, these information are represented by energy functional, by finding the solution minimizing of energy functional, thereby acquire the closed curve of split image, this image partition method comprises that for ill-defined image noisy image has more excellent segmentation effect.

Embodiment four

The embodiment of the invention provides a kind of image partition method, this image partition method is similar to embodiment two, all consider image edge information, area information with image, the difference of this embodiment and embodiment two is, in iterative computation, need not in this example to reinitialize, increased computing velocity.

It will be appreciated that at first cut apart in the calculating at traditional images, level set function can be undergone mutation, in order to remedy the sudden change in the level set function evolutionary process, periodically level set function is reinitialized to the level set function similar to meeting distance function.The equation that reinitializes of standard is:

$\frac{\&PartialD;\mathrm{\&phi;}}{\&PartialD;t}=\mathrm{sign}\left({\mathrm{\&phi;}}_0\right)(1-|\&dtri;\mathrm{\&phi;}\left|\right)---(3-1)$

Wherein, φ ₀Be level set function to be reinitialized, sign is-symbol distance function.The most algorithm that reinitializes is based on partial differential equation or its mutation.Yet there is shortcoming in these methods, namely work as φ ₀And unevenness or φ ₀One side when more precipitous than another side, the moving direction of zero level set function can be very inaccurate.Moreover, when level set function φ and symbolic distance function difference were very big, this moment, traditional Level Set Method was difficult to level set function is reinitialized to the symbolic distance function.In the evolutionary process of time, even iteration several times, level set function also is easy to deviate from the symbolic distance function, and is particularly short inadequately when step-length, deviates from easily.Therefore, the interval that reinitializes often can not be too of a specified duration.

Heavily initialization has extensively been applied to stablize evolution for keeping curve, and obtains good experimental result.But from angle of practice, heavy initialized process still too complicated, computing time is long.

More than about in the description that reinitializes as can be seen, the key in the evolution process is to keep level set function to be similar to the Fu Hai distance function, particularly the zero level collection near.As everyone knows, the symbolic distance function must satisfy

Otherwise function phi satisfies arbitrarily

Function can be expressed as the product of a symbolic distance function and a constant.In view of the symbolic distance function property, proposed as lower integral:

$P\left(\mathrm{\&phi;}\right)=\frac{1}{2}{\&Integral;}_{\mathrm{\&Omega;}}{\left(\right|\&dtri;\mathrm{\&phi;}|-1)}^2\mathrm{dxdy}---(3-2)$

By introducing the compensation of internal energy P (φ), the level set function φ in the evolutionary process will maintain voluntarily and be similar to the symbolic distance function.Therefore, need not to reinitialize process.

In view of above-mentioned explanation, the basis of the energy equation (2-24) that the embodiment of the invention can propose at embodiment two proposes a kind of new energy equation:

$F(c_1,{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000140259140000061.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,\mathrm{\&phi;})=\mathrm{\&mu;P}\left(\mathrm{\&phi;}\right)$

$+\mathrm{\&lambda;}{\&Integral;}_C\mathrm{gds}$

$+{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_1}{\mathrm{\&lambda;}}_1{|u_0(x,y)-c_1|}^2\mathrm{dxdy}$ (3-3)

$+{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_2}{\mathrm{\&lambda;}}_2{|u_0(x,y)-{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000140259140000061.png"\; state="\{\{state\}\}">c</figure-callout>}}_2|}^2\mathrm{dxdy}$

For in conjunction with Level Set Method, zero level collection curve φ and the curved profile C of above definition are associated, be defined as follows:

$\left\{\begin{array}{c}C=\&PartialD;\mathrm{\&omega;}=(x,y)\&Element;\mathrm{\&Omega;}:\mathrm{\&phi;}(x,y)=0,\\ \mathrm{inside}\left(C\right)=\mathrm{\&omega;}=(x,y)\&Element;\mathrm{\&Omega;}:\mathrm{\&phi;}(x,y)>0,\\ \mathrm{outside}\left(C\right)=\mathrm{\&Omega;}\backslash \mathrm{\&omega;}=(x,y)\&Element;\mathrm{\&Omega;}:\mathrm{\&phi;}(x,y)<0\end{array}\right.---(3-4)$

Introduce Heaviside function and Dirac function δ, they are defined as follows:

