CN111652898B

CN111652898B - Active contour model industrial smoke image segmentation method based on cross entropy

Info

Publication number: CN111652898B
Application number: CN202010516043.0A
Authority: CN
Inventors: 王晓峰; 黄前静; 丁泽盛; 韦云声; 邹乐
Original assignee: Hefei University
Current assignee: Hefei University
Priority date: 2020-06-09
Filing date: 2020-06-09
Publication date: 2023-03-28
Anticipated expiration: 2040-06-09
Also published as: CN111652898A

Abstract

An active contour model industrial smoke image segmentation method based on cross entropy belongs to the technical field of industrial smoke emission monitoring. Constructing a cross entropy threshold method, obtaining the minimum cross entropy of an original image and a segmented image, and then obtaining the optimal segmentation basis; constructing an active contour model of cross entropy, and minimizing the cross entropy between a given image and a segmented image; adding an iterative threshold convolution segmentation method, wherein the interface between every two segmented regions is implicitly determined by the characteristic function of the interface, and a regularization term is written into a non-local approximation based on the characteristic function; a coordinate descent method is combined with sequence linear programming, an active contour model industrial smoke image segmentation method based on cross entropy is constructed, and accurate segmentation of industrial smoke images can be achieved. The active contour model based on the cross entropy is obtained by combining the CV model and the cross entropy model, and the iterative threshold convolution algorithm is used for minimizing the energy functional, so that the convergence speed is accelerated.

Description

Active contour model industrial smoke image segmentation method based on cross entropy

Technical Field

The invention belongs to the technical field of industrial smoke emission monitoring, and particularly relates to an active contour model industrial smoke image segmentation method based on cross entropy.

Background

With the development of industrial cities, the emission of industrial smoke dust is continuously increased, and a series of environmental pollution problems such as ecological imbalance, environmental deterioration and the like are caused. It has been shown by investigation that industrial sources remain the most dominant source of atmospheric pollution. Therefore, there is a need to monitor industrial smoke emissions. Image segmentation is a critical part in the monitoring process, and the method needs to be studied deeply.

The level set method is a numerical method for capturing the shape and interface of an object, and is proposed by r.osher and j.a.sethian in 1988. In the Level Set method, a zero Level Set of a high one-dimensional Function is generally used to represent a target contour, which is called a Level Set Function (Level Set Function). Image segmentation based on the level set method is mainly divided into two types: one is level set image segmentation based on an edge model, and the other is level set image segmentation based on a region model. Mumford and Shah et al proposed a region-based geometric active contour model in 1989, which has the greatest disadvantage of high computational complexity. Thus, the Chan-Vese (CV) model is proposed by combining a level set function on the basis of a Mumford-Shah (MS) model by the Chan and the Vese, and the CV model is an improvement on an energy function of the MS model. Based on the CV model, li et al establishes a region-based binary level set segmentation method, avoids the reinitialization process of a level set function, and reduces the complexity of the algorithm. Wang et al propose a new local CV model based on level set method theory, curve evolution and local statistical function, which can well segment images with uneven gray levels. Nosrati et al propose to incorporate two constraints of "Containment" (Containment) and "Exclusion" (Exclusion) into a level set model, which can handle similar regions that appear repeatedly in an image well. The Zhayannan et al uses a threshold-based approach and a mixed Gaussian model to incorporate the gray-level information of the background and target into a CV model that effectively extracts the contours of the target region from a CT image of non-uniform background gray. Zhang Guangdong et al propose a GAC-CV hybrid model, which fuses the edge of an image and region information into the same energy functional, and adopts different segmentation strategies for different segmentation targets, thereby improving the capturing capability of a concave edge. Wangcun proposes an improved CV model, realizes shadow detection of a single-frame color picture by adding shape template constraint and anchor point constraint, and solves the image segmentation problem of large brightness difference of shadows.

