CN111598890A - Level set optimization method for underwater image segmentation - Google Patents

Level set optimization method for underwater image segmentation Download PDF

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CN111598890A
CN111598890A CN202010410102.6A CN202010410102A CN111598890A CN 111598890 A CN111598890 A CN 111598890A CN 202010410102 A CN202010410102 A CN 202010410102A CN 111598890 A CN111598890 A CN 111598890A
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CN111598890B (en
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王慧斌
陈哲
孙杨
沈洁
张振
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Abstract

The invention discloses a level set optimization method for underwater image segmentation, which mainly carries out optimization design on an internal energy function of a level set, namely a regular term, and improves the diffusivity of a regular term diffusion function so as to accelerate the convergence speed and stability of a model; the level set function is normalized through the proposed regular term, so that the reinitialization problem of the model is solved while the character of the symbolic function is maintained, and the segmentation precision lost due to reinitialization is reduced. Compared with the traditional level set method, the improved method has the advantages of higher convergence rate, higher segmentation precision and better robustness for underwater image segmentation.

Description

Level set optimization method for underwater image segmentation
Technical Field
The invention belongs to the technology in the field of image processing, and relates to a level set optimization method for underwater image segmentation.
Background
The reinitialization problem of the level set adds a great computational cost to the model, the model generates oscillation in the process and the segmentation precision is easily lost, and nowadays, many models are proposed for processing the reinitialization problem of the level set. However, due to the influence of an underwater complex optical environment, the difficulty of underwater image segmentation is greater than that of land image segmentation, and how to overcome the interference of noise in an underwater image on a model becomes a big problem. The conventional regular term model theory is simple in hypothesis and difficult to be used for underwater image segmentation, and noise in an underwater complex scene degrades the effect of a regular term, so that the convergence speed of a level set model is slowed down and oscillation is generated.
Oher and Sethian proposed the concept of level set implicit in 1988; malladi and Caselles et al apply this concept in image segmentation in turn; chopp, based on caseles, proposes an energy function and incorporates the level set model in the form of a constraint term. However, the level set function needs to be kept as a symbol distance function in the evolution process, so the level set function needs to be periodically reinitialized to maintain the performance of the model. But the reinitialization of the level set takes a lot of time, increasing the computation cost of the level set function. Based on the M-S model, Chan and Vese et al introduced a homogeneous hypothesis theory and proposed a famous global segmentation model C-V model. The objective function of the model is non-convex and the model still needs to be reinitialized to preserve the regularity of the level set function evolution. Li et al introduced a regularization function based on the model proposed by Caselles, which is essentially based on the level set function of the edge, and after the regularization term is fused, the level set function is kept as a symbolic distance function in the evolution process, so that the model is free from reinitialization and the convergence speed is increased, and the model is represented by a DRLSE1 model. However, the model is unstable in value under special conditions and is easy to have negative influence on the model. In 2010, Li et al proposed an optimized distance regularization level set model to overcome adverse effects on the basis of previous work, enhancing the segmentation performance of the model, which is denoted by DRLSE 2. Zhang et al later proposed a gaussian regularization method, which was introduced into a level set model to achieve local segmentation, and the evolution process of the model was equivalent to the gaussian smoothing process, thereby avoiding the reinitialization process in the level set evolution. It is worth noting that the model can segment the target object quickly, but there is no further investigation on model oscillation. Then Zhang et al further proposed a new diffusion (RD) method for implicit active contours without re-initialization during the evolution process. The method has good performance on images which are divided into weak edges and easy to generate boundary leakage, but the convergence rate of the method is lower than that of a Gaussian regular level set model.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a level set optimization method for underwater image segmentation, which improves the stability and convergence speed of model evolution by improving the diffusivity of a diffusion function in a regular term, solves the problems of reinitialization and slow convergence of a level set and further optimizes the segmentation effect of an underwater image.
