CN101964112A - Adaptive prior shape-based image segmentation method - Google Patents
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Abstract
The invention relates to an adaptive prior shape-based image segmentation method in the technical field of image processing. The influence of noise interference on image segmentation is eliminated by an integer sign function; a constraint variation model is provided for the weight coefficient of a prior shape model and the conventional active contour model needs to be manually adjusted, so that the weight coefficient can be adaptively converged to a stable value; meanwhile, identification-based shape template selection is used for determining a certain prior shape template during segmentation, so that the problem that a prior shape model-based segmentation result cannot be obtained in the prior art is solved.
Description
Technical Field
The invention relates to an image processing method, in particular to an adaptive image segmentation method based on a prior shape.
Background
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 very large, the evolution curve will leak, resulting in a segmentation failure. Moreover, common segmentation models cannot extract meaningful objects if there is noise, clutter, or occlusion in the image. One effective approach is to incorporate some a priori knowledge of the target into the framework of the active contour model. A priori knowledge of the lower layers, for example: information such as gray scale, color, texture and motion is often insufficient to represent target features, and invariance of these features is often not guaranteed in practical applications. In recent years, high-level knowledge, particularly shapes, has been valued by many scholars and incorporated into segmentation models. This type of model is often referred to as a prior shape based image segmentation method. This method has two difficulties: how to first represent and describe the prior shape into a shape model that can be utilized by the segmentation model, and how to second merge the shape model into a traditional segmentation model.
Many scholars have studied this problem. Current research on this problem is broadly divided into two categories: statistical prior models and models based on shape template matching.
In the Statistical prior model, m.e. levento et al published on CVPR (computer vision and pattern recognition international conference) (2000, 1: 1316-. In this context, principal component analysis and kernel principal component analysis are used to extract shape features for estimating the probability density function of a shape. Furthermore, M.Rousson and D.Cremers published on MICCAI (International conference on medical image computing and computer aided intervention) (2005: 757-764) a text "assessment of shape and intensity documents for level set segmentation" ("level set segmentation method for introducing kernel density estimates for shapes"), which contrasts Gaussian distributions, uniform distributions, and kernel density estimates, demonstrating the validity of the kernel density estimates for probability density function estimates for shapes.
In the model based on shape template Matching, N.Paraagios et al published "Matching distance functions" on ECCV (European computer vision International conference) (2002: 775-789): the method is characterized in that a single shape template is adopted as a shape model, an evolution curve evolves towards the shape template through registration of the evolution curve and the shape template, and image segmentation based on the shape template can be realized through manually adjusting weight coefficients between a registration item and a traditional active contour model.
Although the segmentation model based on the prior shape can ensure certain segmentation accuracy when noise, clutter and occlusion exist in the background, the following problems still exist and are not solved: when combining the prior shape model and the traditional active contour model, the weight coefficients between these two terms need to be adjusted manually, and there is no criterion to guide how to adjust the coefficients. If the coefficient is not properly adjusted, a segmentation result based on the prior shape model is often not obtained; most shape models describe images using a symbolic distance function, however, since the space in which the symbolic distance function is located is non-linear, the images described by the statistical shape model and the parametric shape template obtained by linear weighting no longer satisfy the symbolic distance function.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a self-adaptive image segmentation method based on the prior shape, which adopts an integer sign function to overcome the influence of noise interference on image segmentation, and aims at the requirement of manually adjusting the weight coefficients of a prior shape model and a traditional active contour model, provides a constraint variation model to ensure that the weight coefficients can be self-adaptively converged to a stable value, and simultaneously selects a shape template based on identification to determine which prior shape template is adopted during segmentation, thereby avoiding the problem that the segmentation result based on the prior shape model cannot be obtained in the prior art.
The invention is realized by the following technical scheme, and the method comprises 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.
The shape template of the integer symbolic function refers to: 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 LinThe outer edge is LoutWithin C and not at LinPoint in (B) is CinOutside C and not LoutPoint in (B) is CoutThen 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, a and b are integer values, and in the invention, a is 1 and b is 3.
The shape template is as follows: the contour of the prior shape is taken as LoutThe prior shape is expressed as an integer sign function according to the definition of the integer sign function.
The evolution curve is as follows: closed curves in the image plane generally require manual initialization. The invention also adopts integer sign function to describe in the figureClosed curve in image plane, with evolution curve as Lout。
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:
the registration refers to: so that the evolution curve and the shape template are registered. 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, and the method specifically comprises the following steps:
2.1) the sum of squared errors of the evolution curve and the shape template is expressed as: eS(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; eSIs the shape energy, f is a rigid transformation function, specificallyIncluding a translation term Tx,TyRotation term θ and scaling term s, (T)x,TyRepresenting 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,Ty,θ,s}。
2.3) according to the translation term Tx,TyThe shape template is updated by the rotation term theta and the scaling term s.
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;
the similarity degree refers to that: hLK(A,B)=max(hL(A,B),hK(B, A)), wherein:for the improved directed hausdorff distance,represents the kth value in the distance set, the same meaning applies to L, point set a ═ a1,...,amIs all points on the evolution curve, m denotes the number of points in a, and the set of points B ═ B1,...,bnIs the point on the shape template outline, and n represents the number of points in B. Definition of p1K/m and p2When L/n is equal to p1And p2In the range of [0, 1]And p is1And p2The choice of (a) depends on the degree to which the target is occluded. By selecting p1And p2L and K can be determined.