The industrial smoke segmentation is a relatively novel direction. In recent years, some researchers have conducted some research on the direction of industrial smoke segmentation. Zhang Xiaomei et al propose a region-based soot segmentation method, which uses region-based methods such as threshold segmentation, region growing, region splitting and merging methods for soot image segmentation to segment the soot region, but only considers the gray feature of the smoke image, but not other features. Hsu Yen-Chia et al propose an industrial smoke visual detection method, which can rapidly segment smoke areas by combining color modeling, change detection and texture analysis to identify smoke emission, but the algorithm is susceptible to fast-moving wind and clouds. The Wangxing hucho and the like provide an industrial smoke image segmentation method based on background modeling and feature matching, which has a good segmentation effect on motion interferents and complex scene environments, but the segmentation precision needs to be improved. The minimum error threshold smoke image segmentation algorithm based on the improved Bayesian decision theory is provided, the defects of the traditional threshold segmentation smoke image method are overcome, and interference factors such as light change and cloud layers are not considered in the monitoring process. The Wangya and the like provide a method for segmenting industrial smoke dust in a video, an edge motion region is obtained by a background subtraction method, and a smoke dust region is segmented by a region growing algorithm in a uniform space, but the algorithm segments a cloud image and has a small cavity part.

Disclosure of Invention

The invention aims to overcome the defects of the prior art, provides an active contour model industrial smoke dust image segmentation method based on cross entropy, constructs an active contour model based on cross entropy by combining a CV model and a cross entropy model, and minimizes an energy functional by using an iterative threshold convolution algorithm. The method can realize more accurate segmentation effect on the industrial smoke image and has high segmentation efficiency.

In order to solve the technical problem of the invention, the adopted technical scheme is as follows: an active contour model industrial smoke image segmentation method based on cross entropy is characterized in that an image I (x) with a definition domain omega in an industrial smoke image is divided into internal targets omega by a closed curve C ₁ And an external background omega ₂ And in the two homogeneous regions, an optimal contour curve C is constructed through an active contour model based on cross entropy, so that the segmentation of the industrial smoke image is realized.

As a preferred technical scheme of the invention, the segmentation method comprises the following steps:

(1) constructing a cross entropy threshold method, obtaining the minimum cross entropy of the original image and the segmented image, and then obtaining the optimal segmentation basis;

(2) constructing an active contour model of cross entropy, and minimizing the cross entropy between a given image and a segmented image;

(3) adding an iterative threshold convolution segmentation method, wherein the interface between every two segmented regions is implicitly determined by the characteristic function of the segmented regions, and the regularization term is written into a non-local approximation based on the characteristic function; and finally, combining a coordinate descent method with sequential linear programming to construct an unconditional energy decomposition algorithm for solving the cross entropy model.

As a further preferred technical scheme of the invention, the segmentation method comprises the following specific steps of (1):

let two probability distributions be P = { P = ₁ ,p ₂ ,…,p _n } and Q = { Q = ₁ ,q ₂ ,…,q _n And the cross entropy is:

taking the two probability distributions as an original image and a segmented image, wherein the optimal segmentation basis is to minimize the cross entropy between the two images;

assume a threshold value t _c Classifying images into two classes C _0；c ，C _1；c ；C _0；c The representative pixel gray level is 0, \8230;, t _c ]，C _1；c The representative pixel gray level is [ t ] _c +1，…，L-1]Then, the two probability distributions of the original image and the segmented image are:

in formula (6), I (x) is the original image, I _s (x) Is segmenting an image, wherein:

in the formula (7), μ ₀ And mu ₁ The cross entropy between the original image and the segmented image is obtained by the two probability distributions as follows:

order to

The cross entropy of the original image and the segmented image is minimized as follows:

as a further preferred technical scheme of the invention, the segmentation method comprises the following specific steps of step (2):

based on the active contour model of cross entropy, the model objective function is defined as follows:

the objective function is represented by a level set, as follows:

in equation (11), the constant σ is σ =10 ^-4 (ii) a Let lambda ₁ ＝λ ₂ =1, only two segment segmentation is considered, not multi-segment segmentation;

the first two terms of the formula are combined into one term

Instead, it is based on>

Representing the field of the image omega _i Mu is a positive parameter, image I (x) is reduced to I, and the above equation is reduced to:

