CN101964112A

CN101964112A - Adaptive prior shape-based image segmentation method

Info

Publication number: CN101964112A
Application number: CN 201010523614
Authority: CN
Inventors: 刘维平; 杨新; 赵庆
Original assignee: Shanghai Jiao Tong University
Current assignee: Shanghai Jiao Tong University
Priority date: 2010-10-29
Filing date: 2010-10-29
Publication date: 2011-02-02
Anticipated expiration: 2030-10-29
Also published as: CN101964112B

Abstract

An image segmentation method based on prior shape in the field of image processing technology, which uses integer sign function to overcome the influence of noise interference on image segmentation, and manually adjusts the weight coefficients of prior shape model and traditional active contour model according to its needs , a constrained variational model is proposed so that the weight coefficient can be adaptively converged to a stable value, and at the same time, the recognition-based shape template selection is used to determine which prior shape shape template to use during segmentation, avoiding the prior art The problem of not getting segmentation results based on prior shape models.

Description

Adaptive Image Segmentation Method Based on Prior Shape

技术领域technical field

本发明涉及的是一种图像处理的方法，具体是一种自适应的基于先验形状的图像分割方法。The invention relates to an image processing method, in particular to an adaptive image segmentation method based on a priori shape.

背景技术Background technique

活动轮廓模型和水平集方法已经广泛的应用在图像处理和机器视觉当中。然而，当目标的边缘和背景间的差异不是很大的时候，演化曲线将会出现泄漏，导致分割失败。而且，如果图像中存在噪声、杂波或者遮挡的时候，普通的分割模型不能提取出有意义的目标。一个有效的办法是将目标的一些先验知识融入活动轮廓模型的框架中。低层的先验知识，例如：灰度级、颜色、纹理和运动等信息往往不足以表示目标特征，在实际应用中通常不能保证这些特征的不变性。近些年来，高层的知识，尤其是形状被很多学者所重视，并将其融入到分割模型中。这类模型往往被称为基于先验形状的图像分割方法。该方法有两个难点：首先如何将先验形状表示、描述成可以被分割模型利用的形状模型，其次如何将该形状模型融入到传统的分割模型中。Active contour models and level set methods have been widely used in image processing and machine vision. However, when the difference between the edge of the object and the background is not large, the evolution curve will leak, resulting in segmentation failure. Moreover, common segmentation models cannot extract meaningful objects if there is noise, clutter, or occlusion in the image. An effective approach is to incorporate some prior knowledge of the target into the framework of the active contour model. Low-level prior knowledge, such as information such as grayscale, color, texture, and motion, is often insufficient to represent target features, and the invariance of these features is usually not guaranteed in practical applications. In recent years, high-level knowledge, especially shape, has been valued by many scholars and incorporated into segmentation models. Such models are often referred to as prior shape-based image segmentation methods. This method has two difficulties: first, how to represent and describe the prior shape as a shape model that can be utilized by the segmentation model, and second, how to integrate the shape model into the traditional segmentation model.

很多学者对这一问题进行了研究。目前对该问题的研究大致分为两类：统计先验模型和基于形状模板匹配的模型。Many scholars have conducted research on this issue. Current research on this problem can be roughly divided into two categories: statistical prior models and models based on shape template matching.

在统计先验模型中，M.E.Levento等在CVPR(计算机视觉与模式识别国际会议)(2000，1：1316-1323)上发表了“Statistical shape influence in geodesic active contours”(“统计先验模型对测地线活动轮廓模型的影响”)一文，该文率先提出了通过估计形状的概率密度，然后将形状的概率密度和活动轮廓模型融入到贝叶斯框架中的方法。在该文中，主成分分析和核主成分分析被用来提取形状特征，用于估计形状的概率密度函数。另外，M.Rousson和D.Cremers在MICCAI(医学影像计算与计算机辅助介入国际会议)(2005：757-764)上发表了“Eficientkernel density estimation of shape and intensity priors for level set segmentation”(“引入对形状核密度估计的水平集分割方法”)一文，该文对比了高斯分布、一致分布和核密度估计，证明了核密度估计对形状的概率密度函数估计的有效性。In the statistical prior model, M.E. Levento et al. published "Statistical shape influence in geodesic active contours" ("Statistical prior model to test Influence of the Ground Line Active Contour Model”), which pioneered the method of estimating the probability density of the shape and then integrating the probability density of the shape and the active contour model into a Bayesian framework. In this paper, principal component analysis and kernel principal component analysis are used to extract shape features for estimating the probability density function of the shape. In addition, M.Rousson and D.Cremers published "Eficientkernel density estimation of shape and intensity priors for level set segmentation" ("Introduction to A Level Set Segmentation Method for Shape Kernel Density Estimation"), which compares Gaussian distribution, uniform distribution, and kernel density estimation, and proves the effectiveness of kernel density estimation for shape probability density function estimation.

在基于形状模板匹配的模型中，N.Paragios等在ECCV(欧洲计算机视觉国际会议)(2002：775-789)上发表了“Matching distance functions：a shape-to-area variational approach forglobal-to-local registration”(“匹配距离函数-用于全局到局部配准的结合形状和区域的配准方法”)一文，该文提出采用单一形状模板作为形状模型，通过配准演化曲线和形状模板，从而使得演化曲线朝着形状模板演化，通过手动调整该配准项和传统活动轮廓模型间的权值系数即可实现基于形状模板的图像分割。In the model based on shape template matching, N. Paragios et al. published "Matching distance functions: a shape-to-area variational approach forglobal-to-local" at ECCV (European International Conference on Computer Vision) (2002: 775-789). Registration" ("Matching distance function-a registration method combining shape and area for global to local registration"), this paper proposes to use a single shape template as the shape model, and through the registration evolution curve and shape template, so that The evolution curve evolves towards the shape template, and the image segmentation based on the shape template can be realized by manually adjusting the weight coefficient between the registration item and the traditional active contour model.