$H\left(z\right)=\left\{\begin{array}{cc}1,& \mathrm{if\; z}\&GreaterEqual;0\\ 0,& \mathrm{if\; z}<0\end{array}\right.,$ ${\mathrm{\&delta;}}_0\left(z\right)=\frac{d}{\mathrm{dz}}H\left(z\right)---(3-5)$

To including the function g definition of marginal information, can in the present embodiment g be defined as follows according to design to the g definition:

$g(x,y)=\frac{1}{1+{(\&dtri;I(x,y)/K)}^p},p=\mathrm{1,2}---(3-6)$

Therefore, the expression formula of the energy equation shown in the formula (2-20) is converted to following expression:

$F(c_1,{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000140259140000061.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,\mathrm{\&phi;})=\frac{\mathrm{\&mu;}}{2}{\&Integral;}_{\mathrm{\&Omega;}}{\left(\right|\&dtri;\mathrm{\&phi;}|-1)}^2\mathrm{dxdy}$

$+\mathrm{\&lambda;}{\&Integral;}_{\mathrm{\&Omega;}}g\&CenterDot;\mathrm{\&delta;}\left(\mathrm{\&phi;}(x,y)\right)\left|\&dtri;\mathrm{\&phi;}(x,y)\right|\mathrm{dxdy}$

$+{\mathrm{\&lambda;}}_1{\&Integral;}_{\mathrm{\&Omega;}}{|u_0(x,y)-c_1|}^{2}H\left(\mathrm{\&phi;}(x,y)\right)\mathrm{dxdy}---(3-7)$

$+{\mathrm{\&lambda;}}_2{\&Integral;}_{\mathrm{\&Omega;}}{|u_0(x,y)-{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000140259140000061.png"\; state="\{\{state\}\}">c</figure-callout>}}_2|}^2(1-H\left(\mathrm{\&phi;}(x,y)\right))\mathrm{dxdy}$

When other parameters fixedly the time, with respect to c ₁, c ₂Minimize following formula, can obtain:

$c_i={\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_i}u(x,y)\mathrm{dxdy}/{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_i}\mathrm{dxdy},i=\mathrm{1,2}---(3-8)$

Work as c ₁, c ₂In the time of fixedly, minimize above-mentioned partial differential equation with respect to φ, can obtain:

$\frac{\&PartialD;\mathrm{\&phi;}}{\&PartialD;t}=\mathrm{\&mu;}[\mathrm{\&Delta;\&phi;}-\mathrm{div}{\left(\frac{\&dtri;\mathrm{\&phi;}}{|\&dtri;\mathrm{\&phi;}|}\right)]+\mathrm{\&delta;}}_{\mathrm{\&epsiv;}}[\mathrm{\&lambda;}\mathrm{div}\left(g\frac{\&dtri;\mathrm{\&phi;}}{|\&dtri;\mathrm{\&phi;}|}\right)-{\mathrm{\&lambda;}}_1{(u_0-c_1)}^2+{\mathrm{\&lambda;}}_2{(u_0-c_2)}^2]---(3-9)$

Numerical solution for the partial differential equation shown in the formula (3-9) is to formula (3-9) discretize on time and space, according to pixels be divided into image latticed, to be divided into several time periods Δ t the time, formula (3-9) is converted into corresponding difference equation (as formula (3-11)), adopts iterative computation to obtain final numerical solution.

Wherein, the Dirac function that adopts in real image is cut apart is as follows:

${\mathrm{\&delta;}}_{\mathrm{\&epsiv;}}\left(x\right)=\left\{\begin{array}{cc}0,& \left|x\right|>\mathrm{\&epsiv;}\\ \frac{1}{2\mathrm{\&epsiv;}}[1+\cos \left(\frac{\mathrm{\&pi;x}}{\mathrm{\&epsiv;}}\right)],& \left|x\right|\&le;\mathrm{\&epsiv;}\end{array}\right.---(3-10)$

Wherein, adopt the Di Lake function of ε=1 in the present embodiment.Iterative process only needs simple difference, in the following way estimation:

$\frac{{\mathrm{\&phi;}}_{i,j}^{n+1}-{\mathrm{\&phi;}}_{i,j}^n}{\mathrm{\&Delta;t}}=L\left({\mathrm{\&phi;}}_{i,j}^n\right)---(3-11)$

Wherein,

Representative grid (i j) locates the level set function value of the n time iteration,

Be the value of the n+1 time iteration,

Represent the value on formula (3-9) equal sign right side.