/>

wherein the content of the first and second substances,

as a further preferable technical scheme of the invention, the segmentation method comprises the following specific steps of step (3):

in iterative threshold convolution, let the first segment Ω ₁ The characteristic function is:

then the second section omega ₂ Can be implicitly expressed as 1-u (x);

when in use

^ in formula (12)>

Can be approximately expressed as:

in formula (15), denotes convolution; g _τ As a weight function, as shown below:

the fidelity term in equation (13) can be represented as an integral over the entire region Ω by multiplying the cross entropy function of each region by the feature function of the corresponding region, i.e.:

order to

Equation (13) can be written as:

then:

ε＝ε(u,c)＝ε _i (u,c)+ε ^τ (u,c) (20)

wherein, the first and the second end of the pipe are connected with each other,

let β: = u ∈ BV (Ω, R) u = {0,1} }, BV (Ω, R) represents a bounded variational function space, then epsilon (u, c) is minimized using coordinate descent method, assuming an initial guess of u ₀ Finding the minimization factors in order:

c ⁰ ,u ¹ ,c ¹ ,…,u ^k ,c ^k ,…

in general, for u ^k The values are fixed, typically:

wherein S = S ₁ ×S ₂ ×...×S _n ，S _i Is c _i A permissible set of (c); for the cross-entropy model, the convex fidelity term is strictly used, again because of ε ^τ Independently of c, then c ^k Is exactly e _i Global minima with respect to c, namely:

when c is going to ^k When the value is fixed, because of epsilon _i (u,c ^k ) Is linear, epsilon ^τ (u,c ^k ) Is a concave function, then ε (u, c) ^k ) A concave functional, then:

wherein κ is a convex set of β;

order to

After relaxation and linearization, approximating optimization by linear functional minimization on a convex set; since u (x) ≧ 0, it can be executed in the dot state; at a minimum, this can be achieved by:

the beneficial effects of the invention are as follows:

1) The gray values of the background and the target object in the industrial smoke image are very similar, the background contains interferents, and the smoke is difficult to segment by using a traditional segmentation algorithm. The invention utilizes iterative threshold convolution to construct a novel industrial smoke image segmentation method of an active contour image segmentation model based on cross entropy. The iterative threshold convolution algorithm implicitly represents the interface of each image domain by a feature function. The cross-entropy active contour model consists of a regularization term and a fidelity term. Converting the fidelity term into the product of the characteristic function and the cross entropy function through a new algorithm, and obtaining the regularization term by utilizing the functional of the characteristic function and a thermal kernel convolution approximation mode.

2) The active contour model industrial smoke image segmentation method based on the cross entropy can realize accurate segmentation of the industrial smoke image. The active contour model based on the cross entropy is obtained by combining the CV model and the cross entropy model, and the iterative threshold convolution algorithm is used for minimizing the energy functional, so that the convergence speed is accelerated. The experimental results of other models show that the cross entropy model improved algorithm has better result, more accurate segmentation effect and high segmentation efficiency on the segmentation of the industrial smoke dust.

Drawings

The present invention will be described in more detail with reference to the following examples and the accompanying drawings.

FIG. 1 is a flow chart of an iterative threshold convolution algorithm.

Fig. 2 shows a first segmentation result of the gray-scale mura industrial smoke image.

Fig. 3 shows a second segmentation result of the gray-scale mura industrial smoke image.

Fig. 4, 5 and 6 are the segmentation results of three industrial smoke dust images under natural background.

FIG. 7 shows the segmentation result of the industrial smoke image in a complex background.

Detailed Description

The invention discloses an active contour model industrial smoke image segmentation method based on cross entropy, which constructs a new active contour image segmentation model industrial smoke image segmentation method based on cross entropy by utilizing iterative threshold convolution. The iterative threshold convolution algorithm implicitly expresses interfaces of all image domains through characteristic functions, and an active contour model of cross entropy is composed of a regularization term and a fidelity term. Converting the fidelity term into the product of the characteristic function and the cross entropy function through a new algorithm, and obtaining the regularization term by utilizing the functional of the characteristic function and a thermal kernel convolution approximation mode.