上诉基于先验形状的分割模型虽然在当背景中存在噪声、杂波和遮挡的时候也能保证一定的分割精度，但是仍然存在以下问题没有解决：将先验形状模型和传统活动轮廓模型相结合时，需要手动调节这两项间的权值系数，并且没有任何准则来指导如何调整该系数。如果该系数调节不当，往往得不到基于先验形状模型的分割结果；大多数的形状模型采用符号距离函数来描述图像，然而由于符号距离函数所在空间是非线性的，通过线性加权得到的统计形状模型和参数形状模板所描述的图像已经不再满足符号距离函数。Although the segmentation model based on the prior shape can guarantee a certain segmentation accuracy when there is noise, clutter, and occlusion in the background, there are still the following problems that have not been resolved: Combining the prior shape model with the traditional active contour model When , it is necessary to manually adjust the weight coefficient between these two items, and there is no guideline to guide how to adjust the coefficient. If the coefficient is not adjusted properly, the segmentation results based on the prior shape model are often not obtained; most shape models use the signed distance function to describe the image, but because the space where the signed distance function is located is nonlinear, the statistical shape obtained by linear weighting Images described by models and parametric shape templates no longer satisfy the signed distance function.

发明内容Contents of the invention

本发明针对现有技术存在的上述两点不足，提供一种自适应的基于先验形状的图像分割方法，采用整数符号函数克服由于噪声的干扰对图像分割的影响，并针对其需要手动调节先验形状模型和传统活动轮廓模型的权值系数，提出约束变分模型使得该权值系数可以自适应的收敛到稳定值，同时以识别为基础的形状模板选择用以在分割时候确定采用哪个先验形状的形状模板，避免现有技术中得不到基于先验形状模型的分割结果的问题。The present invention aims at the above two deficiencies in the prior art, and provides an adaptive image segmentation method based on the prior shape, which uses integer sign functions to overcome the influence of noise interference on image segmentation, and manually adjusts the priori The weight coefficients of the shape model and the traditional active contour model are tested, and a constrained variational model is proposed so that the weight coefficients can be adaptively converged to a stable value. The shape template of the prior shape avoids the problem that the segmentation result based on the prior shape model cannot be obtained in the prior art.

本发明是通过以下技术方案实现的，本发明包括以下步骤：The present invention is achieved through the following technical solutions, and the present invention comprises the following steps:

第一步、将目标图像的形状表示为形状模板作为先验形状模板库，初始化演化曲线。In the first step, the shape of the target image is represented as a shape template as a prior shape template library, and the evolution curve is initialized.

所述的整数符号函数的形状模板是指：以双边的链表结构C表示形状轮廓，该双边的链表结构的内边缘为L_in，外边缘为L_out，在C内部且不在L_in中的点为C_in，在C外部且不在L_out中的点为C_out，则有作为形状模板的整数符号函数：

其中：(x，y)为目标图像中任一一点的坐标，a和b为整数值，本发明中a＝1，b＝3。The shape template of the integer sign function refers to: the shape outline is represented by a double-sided linked list structure C, the inner edge of the double-sided linked list structure is L _in , the outer edge is L _out , and the point inside C and not _{in Lin} is C _in , and points outside C and not in L _out are C _out , then there are integer sign functions as shape templates:

Wherein: (x, y) is the coordinate of any point in the target image, a and b are integer values, and a=1, b=3 in the present invention.

所述形状模板是指：将先验形状的轮廓作为L_out，根据整数符号函数的定义将先验形状表示为整数符号函数。The shape template refers to: using the contour of the prior shape as L _out , expressing the prior shape as an integer sign function according to the definition of the integer sign function.

所述的演化曲线是指：在图像平面中的闭合曲线，初始化的时候一般需要手动。在本发明中同样采用整数符号函数描述在图像平面中的闭合曲线，其中将演化曲线作为L_out。The evolution curve refers to a closed curve in the image plane, and manual initialization is generally required. In the present invention, integer sign functions are also used to describe closed curves in the image plane, wherein the evolution curve is taken as L _out .

第二步、将演化曲线和先验形状模板库中的形状模板进行逐一配准，并根据配准结果更新形状模板库：The second step is to register the evolution curve and the shape templates in the prior shape template library one by one, and update the shape template library according to the registration results:

所述的配准是指：使得演化曲线和形状模板配准。最小化演化曲线和形状模板的误差平方和，优化尺度、旋转和平移使得误差平方和最小，具体步骤为：The registration refers to: make the evolution curve and the shape template register. Minimize the sum of squares of the evolution curve and the shape template, optimize the scale, rotation and translation to minimize the sum of squares of the error, the specific steps are:

2.1)演化曲线和形状模板的平方误差和表示为：E_S(φ，f)＝∫∫_Ω(φ-ψ(f))²dxdy，其中：ψ和φ分别为形状模板和演化曲线的整数符号函数，具体为：

其中(u，v)为形状模板平面上的点，

其中(x，y)为图像平面上的点；E_S为形状能量，f为刚体变换函数，具体为包括平移项T_x，T_y、旋转项θ和缩放项s，(T_x，T_y表示在x方向和y方向的平移)；2.1) The sum of squared errors of evolution curve and shape template is expressed as: E _S (φ, f) = ∫∫ _Ω (φ-ψ(f)) ² dxdy, where: ψ and φ are the integers of shape template and evolution curve respectively Symbolic functions, specifically:

where (u, v) is a point on the plane of the shape template,

Where (x, y) is a point on the image plane; E _S is the shape energy, f is the rigid body transformation function, specifically Including translation items T _x , T _y , rotation item θ and scaling item s, (T _x , T _y represent translation in the x direction and y direction);

2.2)作为尺度、旋转和平移的梯度下降方程具体为：

其中：p∈{T_x，T_y，θ，s}。2.2) The gradient descent equation as scale, rotation and translation is specifically:

Where: p ∈ {T _x , Ty _y , θ, s}.

2.3)根据平移项T_x，T_y、旋转项θ和缩放项s更新形状模板。2.3) Update the shape template according to the translation term T _x , _Ty , the rotation term θ and the scaling term s.