The technical scheme is as follows: in order to achieve the above object, the present invention provides a level set optimization method for underwater image segmentation, comprising the following steps:
(1) the regular term is optimally designed, and the mode of the integrand function in the regular term is the gradient
Figure BDA0002492843350000021
Is a variable, in
Figure BDA0002492843350000022
And
Figure BDA0002492843350000023
in two intervals, with
Figure BDA0002492843350000024
To constrain
Figure BDA0002492843350000025
Approach to 1 and lie in
Figure BDA0002492843350000026
In the region of (1), utilize
Figure BDA0002492843350000027
And
Figure BDA0002492843350000028
multiply and accelerate
Figure BDA0002492843350000029
A speed approaching 1;
(2) construction of level set energy functional EZ＝EW+ENWherein the regularization term ENInternal energy terms, data items E, forming energy functionalWAn external energy term constituting an energy functional;
(3) initial level set function of phi0＝cos(r1x)cos(r2y) in which r1Is the product of the input underwater image height and pi, r2The product of the width of the input underwater image and pi, wherein (x, y) is the coordinate of a pixel point in the underwater image;
(4) according to
Figure BDA00024928433500000210
Updating a level set function, and increasing the diffusivity of the function by using the proposed regular term in the evolution process to accelerate the convergence speed of the model, wherein t is time, delta t represents a time step, and n represents iteration times;
(5) and (4) judging whether the level set function phi reaches a convergence condition, and if the level set function phi does not reach the convergence condition, skipping to the step (4) to continue evolving the level set.
The optimization regularization term in the step (1) aims to solve the problem of reinitialization and improve convergence rate, and the function of the optimization regularization term is defined as:
Figure BDA00024928433500000211
where Ω represents the entire image domain.
Of the regular term functions, the integrand
Figure BDA00024928433500000212
The expression of (a) is:
Figure BDA0002492843350000031
solving an evolution equation by using an Euler-Lagrange equation for the optimization regularization term:
Figure BDA0002492843350000032
the diffusivity function in the optimization regularization term is:
Figure BDA0002492843350000033
the energy functional synthesis external term E in the step (2)WAnd an internal item ENThe latter overall function EZComprises the following steps:
Figure BDA0002492843350000034
wherein,
Figure BDA0002492843350000035
as data items, ωiIs a conditioning parameter, S is a saliency value extracted from an underwater image, saiIs the average of the saliency inside and outside the contour, i ═ 1,2 is used as a subscript to distinguish between the inside and outside regions of the contour, g represents the edge weight, and H (Φ) is the hervesseld function.
The level set function is solved by a gradient descent method to obtain an evolution equation:
Figure BDA0002492843350000036
and (4) updating and iterating according to the level set evolution equation.
Has the advantages that: the method improves the regular term aiming at the problems of reinitialization and slow convergence, improves the diffusivity of the diffusion function of the regular term, accelerates the convergence speed of the model, and reduces the convergence times required by the curve convergence to the target boundary; and the level set function is regularized through the proposed regular term, the reinitialization problem of the model is solved, and the segmentation precision lost due to reinitialization is further reduced. Experiments show that the level set method provided by the invention can accurately realize underwater image segmentation. Compared with the existing level set method, the method has higher segmentation precision and faster convergence rate for the underwater image.
Drawings
FIG. 1 is a flow chart of an underwater image segmentation method in the present invention.
Fig. 2 is a graph of the underwater original image (a) and the segmentation result (b) when there is no regularization term.
Fig. 3 is a diagram of an underwater original image (a) and a division result (b) when a regularization term is present.
FIG. 4 is a graph comparing the diffusivity equation for the regularization term in the present invention with the diffusivity equation for the regularization term in the DRLSE2 model. The dashed line represents the DRLSE2 diffusivity equation for
Figure BDA0002492843350000041
Curve (c) of (d). The solid line represents the diffusivity equation for the model of the present invention with respect to
Figure BDA0002492843350000042
Curve (c) of (d).