The active contour model industrial smoke dust image segmentation method based on the cross entropy is further explained in detail in the following five aspects:

1. conventional CV model

The traditional CV model is a typical region-based image segmentation algorithm and is proposed on the basis of a simplified MS model. The model indirectly expresses the movable contour line into a zero level set form of a level set function through a curve evolution and level set method. Assume that an image I (x) with a domain of definition Ω is divided into a target Ω by a closed curve C ₁ (interior of C) and background Ω ₂ (outer of C) two homogeneous regions, the mean gray value of each region being C ₁ And c ₂ The CV model is to find the optimal contour. The energy functional is as follows:

in formula (1), I (x) is an original image, C is an optimal contour of evolution, μ is a curve Length weight, ν is an Area weight of a curve-containing region, length (C) represents a perimeter of a curve, area (inside (C)) represents an Area contained by an evolution curve, λ ₁ ，λ ₂ Representing the energy parameter of the inner and outer regions of the curve, generally taking lambda to simplify the computational complexity ₁ ＝λ ₂ ＝1。

The first two terms in the energy functional are regularization terms, and the last two terms are fidelity terms of the evolution of the driving curve. The Heaviside function H (z) and the Dirac function δ (z) were introduced.

An energy functional may be represented in level set form as:

the final evolved partial differential equation is:

after the partial differential equation is established, it is solved. Since the solution of partial differential equations in image processing is usually nonlinear, it is usually numerically calculated using a difference method to obtain a minimum energy functional.

When using the difference method, the time step needs to be set manually. The reasonable time step ensures that the level set function can stably evolve and effectively converge, which is a problem to be solved by using a difference method.

2. Cross entropy threshold algorithm

It is generally accepted that cross entropy is a measure of the information theoretical distance between two probability distributions. Let two probability distributions be P = { P = ₁ ,p ₂ ,…,p _n And Q = { Q = } ₁ ,q ₂ ,…,q _n And the cross entropy is:

for image segmentation, the two probability distributions are taken as the original image and the segmented image, and the optimal segmentation basis should be to minimize the cross entropy between the two images.

Assume a threshold value t _c Classifying images into two classes C _0；c ，C _1；c 。C _0；c The representative pixel gray level is 0, \8230;, t _c ]，C _1；c Representative pixel gray level is t _c +1，…，L-1]Then, the two probability distributions of the original image and the segmented image are:

order to

The cross entropy of the original image and the segmented image is minimized as follows: />

3. Active contour model based on cross entropy

The traditional CV model objective function consists of a fidelity term and a regularization term. The fidelity term measures the integral of the squared difference between the mean of the current segmentation region and the gray level of the original image within the current segmentation region. When the objective function reaches a minimum, the actual gray level of the object within the contour and the calculated gray level difference are minimized.

The invention measures the probability distribution between the original image and the segmented image using a cross entropy model, and selects a threshold to minimize the distance.

Based on the active contour model of the cross entropy, the model objective function is defined as follows:

this objective function is represented by a level set, as follows:

in equation (11), the denominator is prevented from being zero resulting in no solution, so a small constant σ is introduced, taking σ =10 ^-4 。

Let lambda be ₁ ＝λ ₂ =1, only two-segment division is considered, and multi-segment division is not considered. To simplify the calculation, the first two terms of the formula are combined into one term

Instead, it is based on>

Representing the image domain omega _i μ is a positive parameter, and image I (x) is reduced to I, the above equation is reduced to:

wherein the content of the first and second substances,

the two terms of the cross-entropy based active contour model are referred to as the regularization term and the fidelity term, and it can be seen from the above formula that the fidelity term of the calculated variance in the CV model is replaced by the term that calculates the cross-entropy. The main goal of the model is to minimize the cross entropy between the given image and the segmented image.

4. Iterative threshold convolution algorithm

In the conventional CV model, the energy functional is often minimized by using a difference method, which has been used by many scholars. However, this method is limited by the Courant Friedrichs Left (CFL) condition, and has the problems of slow convergence rate, easy falling into local minimum, time-consuming evolution process, etc.