第三步、利用形状相似性度量从所述先验形状模板库中选择形状模板：采用部分豪斯道夫距离方法度量演化曲线与更新后的形状模板的相似性程度，并取出相似性程度最大的形状模板作为识别结果；The third step is to use the shape similarity measure to select a shape template from the prior shape template library: use the partial Hausdorff distance method to measure the degree of similarity between the evolution curve and the updated shape template, and take out the one with the largest similarity. Shape templates as recognition results;

所述的相似性程度是指：H_LK(A，B)＝max(h_L(A，B)，h_K(B，A))，其中：

为改进后的有向豪斯道夫距离，

代表距离集中的第K个值，同样的意义用于L，点集A＝{a₁，...，a_m}为演化曲线上的所有点，m表示A中点的数目，点集B＝{b₁，...，b_n}为形状模板轮廓上的点，n表示B中点的数目。定义p₁＝K/m和p₂＝L/n，则p₁和p₂的范围在[0，1]，且p₁和p₂的选择取决于目标被遮挡的程度。通过选定p₁和p₂就可以确定L和K。The degree of similarity refers to: H _LK (A, B)=max(h _L (A, B), h _K (B, A)), wherein:

is the improved directed Hausdorff distance,

Represents the Kth value in the distance set, the same meaning is used for L, point set A={a ₁ ,..., _am } is all points on the evolution curve, m represents the number of points in A, point set B ={b ₁ ,...,b _n } are points on the outline of the shape template, and n represents the number of points in B. Define p ₁ =K/m and p ₂ =L/n, then the range of p ₁ and p ₂ is [0, 1], and the selection of p ₁ and p ₂ depends on the degree of occlusion of the target. L and K can be determined by selecting p ₁ and p ₂ .

第四步、利用约束变分模型求得识别结果中的形状和灰度之间的权值系数，并结合形状模板和图像灰度信息分割目标图像得到分割结果。The fourth step is to use the constrained variational model to obtain the weight coefficient between the shape and the gray level in the recognition result, and combine the shape template and image gray level information to segment the target image to obtain the segmentation result.

所述的约束变分模型为：The constrained variational model is:

$min min {&Integral; &Integral; &Integral; &Integral;}_{Ω Ω} {λ λ}_{i i} {((I I - - {c c}_{i i}))}^{22} ((- - \frac{φ φ - - b b}{22 b b})) dxdy dxdy + + {&Integral; &Integral; &Integral; &Integral;}_{Ω Ω} {λ λ}_{o o} {((I I - - {c c}_{o o}))}^{22} ((\frac{φ φ + + b b}{22 b b})) dxdy dxdy,,$

s.t.∫∫_Ω(φ-ψ(f))²dxdy＝α∫∫_Ω(2b)²δ(ψ(f)-a)dxdy， _st∫∫Ω (φ-ψ(f)) ^2dxdy ＝ _α∫∫Ω (2b) ^2δ (ψ(f)-a)dxdy,

上述约束变分模型的解析解满足欧拉方程(EE)和LMR，具体如下：The analytical solution of the above constrained variational model satisfies the Euler equation (EE) and LMR, as follows:

$\frac{{λ λ}_{i i}}{22 b b} {((I I - - {c c}_{i i}))}^{22} - - \frac{{λ λ}_{o o}}{22 b b} {((I I - - {c c}_{o o}))}^{22} - - 22 ξ ξ ((φ φ - - ψ ψ ((f f)))) = = 00,,$

∫∫_Ω(φ-ψ(f))²dxdy＝α∫∫_Ω(2b)²δ(ψ(f)-a)dxdy， _∫∫Ω (φ-ψ(f)) ^2dxdy ＝ _α∫∫Ω (2b) ^2δ (ψ(f)-a)dxdy,

其中：ζ为拉格朗日乘子常数，即为将C-V能量函数和形状能量E_S结合起来的权值系数，α是常量，α＝2.5或0.2。Among them: ζ is the Lagrange multiplier constant, that is, the weight coefficient that combines the CV energy function and the shape energy _ES , α is a constant, α=2.5 or 0.2.

所述的拉格朗日乘子常数通过交替计算以下迭代方程，直到φ和ζ达到稳定：The Lagrangian multiplier constants are computed alternately by the following iterative equations until φ and ζ are stabilized:

$\frac{&PartialD; &PartialD; φ φ}{&PartialD; &PartialD; t t} = = \frac{{λ λ}_{i i}}{22 b b} {((I I - - {c c}_{i i}))}^{22} - - \frac{{λ λ}_{o o}}{22 b b} {((I I - - {c c}_{o o}))}^{22} - - 22 ξ ξ ((φ φ - - ψ ψ ((f f)))),,$

$\frac{&PartialD; &PartialD; ξ ξ}{&PartialD; &PartialD; t t} = = {&Integral; &Integral; &Integral; &Integral;}_{Ω Ω} {((φ φ - - ψ ψ ((f f))))}^{22} dxdy dxdy - - α α {&Integral; &Integral; &Integral; &Integral;}_{Ω Ω} {((22 b b))}^{22} δ δ ((ψ ψ ((f f)) - - a a)) dxdy dxdy,,$

其中：

为曲线的演化方程，

为拉格朗日乘子的迭代方程。in:

is the evolution equation of the curve,

Iterative equation for Lagrange multipliers.

本发明技术效果在于：解决了传统的基于先验形状的图像分割方法需要手动调节权值系数的问题(该权值系数用于平衡形状知识和图像本身的灰度级)；并且，本发明可以自适应的选择最相似的形状模板用来指导图像分割；再者，当图像背景存在噪声、杂波，甚至待分割目标被部分遮挡时，本发明仍然能够分割出想要的目标。The technical effect of the present invention is: solve the problem that the traditional shape-based image segmentation method needs to manually adjust the weight coefficient (the weight coefficient is used to balance the shape knowledge and the gray level of the image itself); and, the present invention can Adaptive selection of the most similar shape template is used to guide image segmentation; moreover, when there is noise and clutter in the image background, and even the target to be segmented is partially blocked, the present invention can still segment the desired target.