FIG. 5 is a zero level set contour result graph of the present invention method and several comparative methods for underwater image segmentation. Where (a) is the underwater original image, (b) is the result of the DRLSE2 method, (c) is the result of the RD method, and (d) is the result of the method of the present invention, and (1) - (8) lines represent underwater images of different objects.
FIG. 6 is a graph of the binarization results of the method of the present invention and several comparison methods for underwater image segmentation. In which (a) the underwater original image, (b) the artificially labeled true values, (c) the result of the DRLSE2 method, (d) the RD method, and (e) the results of the inventive method, the lines (1) to (8) representing underwater images of different objects.
Detailed Description
In order to clearly highlight the objects and advantages of the present invention, the present invention will be further described below with reference to the accompanying drawings in the present embodiment, and an implementation process of a level set optimization method for underwater image segmentation disclosed in the present embodiment mainly includes the following steps:
(1) the underwater image is inputted as any one of the images in the (a) column in fig. 5. The optimized regular term function designed by the invention and the image characteristics extracted from the underwater image respectively form an internal energy function and an external energy function of the level set energy functional, wherein the external energy function is formed by the region level characteristics and the edge level characteristics. Where region-level features refer to the intensity of the image. Edge level features refer to the gradients of an image.
The expression of the level set model framework is as follows:
EZ＝EW+EN
in the formula, EWIs a constraint term representing an external energy term. ENRepresents an internal energy function, i.e. a regularization term.
Internal energy function E in the level set modelNThe expression is as follows:
Figure BDA0002492843350000043
wherein
Figure BDA0002492843350000044
The modulus representing the gradient, (x, y) are the coordinates of the pixel points in the underwater image, Ω represents the entire image domain,
Figure BDA0002492843350000045
the functional expression is:
Figure BDA0002492843350000051
in that
Figure BDA0002492843350000052
And
Figure BDA0002492843350000053
on the two intervals, the number of the interval,
Figure BDA0002492843350000054
all are provided with
Figure BDA0002492843350000055
This term is used to constrainGradient of
Figure BDA0002492843350000056
Approaching to 1. In addition, the models are not used singly
Figure BDA0002492843350000057
Such a constraint term is as
Figure BDA0002492843350000058
On the interval of (1), model utilization
Figure BDA0002492843350000059
This term and
Figure BDA00024928433500000510
multiply so that
Figure BDA00024928433500000511
The approach to 1 is faster.
Internal energy function E in the level set modelNBy a regularization term
Figure BDA00024928433500000512
And (3) solving to obtain a modeling equation:
Figure BDA00024928433500000513
according to the regular term function, the diffusivity equation can be obtained as follows:
Figure BDA00024928433500000514
to obtain:
Figure BDA00024928433500000515
combining the diffusivity equation with fig. 4, we find the relevant properties of the diffusivity equation as follows:
1) in that
Figure BDA00024928433500000516
The diffusivity function value h is greater than 0, the function is expressed as forward diffusion, and the model is a gradient
Figure BDA00024928433500000517
Suppressed to 1.
2) In that
Figure BDA00024928433500000518
Is less than 0, then the function is expressed as back diffusion and the model will be
Figure BDA00024928433500000519
Increasing to 1.
3) In that
Figure BDA00024928433500000520
The diffusivity function value h is greater than 0, the function is expressed as forward diffusion, and the model will be
Figure BDA00024928433500000521
Suppressed to 0. As described above, the level set function can be increased or decreased by such adaptation
Figure BDA00024928433500000522
And minimization of the energy function, which in turn drives the model curve to shrink to the desired target boundary.
As shown in FIG. 4, the diffusivity function of the regularization term of the present invention is compared with that of the DRLSE2 model by h2And h1It is shown, to conclude:
1) in that
Figure BDA0002492843350000061
In the interval, the positive and negative of the function values are forward diffusion, and the function value h2Greater than h1Represents the proposed function pair
Figure BDA0002492843350000062
The restraining force is greater than DRLSE2, which makes
Figure BDA0002492843350000063
The speed of the model is faster, namely the model has a faster convergence speed when being used for segmenting the underwater image, and meanwhile, the model only needs less iteration times.