In the active contour model based on the cross entropy, the invention provides an iterative threshold convolution (ICTM) segmentation algorithm of the active contour model based on the cross entropy. In this algorithm, the interface between each two segmented regions is implicitly determined by its eigenfunction, and the regularization term is written in a non-local approximation based on the eigenfunction function. A coordinate descent method is combined with sequential linear programming, and an unconditional energy decomposition algorithm for solving a cross entropy model is constructed.

then the second section omega ₂ Can be implicitly expressed as 1-u (x).

When in use

Is based on formula (12)>

Can be approximately expressed as:

in formula (15), a represents convolution. Wherein G is _τ As a weight function, as shown below:

the fidelity term in equation (13) can be represented as an integral over the whole region Ω by multiplying the cross entropy function of each region by the feature function of the corresponding region, that is:

order to

Then equation (13) can be written as:

then:

ε＝ε(u,c)＝ε _i (u,c)+ε ^τ (u,c) (20)

wherein the content of the first and second substances,

let β: = u ∈ BV (Ω, R) u = {0,1} }, BV (Ω, R) represents a bounded variational function space, then epsilon (u, c) is minimized using coordinate descent method, assuming an initial guess of u ₀ Finding the minimization factors in sequence:

c ⁰ ,u ¹ ,c ¹ ,…,u ^k ,c ^k ,…

in general, for u ^k The values are fixed, typically:

wherein S = S ₁ ×S ₂ ×...×S _n ，S _i Is c _i Is determined. For the cross-entropy model, the convex fidelity term is strictly used, again because of ε ^τ Independently of c, then c ^k Is exactly e _i Global minimum with respect to c, i.e.:

when c is going to ^k When the value is fixed, since _i (u,c ^k ) Is linear,. Epsilon ^τ (u,c ^k ) Is a concave function, then ε (u, c) ^k ) A concave functional, then:

where κ is the convex set of β.

Order to

After relaxation and linearization, the optimization is approximated by linear functional minimization on the convex set. Since u (x) ≧ 0, it can be executed in the dot state. At a minimum, this can be achieved by:

5. iterative threshold convolution algorithm flow

Please refer to fig. 1, wherein c ^k For iteration minimum value, omega is image domain, the invention takes omega = [ -pi, pi] ² And I is an image. The iterative threshold convolution algorithm flow is shown in fig. 1, and specifically includes:

in the iterative threshold convolution algorithm, the interface between two different image domains is implicitly represented by their characteristic functions. The fidelity term is expressed as a linear relation of a characteristic function and a cross entropy function, and iteration is carried out through the product of the characteristic function and the cross entropy function to obtain a minimum value c ^k The minimum of the linear approximation is found. The regularization term is approximated with a thermal kernel convolution function of the feature function, which is performed using a Fast Fourier Transform (FFT). Then calculate phi ^k Then obtaining u by a threshold ^k+1 Finally, the minimum energy functional function u of the formula (12) is obtained through circulation ^s . In addition, due to functional ε ^τ Is always below its linear approximation, so the minimum can be given in equation (20)A smaller value is given. This speeds up the convergence of the iterative threshold convolution, thereby reducing the number of iterations to reach steady state.

The processing results and the comparative effects of the segmentation method of the present invention are described below by examples.

In order to verify the effectiveness of the method in segmenting the industrial smoke image, experiments are respectively carried out on the industrial smoke image with the types of uneven gray scale, natural scene, complex background and the like. The cross entropy-based active contour model (hereinafter, ICTM-CEACM model) (i, which refers to the corresponding number in the drawing and is the same below) constructed by the invention is compared with the traditional CV model (b), LIF model (c), LIC model (d), ICV model (e), LCVSR model (f), SPF model (g) and cross entropy model (FD-CEACM model for short) (h) which is used for minimizing energy functional based on a difference method, and the comparison is mainly carried out from two aspects of segmentation effect and segmentation efficiency.