附图说明Description of drawings

图1不同λ取值对分割结果的影响。Figure 1. The influence of different λ values on the segmentation results.

图2为待分割海星和先验形状模板库。Figure 2 shows the starfish to be segmented and the prior shape template library.

图3为海星分割检测结果。Figure 3 is the starfish segmentation detection results.

图4为海星分割检测的拉格朗日乘子和部分豪斯道夫距离。Figure 4 shows the Lagrangian multipliers and partial Hausdorff distances for starfish segmentation detection.

图5为左心室先验形状模板库。Figure 5 is the template library of the left ventricle prior shape.

图6为左心室分割检测结果。Figure 6 shows the detection results of left ventricle segmentation.

图7为左心室分割检测的部分豪斯道夫距离和拉格朗日乘子。Figure 7 shows partial Hausdorff distances and Lagrangian multipliers for left ventricle segmentation detection.

图8为行人分割检测结果。Figure 8 shows the detection results of pedestrian segmentation.

图9为行人分割检测的部分豪斯道夫距离和拉格朗日乘子。Figure 9 shows part of the Hausdorff distance and Lagrangian multipliers for pedestrian segmentation detection.

图10为不同视点观察下的兵马俑分割检测先验形状模板库。Figure 10 shows the prior shape template library for segmentation detection of terracotta warriors and horses under observation from different viewpoints.

图11为不同视点观察下的兵马俑分割检测结果。Figure 11 shows the segmentation detection results of the terracotta warriors and horses observed from different viewpoints.

具体实施方式Detailed ways

下面对本发明的实施例作详细说明，本实施例在以本发明技术方案为前提下进行实施，给出了详细的实施方式和具体的操作过程，但本发明的保护范围不限于下述的实施例。The embodiments of the present invention are described in detail below. This embodiment is implemented on the premise of the technical solution of the present invention, and detailed implementation methods and specific operating procedures are provided, but the protection scope of the present invention is not limited to the following implementation example.

本实施例包括以下步骤：This embodiment includes the following steps:

第一步、初始化演化曲线(分割结果)，并将目标图像的形状表示为整数符号函数的形状模板作为先验形状模板库：The first step is to initialize the evolution curve (segmentation result), and represent the shape of the target image as a shape template of an integer sign function as a priori shape template library:

将形状表示为整数符号距离函数：假设轮廓为C，将其表示为双边的链表结构：内边缘L_in和外边缘L_out。定义在C内部且不在L_in中的点为C_in；在C外部且不在L_out中的点为C_out。Express the shape as an integer signed distance function: Assuming the contour is C, express it as a two-sided linked list structure: the inner edge L _in and the outer edge L _out . A point defined inside C and not in L _in is C _in ; a point outside C and not in L _out is C _out .

$φ φ ((x x,, y the y)) = = \{\begin{matrix} - - b b,, ((x x,, y the y)) &Element; &Element; {C C}_{in in} \\ - - a a,, ((x x,, y the y)) &Element; &Element; {L L}_{in in} \\ a a,, ((x x,, y the y)) &Element; &Element; {L L}_{out out} \\ b b,, ((x x,, y the y)) &Element; &Element; {C C}_{out out} \end{matrix},,$

其中(x，y)为当前点的坐标，a和b为整数值，本实施例中令a＝1，b＝3。Where (x, y) is the coordinates of the current point, a and b are integer values, and a=1, b=3 in this embodiment.

第二步、将图像分割结果和预置的形状库中的形状模板逐一配准，并根据配准结果更新形状模板库：The second step is to register the image segmentation results with the shape templates in the preset shape library one by one, and update the shape template library according to the registration results:

假设分别用整数符号函数ψ和φ分别代表某个形状模板和演化曲线。通过最优化其误差平方和(最优化旋转、平移和缩放项)，可将其配准。ψ和φ的误差平方和定义如下：Assume that a certain shape template and evolution curve are represented by integer signed functions ψ and φ, respectively. They can be registered by optimizing their sum of squared errors (optimizing rotation, translation and scaling terms). The sum of squared errors for ψ and φ is defined as follows:

E_S(φ，f)＝∫∫_Ω(φ-ψ(f))²dxdyE _S (φ, f)＝ _∫∫Ω (φ-ψ(f)) ² dxdy

其中，E_S为形状能量，f为刚体变换函数，包括平移项T_x，T_y、旋转项θ和缩放项s。Among them, E _S is the shape energy, f is the rigid body transformation function, including the translation term T _x , Ty _y , the rotation term θ and the scaling term s.

配准可以通过梯度下降法来实现，并且，刚体变换参数的最大梯度下降方向如下：Registration can be achieved by the gradient descent method, and the maximum gradient descent direction of the rigid body transformation parameters is as follows:

$\frac{&PartialD; &PartialD; p p}{&PartialD; &PartialD; t t} = = 22 {&Integral; &Integral; &Integral; &Integral;}_{Ω Ω} ((ψ ψ ((f f)) - - φ φ)) &dtri; &dtri; ψ ψ \frac{&PartialD; &PartialD; f f}{&PartialD; &PartialD; p p} dxdy dxdy$

其中，p∈{T_x，T_y，θ，s}。where p∈{T _x ,T _y ,θ,s}.

根据所求得的平移项T_x，T_y、旋转项θ和缩放项s，更新该形状模板。The shape template is updated according to the calculated translation terms T _x , _Ty , rotation term θ and scaling term s.