2) In that
Figure BDA0002492843350000064
In the interval, all belong to backward diffusion, and the function value h2Is still greater than h1Similarly, the proposed function pair
Figure BDA0002492843350000065
Is greater than DRLSE2, such that
Figure BDA0002492843350000066
Is faster.
3) For the interval
Figure BDA0002492843350000067
Both the proposed function and the DRLSE2 model guarantee the symbolic distance function property away from the zero level set
Figure BDA0002492843350000068
The external energy function E in the level set modelWExpressed as:
Figure BDA0002492843350000069
in the model, g represents the edge weight and the level set function phi represents the curve profile. OmegaiIs an adjustment parameter, H (phi) denotes the Hervesseld function, S is a saliency value extracted from an underwater image, saiIs the average of the saliency inside and outside the contour, i is used as a subscript to distinguish the inside and outside regions of the contour, and (x, y) is the pixel point coordinates in the underwater image.
The expression of the edge detector in the level set model is as follows:
Figure BDA00024928433500000610
wherein I is an input image, GσIs a gaussian kernel with a standard deviation of sigma,
Figure BDA00024928433500000611
for gradient operation, a convolution operation is denoted.
The Heaviside function is:
Figure BDA00024928433500000612
the region features in the level set model are extracted by a significance method:
S(x,y)＝|I(x,y)-IGass(x,y)|
wherein I is an input image, IGassRepresenting the image after processing with a gaussian filter.
In the region feature extraction method IGassIs defined as:
IGass(x,y)＝κζ*I(x,y)
extracting k in the Gaussian image equationζIs a gaussian kernel with a standard deviation ζ.
The region characteristics in the level set model are extracted by a significance method, and the expression of the significance inside and outside the outline is as follows:
Figure BDA0002492843350000071
Figure BDA0002492843350000072
and finally, the energy functional of the level set model is as follows:
Figure BDA0002492843350000073
(2) initializing a level set function, evolving a level set model, and enhancing the segmentation performance of the model on the underwater image by using the optimized regular term.
The initial level set function is:
φ0＝cos(r1x)cos(r2y)
in the initial function r1For inputting the product of the height of the underwater image and pi, r2The product of the width of the underwater image and pi is input, and (x, y) is the coordinate of a pixel point in the underwater image.
The model is solved by a gradient descent method:
Figure BDA0002492843350000074
and obtaining the following by calculating the partial derivative of the energy function:
wherein div represents the divergence, and solving the energy functional to obtain a level set evolution equation:
Figure BDA0002492843350000081
the present invention uses a quantitative standard Jaccard Similarity (JS) standard to accurately evaluate the segmentation performance of these methods. JS Standard, theoretically two sets P1And P2The ratio of the intersection of (a) to their union, the formula is:
Figure BDA0002492843350000082
the closer the JS value is to 1, the more P is represented1The closer to P2The higher the segmentation accuracy of the model. P1Represents the result of the segmentation, and P2Representing the standard value of the manual annotation.
The selected underwater image samples are divided into two types in terms of characteristics, one type is represented by fuzzy image details and less background interference, and the degree of distinction between a target and a background in the images is lower; one category appears to be strong noise, and the objects in such images are often mixed with complex background interference, which presents a great challenge to the segmentation model.
TABLE 1 quantitative comparison table of level set model segmentation results
Figure BDA0002492843350000083
It can be seen from fig. 2 and fig. 3 that the segmentation result of the present invention is significantly better than the segmentation result of the model without the regularization term, and although the target region is extracted from the result of the model without the regularization term, the model without the regularization term has a large amount of point noise, and the model is not reinitialized by the regularization term of the present invention, so that the accuracy is not lost.