In the usage level diversity method carries out process that image cuts apart, need to calculate each Δ t constantly, each net point in the full images scope is to the distance of current outline line, tries to achieve distance and be zero point Connect all these then successively and put to regain new preliminary examination contour curve, so iterate to cut apart up to image and finish.

Above-mentioned is that the embodiment of the invention provides a kind of image edge information of not only considering, also considers the image splitting scheme of the area information of image.As shown in Figure 5, this scheme specifically comprises in the implementation of computing machine:

Step 401: initialization zero level collection profile is assumed to be φ ₀

Wherein, initialization zero level collection profile φ ₀It can be the closed curve of picked at random.

Step 402: at each Δ t constantly, the formula on computing formula (3-9) equal sign the right remembers that its value is

Wherein, in the formula (3-9), μ, λ, λ ₁, λ ₂Be the constant coefficient of selecting according to actual conditions, other parameter can be by obtaining pending image calculation in the formula (3-9).Need to prove that also the partial differential equation shown in the formula (3-9) is by having comprised image edge information, image area information, and keep the energy equation of the internal energy P of level set function φ and symbolic distance approximation to function to be converted to.Wherein, the image edge information in the energy equation is represented that by edge indicator function g the image area information in the energy equation is embodied by formula (2-7), and image area information is represented by the variance of curve interior zone and the variance of curve perimeter.

Step 403: according to formula (3-11), and known initialization zero level collection profile, iterative computation

For example: when initialization zero level collection profile is φ ₀, calculate by step 202 Then

Can obtain easily with reference to following formula (2-29).

Get access to reference to formula (3-12) iteration

Step 404: when

With

Value identical (perhaps approximate identical), then iteration finishes, otherwise continues next iteration.

The closed curve that the point that iteration acquires after finishing forms is cut apart image.

Image partition method by embodiment of the invention explanation, this method is not only considered image edge information, also consider the area information of image, in the design of energy functional, increased simultaneously the compensation P (φ) of internal energy, these information are represented by energy functional, by finding the solution minimizing of energy functional, thereby acquire the closed curve of split image, this image partition method is for ill-defined image, comprise that noisy image has more excellent segmentation effect, and need not initialization, reduced the complexity of calculating.

Under the following three kinds of situations of giving an example out, the experimental result that the image partition method that adopts embodiment four to provide obtains, and this experimental result and prior art compared.Specific as follows:

Situation one: the image to a plurality of objects is cut apart.

The effect that the method that adopts present embodiment to provide as first behavior among Fig. 6 is cut apart, adopt Chunming Li method gained experimental result as second behavior among Fig. 6, two kinds of method initial profile lines are identical, in the ChunmingLi method, v=3.0 is positive number, outline line develops and can only inwardly contract, so the object representation that has in the net result is imperfect, and for example the arm segment of the shank of toy doggie and the right rag baby all is not included in the net result.And the method that present embodiment provides has well solved the problems referred to above, because improved dividing method is based on area information, contracting still extends out in the outline line so do not need to specify, and initialization profile at an arbitrary position all can obtain good segmentation result.The iterations aspect, Chunming Li method is lasted 17.19 seconds through 589 iteration, and the method that present embodiment provides is only used iteration 22 times, lasts 1.03 seconds.

Situation two: the image that noise is arranged is cut apart.

The effect that the method that adopts present embodiment to provide as first behavior among Fig. 7 is cut apart adopts Chunming Li method gained experimental result as second behavior among Fig. 6, and two kinds of method initial profile lines are identical.Contour curve can't effectively be crossed noise and arrive object bounds in Chunming Li method, because this method is based on rim detection, it is the edge that the noise in the image also is construed to, so can't effectively develop, still can't restrain through 2000 iteration, be 20.66 seconds operation time.The method that present embodiment provides can effectively be cut apart noise image, and iterations only is 32 times, and be 0.92 second operation time.

Situation three: cut apart ill-defined image is arranged.