第三步、利用形状相似性度量从所述先验形状模板库中选择形状模板：部分豪斯道夫距离在比较两个形状的部分相似性时具有很好的效果。当目标物体存在部分遮挡时，使用部分豪斯道夫距离同样可以对物体进行识别。在前面所述的有向豪斯道夫距离的定义中将全局最大值改为第K个值，即得到改进后的有向豪斯道夫距离：The third step is to select a shape template from the prior shape template library by using the shape similarity measure: the partial Hausdorff distance has a good effect when comparing the partial similarity of two shapes. When the target object is partially occluded, the object can also be identified by using the partial Hausdorff distance. In the definition of the directed Hausdorff distance mentioned above, the global maximum value is changed to the Kth value, which is the improved directed Hausdorff distance:

${h h}_{K K} ((B B,, A A)) = = {K K}_{a a &Element; &Element; A A}^{th the th} \underset{b b &Element; &Element; B B}{min min} | | | | a a - - b b | | | |$

其中，

代表距离集中的第K个值。in,

Represents the Kth value in the distance set.

于是，部分豪斯道夫距离的定义如下：Then, the partial Hausdorff distance is defined as follows:

演化曲线上的所有点构成点集A，形状模板轮廓上的点构成点集B。部分豪斯道夫距离的定义式中含有两个参数p₁＝K/m和p₂＝L/n，p₁和p₂的范围是[0，1]。p₁和p₂的选择取决于目标被遮挡的程度。先验形状模板库里的每一个形状模板都将与演化曲线分别计算部分豪斯道夫距离，与演化曲线最相似的形状模板，即部分豪斯道夫距离值最小的形状模板，将被选择用于指导曲线的演化。All points on the evolution curve constitute point set A, and points on the contour of the shape template constitute point set B. The definition formula of the partial Hausdorff distance contains two parameters p ₁ =K/m and p ₂ =L/n, and the range of p ₁ and p ₂ is [0,1]. The choice of _p1 and _p2 depends on the degree of object occlusion. Each shape template in the prior shape template library will calculate the partial Hausdorff distance with the evolution curve, and the shape template most similar to the evolution curve, that is, the shape template with the smallest partial Hausdorff distance value, will be selected for guide the evolution of the curve.

本实施例中采用形状识别方法从形状模板库中选择形状模板，避免了由于符号距离函数的非线性性带来的形状表示的不准确。In this embodiment, the shape recognition method is used to select the shape template from the shape template library, which avoids inaccurate shape representation caused by the nonlinearity of the sign distance function.

在第一阶段中，令p₁＝p₂＝0.8；在第二阶段中，令p₁＝p₂＝0.95；In the first stage, let p ₁ =p ₂ =0.8; in the second stage, let p ₁ =p ₂ =0.95;

第四步、利用提出的约束变分模型求得形状和灰度间的权值系数，并结合所述形状模板和图像灰度信息分割所述目标图像得到新的分割结果：本实施例提出的约束变分模型如下：The fourth step, using the proposed constraint variational model to obtain the weight coefficient between the shape and grayscale, and combining the shape template and image grayscale information to segment the target image to obtain a new segmentation result: the proposed The constrained variational model is as follows:

$min min {&Integral; &Integral; &Integral; &Integral;}_{Ω Ω} {λ λ}_{i i} {((I I - - {c c}_{i i}))}^{22} ((- - \frac{φ φ - - b b}{22 b b})) dxdy dxdy + + {&Integral; &Integral; &Integral; &Integral;}_{Ω Ω} {λ λ}_{o o} {((I I - - {c c}_{o o}))}^{22} ((\frac{φ φ + + b b}{22 b b})) dxdy dxdy$

s.t.∫∫_Ω(φ-ψ(f))²dxdy＝α∫∫_Ω(2b)²δ(ψ(f)-a)dxdy _st∫∫Ω (φ-ψ(f)) ² dxdy＝ _α∫∫Ω (2b) ² δ(ψ(f)-a)dxdy

其解析解须满足欧拉方程(EE)和LMR，具体如下：Its analytical solution must satisfy the Euler equation (EE) and LMR, as follows:

$\frac{{λ λ}_{i i}}{22 b b} {((I I - - {c c}_{i i}))}^{22} - - \frac{{λ λ}_{o o}}{22 b b} {((I I - - {c c}_{o o}))}^{22} - - 22 ξ ξ ((φ φ - - ψ ψ ((f f)))) = = 00$

ζ＝constantζ=constant

∫∫_Ω(φ-ψ(f))²dxdy＝α∫∫_Ω(2b)²δ(ψ(f)-a)dxdy _∫∫Ω (φ-ψ(f)) ² dxdy＝ _α∫∫Ω (2b) ² δ(ψ(f)-a)dxdy

其中，ζ为拉格朗日乘子(LM)，α是一个常量。Among them, ζ is the Lagrangian multiplier (LM), and α is a constant.

这里的拉格朗日乘子ζ即为将C-V能量函数和形状能量E_S结合起来的权值系数。但是，由于难以得到φ和ζ的解析解，本方法给出演化曲线和拉格朗日乘子的迭代计算方法，具体如下：The Lagrange multiplier ζ here is the weight coefficient that combines the CV energy function and the shape energy _ES . However, since it is difficult to obtain the analytical solutions of φ and ζ, this method gives an iterative calculation method for evolution curves and Lagrangian multipliers, as follows:

$\frac{&PartialD; &PartialD; φ φ}{&PartialD; &PartialD; t t} = = \frac{{λ λ}_{i i}}{22 b b} {((I I - - {c c}_{i i}))}^{22} - - \frac{{λ λ}_{o o}}{22 b b} {((I I - - {c c}_{o o}))}^{22} - - 22 ξ ξ ((φ φ - - ψ ψ ((f f))))$

$\frac{&PartialD; &PartialD; ξ ξ}{&PartialD; &PartialD; t t} = = {&Integral; &Integral; &Integral; &Integral;}_{Ω Ω} {((φ φ - - ψ ψ ((f f))))}^{22} dxdy dxdy - - α α {&Integral; &Integral; &Integral; &Integral;}_{Ω Ω} {((22 b b))}^{22} δ δ ((ψ ψ ((f f)) - - a a)) dxdy dxdy$

其中，

为曲线的演化方程，

为拉格朗日乘子的迭代方程。通过交替地计算这两个方程直到φ和ζ达到稳定，就可以得到最终的演化曲线。in,

is the evolution equation of the curve,

Iterative equation for Lagrange multipliers. By computing these two equations alternately until φ and ζ are stable, the final evolution curve can be obtained.