The experimental environment is a CPU model Intel Core i5-4210U, the main frequency is 2.40GHz, the memory is 8GB, the simulation software MatlabR2018b, and the operating system is Windows 10. The sizes of the six industrial smoke dust image original images (a) in the drawings 2-7 in the specification are 358 × 208, 400 × 241, 678 × 432, 282 × 169, 481 × 274 and 470 × 310 respectively. The parameters of all methods are set to optimum respectively.

Example 1

FIG. 2 shows a first segmentation result of the gray uneven industrial smoke dust image, wherein (a) an original image, (b) a CV model segmentation result, (c) a LIF model segmentation result, (d) a LIC model segmentation result, (e) an ICV model segmentation result, (f) a LCVSR model segmentation result, (g) an SPF model segmentation result, (h) a FD-CEACM model segmentation result, and (i) an ICTM-CEACM model segmentation result.

In fig. 2, the target smoke is of a uniform gray scale type, but the background has non-uniform gray scale, and the background contains interfering objects and chimneys for discharging the target, which all bring certain difficulties to the segmentation of the smoke. As can be seen from the experimental result shown in FIG. 2, the SPF model and the ICTM-CEACM model have better segmentation effects, so that the target is well segmented and is not interfered by a background object. The symbol distance function of the SPF model can effectively prevent the outline from moving at a weak edge or a fuzzy edge, so that the smoke dust segmentation effect is good; the ICTM algorithm of the CEACM model implicitly expresses the interface of each division domain through the characteristic function, and has a good division effect on the smoke dust image with uneven gray scale.

The LIF model and the FD-CEACM model have the worst effect, the target object is not completely segmented, the LIF model is an active contour model based on image local gray information and is sensitive to an initial contour, and the segmentation effect is caused by the difference of the initial contour; the FD algorithm of the CEACM model is limited by the CFL condition, and is prone to fall into a local minimum, so that the target is not segmented. In addition, other models completely segment the target object, but are influenced by background objects, and interferents are also segmented. The CV model and the ICV model are based on the global information of the image, the image is composed of two areas which are approximate to constant values, and therefore the segmentation effect on the image with uneven gray scale is poor; the LIC model is based on the gradient information of the image, the image edge is well processed, not only the target object is segmented, but also the interference object is segmented; the significance detection of the LCVSR model can provide a rough contour of the object, failing to distinguish between objects and interferents, thus segmenting both objects.

Example 2

Fig. 3 is a second segmentation result of gray non-uniform industrial smoke dust image, in which (a) an original image, (b) a CV model segmentation result, (c) a LIF model segmentation result, (d) a LIC model segmentation result, (e) an ICV model segmentation result, (f) a LCVSR model segmentation result, (g) an SPF model segmentation result, (h) an FD-CEACM model segmentation result, and (i) an ICTM-CEACM model segmentation result.

Under windy conditions, the smoke and dust is easily affected by the wind, and then uneven distribution is caused. In fig. 3, the smoke of the target object is of a gray-scale non-uniform type, and the smoke concentration blown by wind is small and negligible, and the smoke concentration is determined as the target object mainly considering the region with high smoke concentration. For background objects, the gray scale is also of a non-uniform type and contains interferents, and meanwhile, the gray scale intensity difference between the target object and the background object is not large, which has great difficulty in segmentation of many algorithms.

From the experimental results, it can be found that in (b) - (g) of fig. 3, the interferent is segmented while the target is segmented, and only (h) and (i) have no interferent, but the contour of the target in (h) is not completely segmented, and only (i) has the best segmentation effect, which is the result obtained by the CEACM model based on the ICTM algorithm.

(h) And (i) the difference is different from a segmentation algorithm, the former is a difference method, the latter is iterative threshold convolution, the time step of the difference method is artificially set, and a reasonable value is difficult to find, so that the contour is not completely segmented. In contrast, the iteration threshold convolution implicitly expresses the interfaces of the two segmentation areas through the characteristic function, the fidelity term is constructed by the linear function of the characteristic function, and the regularization term is approximated by the thermonuclear convolution function to obtain a relatively complete smoke segmentation contour.