The effect that the method that adopts present embodiment to provide as first behavior among Fig. 8 is cut apart adopts Chunming Li method gained experimental result as second behavior among Fig. 8, and two kinds of method initial profile lines are identical.Former figure is the nebula image, even naked eyes also can't shrewd its border.Adopt the peripheral boundary that finds that Chunming Li method can only blur, can't further inwardly tighten.Through the basic no change of image outline after 1000 times the iteration, manual with its end, be 132.32 seconds operation time.The method that present embodiment provides has accurately found object outline in the nebula image, and iterations is 45 times, 3.11 seconds operation time.

By giving an example of above three kinds of experimental results, find that the image partition method that the embodiment of the invention provides has better segmentation effect for edge fog, image noisy, a plurality of objects.

Embodiment five

The embodiment of the invention provides a kind of image segmenting device, and as shown in Figure 9, this device comprises: first initialization unit, 501, the first computing units, 502, the second computing units 503 reinitialize unit 504 and first judging unit 505.

Wherein, first initialization unit 501 is used for initialization zero level collection profile;

Need to prove that initialization zero level collection profile can be the closed curve of choosing at random.

First computing unit 502 is used for image parameter information and N sub-level collection profile with pending image, and the partial differential equation that substitution is preset is calculated the difference of N sub-level set function; Wherein, the described partial differential equation that presets is obtained by the energy equation conversion that has comprised image edge information and image area information; Zero level collection profile when the N value is 0 is initialized zero level collection profile;

For the ease of understanding present embodiment, general dotted line evolutionary model is realized thinking brief description that image is cut apart herein.The curve evolvement model can comprise:

The first step: be that energy function (as E (u)) is asked minimization problem, i.e. minE (u) with curve evolvement;

Second step: adopt the variational method, the energy function minimization problem is converted to corresponding Euler-Lagrange equation

The problem of finding the solution;

The 3rd step: find the solution equation in second step by the gradient descent method, obtain the curve evolvement equation that t in time develops;

The 4th step: introduce the Level Set Method of curve, obtain the level set EVOLUTION EQUATION of curve;

The 5th step: the level set equation carry out numerical discretizationization, carry out iteration according to corresponding difference equation and obtain the final curve of cutting apart.In the realization operation of computing machine, calculate all and in the 5th step, carry out.

By above five operations, to the thinking of curve evolvement by basic understanding.All unit modules were used for realizing to the 5th step of curve evolvement thinking in this device.Difference with the prior art is, in embodiments of the present invention, considers in the energy equation to have comprised image edge information and image area information that making can have better segmentation effect to ill-defined image by this image segmenting device.

Image edge information in the said energy equation can be to be represented by edge indicator function g, image area information in the energy equation is embodied by formula (2-7), can be understood as image area information and represents by the variance of curve interior zone and the variance of curve perimeter.

Second computing unit 503 is used for the difference with initialization zero level collection profile and described N sub-level set function, and the iterative formula that substitution is preset calculates the zero level collection curve of iteration the N+1 time;

Reinitialize unit 504, be used for timing according to zero level collection curve and symbolic distance function that current iteration calculates, reinitialize level set function;

Then, first computing unit 502 also is used for image parameter information and the described level set function that reinitializes with pending image, and the partial differential equation that substitution is preset is calculated the difference of M sub-level set function; Level set function when the M value is 0 is initialized level set function again; Second computing unit 503 also is used for the described difference that reinitializes level set function and described M sub-level set function, and the iterative formula that substitution is preset calculates the zero level collection curve of iteration the M+1 time.

It will be appreciated that, in the calculating by 503 execution of second computing unit, level set function can be undergone mutation, and in order to remedy the sudden change in the level set function evolutionary process, need periodically level set function be reinitialized to the function with the symbolic distance functional similarity.Reinitializing unit 504 timing initialization zero level collection profiles is not picked at random, is according to the symbolic distance function each point on the image that represents level set to be carried out assignment again, thereby obtains the initialization contour curve.

First judging unit 505; For judging whether the zero level collection curve that current iteration calculates is identical with the zero level collection curve that last iterative computation goes out, if iteration finishes, and if not, notifies second computing unit 503.

The zero level collection curve that iteration finishes to obtain is the curve of split image.

Image segmenting device by embodiment of the invention explanation, this device is not only considered image edge information, also consider the area information of image, these information are represented by energy functional, by finding the solution minimizing of energy functional, thereby acquire the closed curve of split image, this image partition method comprises that for ill-defined image noisy image has more excellent segmentation effect.