本实施例中，ζ的值是自适应变化的，能够根据图像和形状模板识别的情况自动收敛到稳定状态，这就避免了该权值系数的手动调节。In this embodiment, the value of ζ is adaptively changed, and can automatically converge to a stable state according to the situation of image and shape template recognition, which avoids manual adjustment of the weight coefficient.

在第一阶段中，令α＝2.5；在第二阶段中，令α＝0.2；In the first stage, let α=2.5; in the second stage, let α=0.2;

第五步、如果拉格朗日乘子ζ和水平集函数φ都稳定，即可得到分割结果。The fifth step, if the Lagrange multiplier ζ and the level set function φ are both stable, the segmentation result can be obtained.

下面以海星分割检测、心脏超声图像中左心室分割检测、行人分割检测和不同视点观察下的兵马俑分割检测来演示本实施例的技术效果。并且，在心脏超声图像中左心室分割检测中，将本实施例的分割效果与传统C-V模型的分割效果进行对比，以显示本实施例的显著优点。The technical effects of this embodiment will be demonstrated below with starfish segmentation detection, left ventricle segmentation detection in echocardiographic images, pedestrian segmentation detection, and terracotta warriors and horses segmentation detection under observation from different viewpoints. Moreover, in the segmentation detection of the left ventricle in the echocardiographic image, the segmentation effect of this embodiment is compared with that of the traditional C-V model to show the significant advantages of this embodiment.

海星分割检测的目的是将图2.(a)中海星分割出来，使用的是如图2.(b)，(c)，(d)所示的三个不同形状模板的先验形状库，其中图2.(b)和图2.(c)分别是两个不同的先验海星形状，而图2.(d)是手形状。海星分割结果如图3所示，其中图3.(b)是第一阶段分割的结果(相应迭代次数为75)，图3.(c)-(f)是分割和配准结果。海星与图像背景及海星自己的影子分离开来，并且其被沙滩遮挡的触手亦被重建出来。图3.(d)和图3.(e)显示：海星形状的形状模板能够与演化曲线相配，而人手形状的形状模板则不能。图4.(a)显示在本实施例方法的两个阶段自适应地计算得到拉格朗日乘子，并且最终收敛于稳定状态。图4.(b)显示部分豪斯道夫距离的值。在图4.(b)中可以看出图2.(c)中的形状模板与演化曲线的相似性最大。即使目标物体存在部分遮挡、或者受杂波、噪声的影响，利用豪斯道夫距离都能够从先验形状集中选择出合适的形状模板。The purpose of starfish segmentation detection is to segment the starfish in Figure 2.(a), using a priori shape library of three different shape templates as shown in Figure 2.(b), (c), and (d). Among them, Fig. 2.(b) and Fig. 2.(c) are two different prior starfish shapes respectively, and Fig. 2.(d) is the hand shape. The starfish segmentation results are shown in Figure 3, where Figure 3.(b) is the result of the first-stage segmentation (the corresponding number of iterations is 75), and Figure 3.(c)-(f) are the segmentation and registration results. The starfish was isolated from the image background and its own shadow, and its tentacles occluded by the sand were reconstructed. Figure 3.(d) and Figure 3.(e) show that the shape template in the shape of a starfish can fit the evolution curve, but the shape template in the shape of a human hand cannot. Figure 4. (a) shows that the Lagrangian multipliers are adaptively calculated in two stages of the method of this embodiment, and finally converge to a steady state. Figure 4. (b) shows the value of partial Hausdorff distance. In Fig. 4.(b), it can be seen that the shape template in Fig. 2.(c) has the greatest similarity with the evolution curve. Even if the target object is partially occluded or affected by clutter or noise, the Hausdorff distance can be used to select a suitable shape template from the prior shape set.

心脏超声图像中左心室分割检测的目的是从心脏超声图像中分割出左心室。检测所用到的左心室先验形状模板库如图5。图6是采用本实施例方法的分割结果，其中图6.(e)显示了仅利用C-V模型，没有结合先验形状分析的检测结果，图中演化曲线在弱边界处出现了泄漏问题；并且，由于C-V模型以分段常数的形式表示M-S模型，很显然C-V模型不能应对例如图6.(e)中心室目标灰度分布不均匀的情况。而采用本方法的分割方法能够在灰度分布不均匀的区域重建丢失的形状，如图6.(d)所示。图6中(f)-(j)显示了配准结果。配准在第一阶段完成，将其结果投影到第二阶段的分割结果上。在图6.(j)中，图5.(e)的形状模板与演化曲线失配，这是图6.(c)中的边界泄漏造成的影响，从图7.(a)中可看出其相应的部分豪斯道夫距离(标注为e的曲线)相对比较大。图7显示了该检测的部分豪斯道夫距离和拉格朗日乘子。图7.(a)中，标注为“d”的曲线在经过若干次迭代之后部分豪斯道夫距离相对较小，因此它对应的形状模板(图5.(d))被选择出来，用于指导图6中的曲线演化。The purpose of left ventricle segmentation detection in echocardiographic images is to segment the left ventricle from echocardiographic images. The left ventricle prior shape template library used in the detection is shown in Figure 5. Fig. 6 is the segmentation result using the method of this embodiment, wherein Fig. 6.(e) shows the detection results using only the C-V model without prior shape analysis, and the evolution curve in the figure has a leakage problem at the weak boundary; and , since the C-V model expresses the M-S model in the form of piecewise constants, it is obvious that the C-V model cannot cope with the uneven distribution of the target gray level in Figure 6. (e) for example. However, the segmentation method using our method can reconstruct the lost shape in the region with uneven gray distribution, as shown in Fig. 6.(d). (f)-(j) in Figure 6 show the registration results. Registration is done in the first stage, and its result is projected onto the segmentation results in the second stage. In Fig. 6.(j), the shape template of Fig. 5.(e) does not match the evolution curve, which is the effect caused by the boundary leakage in Fig. 6.(c), which can be seen from Fig. 7.(a) The corresponding part of the Hausdorff distance (curve marked e) is relatively large. Figure 7 shows the partial Hausdorff distance and Lagrangian multipliers for this detection. In Fig. 7.(a), the part of the Hausdorff distance of the curve marked "d" is relatively small after several iterations, so its corresponding shape template (Fig. 5.(d)) is selected for Guide the curve evolution in Figure 6.