Example 3

Fig. 4, 5 and 6 are the segmentation results of three industrial smoke images under natural background, the first row: original image, second line: CV model segmentation results, third row: LIF model segmentation result, fourth row: LIC model segmentation results, fifth row: ICV model segmentation results, line six: LCVSR model segmentation results, seventh row: SPF model segmentation results, eighth row: FD-CEACM model segmentation results, ninth row: and (5) performing ICTM-CEACM model segmentation.

From the three figures, fig. 4, 5 and 6, it can be seen that this is an image of industrial smoke against a natural background. Compared with the image with uneven gray scale and the image with complex background, the industrial smoke image under the natural background is simpler. The image is mainly of an object, a disturbing object and a background. From the experimental results, it can be seen that the complete contour of the segmented target object is an SPF model and an ICTM-CEACM model, the SPF model mainly has a great effect on the edge of the contour, and can effectively prevent movement for weak edges and fuzzy edges, so that interferents cannot be segmented. The ICTM-CEACM model can well divide a model containing an interfering object by combining the cross entropy model and the CV model, and minimizes an energy functional through an ICTM algorithm, so that a better effect of dividing a smoke dust image is achieved. Other models have their own limitations, and thus have missing parts in the segmented interferents or segmented target regions.

Example 4

FIG. 7 shows the segmentation results of the industrial smoke image under a complex background, (a) the original image, (b) the CV model segmentation result, (c) the LIF model segmentation result, (d) the LIC model segmentation result, (e) the ICV model segmentation result, (f) the LCVSR model segmentation result, (g) the SPF model segmentation result, (h) the FD-CEACM model segmentation result, and (i) the ICTM-CEACM model segmentation result.

As can be observed from fig. 7, the background of the image of the industrial smoke is very complex, wherein there are chimneys, buildings and some greening environments, and in case of wind, the segmentation target selects the area with higher smoke concentration, and ignores the part with lower smoke concentration due to wind. From the experimental results, it can be seen that the images (b) - (h) in fig. 7 do not process the complex background well, and all the images appear in the segmentation result, and only in the image (i), the ICTM algorithm does not segment all background objects, but segments only the smoke target object. The CEACM model is based on global information of an image by combining a CV model and a cross entropy model, an algorithm of the model is improved, and an ICTM minimum energy functional is used, so that the industrial smoke dust image with a complex background is well segmented.

TABLE 1 comparison of iteration counts for each segmentation algorithm

Model (model)	FIG. 2	FIG. 3	FIG. 4	FIG. 5	FIG. 6	FIG. 7
							CV	1000	500	1500	1200	1500	1000
LIF	3200	4520	3000	3000	2400	1520
							LIC	200	50	20	200	200	60
ICV	10	30	35	40	100	15
							LCVSR	150	30	50	100	200	100
SPF	150	150	160	120	150	200
							FD-CEACM	2500	2000	1500	2500	1500	2000
ICTM-CEACM	56	38	115	122	62	50

TABLE 2 run time(s) comparison of various segmentation algorithms

Model (model)	FIG. 2 is a schematic view of a display device	FIG. 3	FIG. 4	FIG. 5	FIG. 6	FIG. 7
							CV	47.852927	23.727749	249.134794	48.392834	134.075902	97.067031
LIF	80.730374	137.613049	334.062724	55.580871	101.049638	68.363201
							LIC	38.667522	14.192681	23.755176	27.502696	107.362301	36.018894
ICV	2.705065	5.366745	10.191056	5.363435	16.686704	5.109138
							LCVSR	5.47776	1.901569	8.880128	3.462437	16.290254	9.900739
SPF	2.511585	3.01159	8.474409	3.371965	4.481159	7.063372
							FD-CEACM	177.197747	144.634112	292.006823	155.4888	143.065807	235.007526
ICTM-CEACM	14.252792	10.274156	65.623481	21.281447	27.708123	21.737091