The explanation of the image partition method that the explanation of the image partition method that provides about present embodiment also can reference example one, three provides.

Embodiment six

The embodiment of the invention provides a kind of image segmenting device, and as shown in figure 10, this device comprises: second initialization unit, 601, the three computing units 602, the four calculate single 603 and second judging unit 604.

Wherein, second initialization unit 601 is used for initialization zero level collection profile;

The 3rd computing unit 602 is used for image parameter information and N sub-level collection profile with pending image, and the partial differential equation that substitution is preset is calculated the difference of N sub-level set function; Wherein, the described partial differential equation that presets is by having comprised image edge information, and the energy equation conversion of the internal energy of image area information and maintenance zero level set function and symbolic distance functional similarity obtains; Zero level collection profile when the N value is 0 is initialized zero level collection profile;

Wherein, image edge information in the energy equation is represented by edge indicator function g, image area information in the energy equation is embodied by formula (2-7), can be understood as image area information and represents by the variance of curve interior zone and the variance of curve perimeter.

The 4th calculates singly 603, is used for the difference with initialization zero level collection profile and described N sub-level set function, and the iterative formula that substitution is preset calculates the zero level collection curve of iteration the N+1 time;

Second judging unit 604 is for judging whether the zero level collection curve that current iteration calculates is identical with the zero level collection curve that last iterative computation goes out, if iteration finishes, and if not, notifies the 4th computing unit.

Image segmenting device by embodiment of the invention explanation, this device is not only considered image edge information, also consider the area information of image, and make zero level set function φ and symbolic distance function keep similar internal energy P, these information are represented by energy functional, by finding the solution minimizing of energy functional, thereby acquire the closed curve of split image, this image partition method is for ill-defined image, comprise that noisy image has more excellent segmentation effect, and need not initialization, reduced the complexity of calculating.

The explanation of the image partition method that the explanation of the image partition method that provides about present embodiment also can reference example two, four provides.

One of ordinary skill in the art will appreciate that all or part of step that realizes in above-described embodiment method is to instruct relevant hardware to finish by program, described program can be stored in a kind of computer-readable recording medium, the above-mentioned storage medium of mentioning can be ROM (read-only memory), disk or CD etc.

More than a kind of image partition method provided by the present invention and device are described in detail, for one of ordinary skill in the art, thought according to the embodiment of the invention, part in specific embodiments and applications all can change, in sum, this description should not be construed as limitation of the present invention.

Claims (12)

1. an image partition method is characterized in that, described method comprises:

Initialization zero level collection profile;

With image parameter information and the N sub-level collection profile of pending image, the partial differential equation that substitution is preset is calculated the difference of N sub-level set function; Wherein, the described partial differential equation that presets is obtained by the energy equation conversion that has comprised image edge information and image area information; N is zero-based integer, and the zero level collection profile when the N value is 0 is initialized zero level collection profile;

With the difference of initialization zero level collection profile and described N sub-level set function, the iterative formula that substitution is preset calculates the zero level collection curve of iteration the N+1 time;

Regularly zero level collection curve and the symbolic distance function that calculates according to current iteration reinitializes level set function;

With image parameter information and the described level set function that reinitializes of pending image, the described partial differential equation of substitution is calculated the difference of M sub-level set function; M is zero-based integer, and the level set function when the M value is 0 is initialized level set function again;

With the described difference that reinitializes level set function and described M sub-level set function, the iterative formula that substitution is preset calculates the zero level collection curve of iteration the M+1 time;

Judge whether the zero level collection curve that current iteration calculates is identical with the zero level collection curve that last iterative computation goes out, if identical, iteration finishes.

2. method according to claim 1 is characterized in that, described method also comprises:

If the zero level collection curve that the zero level collection curve that current iteration calculates and last iterative computation go out is inequality, repeat described iterative computation zero level collection curve.

3. method according to claim 1 is characterized in that, described image edge information represents that by the edge indicator function described image area information is represented by the variance of curve interior zone and the variance of curve perimeter.