行人分割检测的目的是分割出图像中的行人。本实施例从一个人行走的连续图像中选出11张图像作为先验形状库，并将这11张图像重叠在图8.(b)中的初始演化曲线上。虽然目标物身着大衣，采用本实施例的分割方法仍然可以分割出行人本身，如图8.(d)。图9显示了行人分割检测的部分豪斯道夫距离和拉格朗日乘子。图9.(a)中标注为(e)-(o)的曲线的稳定状态对应的是图8.(e)-(o)中的部分豪斯道夫距离。在经过329次迭代之后，拉格朗日乘子的值也将达到稳定，如图9.(b)。需要特别指出的是：在本实施例中，第一阶段α＝2.5，p₁＝p₂＝0.8；考虑到第一阶段的配准结果比较粗略，并且一些部分豪斯道夫距离值比较接近，所以在检测第二阶段没有一次性将参数设置为固定值，而是让这些参数逐渐由第一阶段的值变化为α＝0.3，p₁＝p₂＝0.95，这样做可以让识别的过程和形状模板的选择更加精确。The purpose of pedestrian segmentation detection is to segment the pedestrians in the image. In this embodiment, 11 images are selected from the continuous images of a person walking as a priori shape library, and these 11 images are superimposed on the initial evolution curve in Fig. 8.(b). Although the target is wearing a coat, the segmentation method of this embodiment can still segment the pedestrian itself, as shown in Figure 8.(d). Figure 9 shows partial Hausdorff distances and Lagrangian multipliers for pedestrian segmentation detection. Figure 9. The steady state of the curve labeled (e)-(o) in (a) corresponds to the partial Hausdorff distance in Figure 8. (e)-(o). After 329 iterations, the value of the Lagrangian multiplier will also reach stability, as shown in Figure 9.(b). It should be pointed out that: in this embodiment, the first stage α=2.5, p ₁ =p ₂ =0.8; considering that the registration results of the first stage are relatively rough, and some Hausdorff distance values are relatively close, Therefore, in the second stage of detection, the parameters are not set to fixed values at one time, but these parameters are gradually changed from the value of the first stage to α=0.3, p ₁ =p ₂ =0.95, which can make the recognition process and The selection of shape templates is more precise.

不同视点观察下的兵马俑分割检测选用如图10所示的25张形状模板构成兵马俑的先验形状模板库，这些形状模板是通过对3D兵马俑多视点观察得到的2D图像。在图11中，人为地在原始待分割图像上添加了高斯噪声，并且对兵马俑添加了部分遮挡。在第一阶段令部分豪斯道夫距离值为0.6，这是因为这种遮挡将对采用部分豪斯道夫距离的形状模板选择带来较为严重的干扰。对于传统的活动轮廓模型，此类噪声和遮挡将会严重影响模型的分割效果，但是使用本实施例的分割方法则可以重建出目标物体遗失的部分。Segmentation detection of terracotta warriors and horses under observation from different viewpoints. 25 shape templates as shown in Figure 10 are selected to form the prior shape template library of terracotta warriors and horses. These shape templates are 2D images obtained by observing 3D terracotta warriors and horses from multiple viewpoints. In Figure 11, Gaussian noise is artificially added to the original image to be segmented, and partial occlusion is added to the terracotta warriors. In the first stage, the value of the partial Hausdorff distance is set to 0.6, because this kind of occlusion will seriously interfere with the shape template selection using the partial Hausdorff distance. For the traditional active contour model, such noise and occlusion will seriously affect the segmentation effect of the model, but the missing part of the target object can be reconstructed by using the segmentation method of this embodiment.

上述实施例结果证明：只要提供足够多的先验形状模板，即使是对不同视点观察得到的图像，使用本方法的方法仍然可以识别和分割出目标物体。The results of the above embodiments prove that as long as enough prior shape templates are provided, the method of this method can still identify and segment the target object even if the images are observed from different viewpoints.

Claims

1. An adaptive image segmentation method based on prior shape is characterized by comprising the following steps:

firstly, expressing the shape of a target image as a shape template to serve as a prior shape template library, and initializing an evolution curve;

secondly, registering the evolution curve and the shape templates in the prior shape template library one by one, and updating the shape template library according to a registration result:

thirdly, selecting a shape template from the prior shape template library by using the shape similarity measurement: measuring the similarity degree of the evolution curve and the updated shape template by adopting a partial Hausdorff distance method, and taking the shape template with the maximum similarity degree as an identification result;

and fourthly, solving a weight coefficient between the shape and the gray in the recognition result by using a constraint variation model, and segmenting the target image by combining the shape template and the image gray information to obtain a segmentation result.

2. The adaptive a priori shape based image segmentation method of claim 1, wherein the shape template of the integer sign function is: the shape outline is represented by a double-sided linked list structure C, and the inner edge of the double-sided linked list structure is L_inThe outer edge is L_outWithin C and not at L_inPoint in (B) is C_inOutside C and not L_outPoint in (B) is C_outThen there is an integer sign function as the shape template:

wherein: and (x, y) is the coordinate of any one point in the target image, wherein a is 1, and b is 3.

3. The adaptive a priori shape based image segmentation method of claim 1, wherein the shape template is: the contour of the prior shape is taken as L_outThe prior shape is expressed as an integer sign function according to the definition of the integer sign function.