Tables 1 and 2 list the number of iterations and run time for each segmentation algorithm. It can be seen from the table that the runtime is approximately positively correlated with the number of iterations, and when the number of iterations is relatively large, the runtime is correspondingly increased. It can be found from the table that the iteration times and the running times of CV, LIF and FD-CEACM models are larger than those of other models, the traditional CV model has higher computational complexity of curve-driven force, the LIF model is used for calculating image area information, so the calculation amount of the models is increased, and the FD-CEACM model is a fidelity term calculated by logarithm and has relatively low speed. The number of iterations is small compared to the run time for ICV models, which are level set functions without initialization, and LCVSR models, which do not contain curvatures and other complex differential terms. The LCVSR model extracts an initial contour through significance detection and then performs segmentation, and both models are susceptible to interference of interferents and have poor segmentation effect. The SPF model has the characteristics of global and local, the iteration time is relatively short, but the iteration frequency is relatively high. The CEACM model based on the ICTM has certain applicability to industrial smoke dust in various scenes, and obtains relatively good segmentation effect. Under the condition of obtaining the same segmentation effect, the iteration time and the iteration times of segmentation are superior to those of other models.

The foregoing is merely exemplary and illustrative of the principles of the present invention and various modifications, additions and substitutions of the specific embodiments described herein may be made by those skilled in the art without departing from the principles of the present invention or exceeding the scope of the claims set forth herein.

Claims

1. The active contour model industrial smoke dust image segmentation method based on the cross entropy is characterized by comprising the following steps of: an image I (x) with a defined field omega in the industrial smoke image is divided into an internal target omega by a closed curve C ₁ And an external background omega ₂ The two homogeneous regions construct an optimal contour curve C through an active contour model based on cross entropy, so that the segmentation of the industrial smoke image is realized, and the method specifically comprises the following steps:

let two probability distributions be P = { P = ₁ ,p ₂ ,…,p _n And Q = { Q = } ₁ ,q ₂ ,…,q _n And the cross entropy is:

taking the two probability distributions as an original image and a segmented image, wherein the segmentation basis is to minimize the cross entropy between the two images;

in formula (6), I (x) is the original image, I _s (x) Is a segmented image, wherein:

in the formula (7), μ ₀ And mu ₁ The cross entropy between the original image and the segmentation image is obtained by the two probability distributions as follows:

order to

the objective function is represented by a level set, as follows:

in equation (11), the constant σ is σ =10 ^-4 (ii) a Let lambda be ₁ ＝λ ₂ =1, only two-segment division is considered, without considering multi-segment division;

combining the first two terms of the formula into one term

Instead, it is based on>

(3) adding an iterative threshold convolution segmentation method, wherein the interface between every two segmented regions is implicitly determined by the characteristic function of the interface, and a regularization item is written into a non-local approximation based on the characteristic function; finally, combining a coordinate descent method with sequential linear programming to construct an unconditional energy decomposition algorithm for solving a cross entropy model;

then the second section omega ₂ Is implicitly expressed as 1-u (x);

when τ < 1, in formula (12)

The approximation is represented as:

in formula (15), a represents convolution; g _τ As a function of weight, as shown in the following equation:

the fidelity term in equation (13) is represented in the form of an integral over the entire region Ω by multiplying the cross entropy function of each region by the feature function of the corresponding region, i.e.:

order to

Equation (13) is written as:

then:

ε＝ε(u,c)＝ε _i (u,c)+ε ^τ (u,c) (20)

let β: and (c) using a coordinate descent method to minimize ε (u, c), assuming an initial guess of u, as ₀ Finding the minimization factors in order:

c ⁰ ,u ¹ ,c ¹ ,…,u ^k ,c ^k ,…

for u ^k The values are fixed, having:

wherein S = S ₁ ×S ₂ ×...×S _n ，S _i Is c _i The allowable set of (a); for the cross-entropy model, the convex fidelity term is used strictly, again because ε ^τ Independently of c, then c ^k Is exactly epsilon _i Global minima with respect to c, namely:

when c is going to ^k When the value is fixed, because of epsilon _i (u,c ^k ) Is linear,. Epsilon ^τ (u,c ^k ) Is a concave function, then ε (u, c) ^k ) A concave functional, then:

wherein κ is a convex set of β;

order to

After relaxation and linearization, approximating optimization by linear functional minimization on a convex set; since u (x) ≧ 0, it executes in the dot state; at a minimum, this is obtained by the following formula:

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