4. an image partition method is characterized in that, described method comprises:

Initialization zero level collection profile;

With image parameter information and the N sub-level collection profile of pending image, the partial differential equation that substitution is preset is calculated the difference of N sub-level set function; Wherein, the described partial differential equation that presets is by having comprised image edge information, and the energy equation conversion of the internal energy of image area information and maintenance zero level set function and symbolic distance functional similarity obtains; N is zero-based integer, and the zero level collection profile when the N value is 0 is initialized zero level collection profile;

With the difference of initialization zero level collection profile and described N sub-level set function, the iterative formula that substitution is preset calculates the zero level collection curve of iteration the N+1 time;

Judge whether the zero level collection curve that current iteration calculates is identical with the zero level collection curve that last iterative computation goes out, if identical, iteration finishes.

5. method according to claim 4 is characterized in that, described method also comprises:

If the zero level collection curve that the zero level collection curve that current iteration calculates and last iterative computation go out is inequality, repeat described iterative computation zero level collection curve.

6. method according to claim 4 is characterized in that, described image edge information represents that by the edge indicator function described image area information is represented by the variance of curve interior zone and the variance of curve perimeter.

7. an image segmenting device is characterized in that, described device comprises:

First initialization unit, first computing unit, second computing unit reinitializes unit and first judging unit;

Described first initialization unit is used for initialization zero level collection profile;

Described first computing unit is used for image parameter information and N sub-level collection profile with pending image, and the partial differential equation that substitution is preset is calculated the difference of N sub-level set function; Wherein, the described partial differential equation that presets is obtained by the energy equation conversion that has comprised image edge information and image area information; N is zero-based integer, and the zero level collection profile when the N value is 0 is initialized zero level collection profile;

Described second computing unit is used for the difference with initialization zero level collection profile and described N sub-level set function, and the iterative formula that substitution is preset calculates the zero level collection curve of iteration the N+1 time;

The described unit that reinitializes is used for timing according to zero level collection curve and symbolic distance function that current iteration calculates, reinitializes level set function; Then, described first computing unit also is used for image parameter information and the described level set function that reinitializes with pending image, and the described partial differential equation of substitution is calculated the difference of M sub-level set function; M is zero-based integer, and the level set function when the M value is 0 is initialized level set function again; Described second computing unit also is used for the described difference that reinitializes level set function and described M sub-level set function, and the iterative formula that substitution is preset calculates the zero level collection curve of iteration the M+1 time;

Described first judging unit, for judging whether the zero level collection curve that current iteration calculates is identical with the zero level collection curve that last iterative computation goes out, if identical, iteration finishes.

8. device according to claim 7, it is characterized in that, if it is inequality that described first judging unit also is used for the zero level collection curve that zero level collection curve that current iteration calculates and last iterative computation go out, notify described second computing unit to repeat described iterative computation zero level collection curve.

9. device according to claim 7 is characterized in that, described image edge information represents that by the edge indicator function described image area information is represented by the variance of curve interior zone and the variance of curve perimeter.

10. an image segmenting device is characterized in that, described device comprises:

Second initialization unit, the 3rd computing unit, the 4th calculates single and second judging unit;

Described second initialization unit is used for initialization zero level collection profile;

Described the 3rd computing unit is used for image parameter information and N sub-level collection profile with pending image, and the partial differential equation that substitution is preset is calculated the difference of N sub-level set function; Wherein, the described partial differential equation that presets is by having comprised image edge information, and the energy equation conversion of the internal energy of image area information and maintenance zero level set function and symbolic distance functional similarity obtains; N is zero-based integer, and the zero level collection profile when the N value is 0 is initialized zero level collection profile;

The described the 4th calculates singly, is used for the difference with initialization zero level collection profile and described N sub-level set function, and the iterative formula that substitution is preset calculates the zero level collection curve of iteration the N+1 time;

Described second judging unit, for judging whether the zero level collection curve that current iteration calculates is identical with the zero level collection curve that last iterative computation goes out, if identical, iteration finishes.

11. device according to claim 10, it is characterized in that, if it is inequality that described second judging unit also is used for the zero level collection curve that zero level collection curve that current iteration calculates and last iterative computation go out, notify described the 4th computing unit to repeat described iterative computation zero level collection curve.

12. device according to claim 10 is characterized in that, described image edge information represents that by the edge indicator function described image area information is represented by the variance of curve interior zone and the variance of curve perimeter.

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