4. The adaptive a priori shape based image segmentation method as set forth in claim 1, wherein the evolution curve is: describing a closed curve in the image plane using an integer sign function, with the evolution curve as L_out。

5. The adaptive a priori shape based image segmentation method as set forth in claim 1, wherein the registration is: so that the evolution curve and the shape template are registered. And minimizing the sum of squares of errors of the evolution curve and the shape template, and optimizing the scale, the rotation and the translation to minimize the sum of squares of errors.

6. The adaptive a priori shape based image segmentation method as set forth in claim 1 or 5, wherein the registering specifically comprises:

2.1) the sum of squared errors of the evolution curve and the shape template is expressed as: e_S(φ，f)＝∫∫_Ω(φ-ψ(f))²dxdy, wherein: psi and phi are integer sign functions of the shape template and the evolution curve respectively, and specifically are as follows:where (u, v) is a point on the shape template plane,

where (x, y) is a point on the image plane; e_SIs the shape energy, f is a rigid transformation function, specifically

Including a translation term T_x，T_yRotation term θ and scaling term s, (T)_x，T_yRepresenting translation in the x-direction and the y-direction);

2.2) gradient descent equations as scale, rotation and translation are specifically:

wherein: p is an element of { T ∈_x，T_y，θ，s}。

2.3) according to the translation term T_x，T_yThe shape template is updated by the rotation term theta and the scaling term s.

7. The adaptive a priori shape based image segmentation method of claim 1, whereinThe similarity degree refers to: h_LK(A，B)＝max(h_L(A，B)，h_K(B, A)), wherein:

for the improved directed hausdorff distance,

representing the Kth value in the distance set, point set A ═ a₁，...，a_mIs all points on the evolution curve, m denotes the number of points in a, and the set of points B ═ B₁，...，b_nIs the point on the outline of the shape template, n denotes the number of points in B, p₁K/m and p₂When L/n is equal to p₁And p₂In the range of [0, 1]And p is₁And p₂Depending on the degree to which the object is occluded, by selecting p₁And p₂L and K are determined.

8. The adaptive prior shape based image segmentation method as set forth in claim 1, wherein the constrained variational model is:

<math><mrow><mi>min</mi><msub><mrow><mo>&Integral;</mo><mo>&Integral;</mo></mrow><mi>Ω</mi></msub><msub><mi>λ</mi><mi>i</mi></msub><msup><mrow><mo>(</mo><mi>I</mi><mo>-</mo><msub><mi>c</mi><mi>i</mi></msub><mo>)</mo></mrow><mn>2</mn></msup><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mi>φ</mi><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mi>b</mi></mrow></mfrac><mo>)</mo></mrow><mi>dxdy</mi><mo>+</mo><msub><mrow><mo>&Integral;</mo><mo>&Integral;</mo></mrow><mi>Ω</mi></msub><msub><mi>λ</mi><mi>o</mi></msub><msup><mrow><mo>(</mo><mi>I</mi><mo>-</mo><msub><mi>c</mi><mi>o</mi></msub><mo>)</mo></mrow><mn>2</mn></msup><mrow><mo>(</mo><mfrac><mrow><mi>φ</mi><mo>+</mo><mi>b</mi></mrow><mrow><mn>2</mn><mi>b</mi></mrow></mfrac><mo>)</mo></mrow><mi>dxdy</mi><mo>,</mo></mrow></math>

s.t.∫∫_Ω(φ-ψ(f))²dxdy＝α∫∫_Ω(2b)²δ(ψ(f)-a)dxdy，

the analytic solution of the constraint variational model satisfies Euler Equation (EE) and LMR, which is as follows:

∫∫_Ω(φ-ψ(f))²dxdy＝α∫∫_Ω(2b)²δ(ψ(f)-a)dxdy，

wherein: ζ is a lagrange multiplier constant, that is, a weight coefficient combining the C-V energy function and the shape energy ES, and α is 2.5 or 0.2.

9. The adaptive prior shape based image segmentation method as claimed in claim 1, wherein the lagrange multiplier constants are calculated by alternately computing the following iterative equations until phi and ζ stabilize:

<math><mrow><mfrac><mrow><mo>&PartialD;</mo><mi>φ</mi></mrow><mrow><mo>&PartialD;</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><msub><mi>λ</mi><mi>i</mi></msub><mrow><mn>2</mn><mi>b</mi></mrow></mfrac><msup><mrow><mo>(</mo><mi>I</mi><mo>-</mo><msub><mi>c</mi><mi>i</mi></msub><mo>)</mo></mrow><mn>2</mn></msup><mo>-</mo><mfrac><msub><mi>λ</mi><mi>o</mi></msub><mrow><mn>2</mn><mi>b</mi></mrow></mfrac><msup><mrow><mo>(</mo><mi>I</mi><mo>-</mo><msub><mi>c</mi><mi>o</mi></msub><mo>)</mo></mrow><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>ξ</mi><mrow><mo>(</mo><mi>φ</mi><mo>-</mo><mi>ψ</mi><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math>

<math><mrow><mfrac><mrow><mo>&PartialD;</mo><mi>ξ</mi></mrow><mrow><mo>&PartialD;</mo><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mrow><mo>&Integral;</mo><mo>&Integral;</mo></mrow><mi>Ω</mi></msub><msup><mrow><mo>(</mo><mi>φ</mi><mo>-</mo><mi>ψ</mi><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow><mo>)</mo></mrow><mn>2</mn></msup><mi>dxdy</mi><mo>-</mo><mi>α</mi><msub><mrow><mo>&Integral;</mo><mo>&Integral;</mo></mrow><mi>Ω</mi></msub><msup><mrow><mo>(</mo><mn>2</mn><mi>b</mi><mo>)</mo></mrow><mn>2</mn></msup><mi>δ</mi><mrow><mo>(</mo><mi>ψ</mi><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow><mo>-</mo><mi>a</mi><mo>)</mo></mrow><mi>dxdy</mi><mo>,</mo></mrow></math>

wherein:

in the form of an evolution equation of a curve,

an iterative equation that is a lagrange multiplier.