Qualitative results fig. 5 further illustrates that the present invention achieves its theoretical effect, has better convergence, and has better segmentation effect on underwater images. In order to fully illustrate the auxiliary effect of the proposed regularization term on the model, the invention quantifies and compares the results of qualitative experiments. From table 1 it can be seen that the JS value score of the present invention is first, illustrating the superiority of the method of the present invention over the two comparison algorithms. In addition, the calculation time and convergence times of the model evolution are counted. The run-time results are shown in Table 1, where the run-times are the CPU time required for the model to complete convergence, and it can be seen that the time spent by the model of the present invention is also ranked first.
In addition, on the premise of ensuring that each algorithm obtains the optimal result, comparing the iteration times of completing the segmentation of the algorithms, the number of the DRLSE2 models is 320, the number of the RD models is 400, and the iteration times of the method is 40. The RD algorithm, although more accurate than the DRLSE2 method in segmentation, iterates slower on this model. The method is obtained by integrating two indexes of the segmentation precision JS and the iteration times, is superior to a comparison method, and can prove the excellent performance of the method.

Claims (6)

1. A level set optimization method for underwater image segmentation is characterized by comprising the following steps: comprises the following steps:
(1) the regular term is optimally designed, and the mode of the integrand function in the regular term is the gradient
Figure FDA0002492843340000011
Is a variable, in
Figure FDA0002492843340000012
And
Figure FDA0002492843340000013
in two intervals, with
Figure FDA0002492843340000014
To constrain
Figure FDA0002492843340000015
Approach to 1 and lie in
Figure FDA0002492843340000016
In the interval of (1), use
Figure FDA0002492843340000017
And
Figure FDA0002492843340000018
multiply and accelerate
Figure FDA0002492843340000019
A speed approaching 1;
(2) construction of level set energy functional EZ＝EW+ENWherein the regularization term ENIs an internal energy term of an energy functional, data item EWIs an external energy term of the energy functional;
(3) initial level set function of phi0＝cos(r1x)cos(r2y) in which r1Is the product of the height of the input underwater image and pi, r2The product of the width of the input underwater image and pi, wherein (x, y) is the coordinate of a pixel point in the underwater image;
(4) according to the equation
Figure FDA00024928433400000110
Updating a level set function, improving the function diffusivity by using an optimization regular term in the evolution process, and accelerating the convergence speed of the model, wherein t is time, delta t represents a time step, and n represents iteration times;
(5) and (4) judging whether the level set function phi reaches a convergence condition, and if the level set function phi does not reach the convergence condition, skipping to the step (4) to continue evolving the level set.
2. The method of claim 1, wherein the method comprises: the optimization regularization term function in the step (1) is defined as:
Figure FDA00024928433400000111
where Ω represents the entire image domain, the integrand
Figure FDA00024928433400000112
The expression of (a) is:
Figure FDA00024928433400000113
3. the method of claim 2, wherein the level set optimization is performed by: solving an evolution equation by using an Euler-Lagrange equation for the optimization regularization term as follows:
Figure FDA00024928433400000114
wherein div represents the divergence.
4. The method of claim 2, wherein the level set optimization is performed by: the diffusivity function in the regularization term is:
Figure FDA0002492843340000021
5. the method of claim 2, wherein the level set optimization is performed by: the energy functional synthesis external term E in the step (2)WAnd an internal item ENThe latter overall function EZComprises the following steps:
Figure FDA0002492843340000022
wherein,
Figure FDA0002492843340000023
as data items, ωiIs a conditioning parameter, S is a saliency value extracted from an underwater image, saiIs the average of the saliency inside and outside the contour, i ═ 1,2 is used as a subscript to distinguish between the inside and outside regions of the contour, g represents the edge weight, and H (Φ) is the hervesseld function.
6. The method of claim 5, wherein the level set optimization comprises: after the level set function is solved by a gradient descent method, a level set evolution equation is obtained as follows:
Figure FDA0002492843340000024
wherein, div represents the divergence,
Figure FDA0002492843340000025
and (4) updating and iterating according to the level set evolution equation in the step (4) as a diffusion rate function.
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