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.
The constraint variation model is as follows:
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: zeta is a Lagrange multiplier constant, namely a C-V energy function and a shape energy ESThe combined weight coefficient, α, is a constant, α ═ 2.5 or 0.2.
The Lagrange multiplier constants are calculated by alternately calculating the following iterative equations until phi and zeta stabilize:
wherein:evolution of curvesThe process is carried out by the following steps,an iterative equation that is a lagrange multiplier.
The invention has the technical effects that: the problem that a traditional image segmentation method based on the prior shape needs to manually adjust the weight coefficient (the weight coefficient is used for balancing shape knowledge and the gray level of the image per se) is solved; in addition, the method can self-adaptively select the most similar shape template to guide image segmentation; moreover, when noise and clutter exist in the image background and even the target to be segmented is partially shielded, the method can still segment the desired target.
Drawings
Figure 1 effect of different lambda values on the segmentation results.
FIG. 2 is a database of starfishes to be segmented and prior shape templates.
Fig. 3 shows the starfish segmentation detection results.
Fig. 4 shows lagrange multipliers and partial hausdorff distances for starfish segmentation detection.
FIG. 5 is a library of left ventricular prior shape templates.
Fig. 6 shows the left ventricle segmentation test results.
FIG. 7 is a partial Hausdorff distance and Lagrangian multiplier for left ventricular segmentation detection.
Fig. 8 shows a pedestrian segmentation detection result.
Fig. 9 shows part of the hausdorff distance and lagrange multiplier for pedestrian segmentation detection.
FIG. 10 is a terracotta warriors segmentation detection prior shape template library under observation from different viewpoints.
Fig. 11 shows the segmentation detection results of terracotta soldiers and horses observed from different viewpoints.
Detailed Description
The following examples are given for the detailed implementation and specific operation of the present invention, but the scope of the present invention is not limited to the following examples.
The embodiment comprises the following steps:
the method comprises the following steps of firstly, initializing an evolution curve (segmentation result), and taking a shape template which expresses the shape of a target image as an integer sign function as a prior shape template library:
the shape is expressed as an integer signed distance function: assuming the contour is C, it is represented as a two-sided linked list structure: inner edge LinAnd an outer edge Lout. Is defined within C and not at LinPoint in (B) is Cin(ii) a Outside C and not LoutPoint in (B) is Cout。
Where (x, y) is the coordinate of the current point, a and b are integer values, and in this embodiment, let a be 1 and b be 3.
Secondly, registering the image segmentation result and the shape templates in a preset shape library one by one, and updating the shape template library according to the registration result:
it is assumed that integer sign functions ψ and φ represent a certain shape template and evolution curve, respectively. They can be registered by optimizing their sum of squared errors (optimizing the rotation, translation and scaling terms). The sum of the squared errors of ψ and φ is defined as follows:
ES(φ,f)=∫∫Ω(φ-ψ(f))2dxdy
wherein E isSIs the shape energy, f is a rigid body transformation function including a translation term Tx,TyA rotation term θ and a scaling term s.
The registration may be achieved by a gradient descent method, and the maximum gradient descent direction of the rigid body transformation parameters is as follows:
wherein p ∈ { T }x,Ty,θ,s}。
According to the obtained translation term Tx,TyA rotation term theta and a scaling term s,the shape template is updated.
Thirdly, selecting a shape template from the prior shape template library by using the shape similarity measurement: the partial Hausdorff distance has a good effect in comparing the partial similarity of two shapes. When the target object has partial occlusion, the object can be identified by using partial Hausdorff distance. In the above definition of the directed hausdorff distance, the global maximum value is changed to the kth value, that is, the improved directed hausdorff distance is obtained:
Thus, the partial Hausdorff distance is defined as follows:
all points on the evolution curve constitute a set of points a and points on the shape template contour constitute a set of points B. The definition formula of the partial Hausdorff distance contains two parameters p1K/m and p2=L/n,p1And p2Is in the range of [0, 1]。p1And p2The choice of (a) depends on the degree to which the target is occluded. Each shape template in the prior shape template library and the evolution curve are respectively calculatedThe shape template with the most similar to the evolution curve, i.e. the shape template with the smallest value of the partial Hausdorff distance, is selected to guide the evolution of the curve.
In the embodiment, the shape template is selected from the shape template library by adopting a shape recognition method, so that the inaccuracy of shape representation caused by the nonlinearity of a symbol distance function is avoided.
In the first stage, let p1=p20.8; in the second stage, let p1=p2=0.95;
Fourthly, solving a weight coefficient between the shape and the gray by using the proposed constraint variation model, and segmenting the target image by combining the shape template and the image gray information to obtain a new segmentation result: the constraint variational model proposed in this embodiment is as follows:
s.t.∫∫Ω(φ-ψ(f))2dxdy=α∫∫Ω(2b)2δ(ψ(f)-a)dxdy
the analytic solution of the method needs to satisfy the Euler Equation (EE) and the LMR, and the method specifically comprises the following steps:
ζ=constant
∫∫Ω(φ-ψ(f))2dxdy=α∫∫Ω(2b)2δ(ψ(f)-a)dxdy
where ζ is the Lagrange Multiplier (LM) and α is a constant.
The Lagrange multiplier ζ is the C-V energy function and the shape energy ESThe combined weight coefficients. However, since it is difficult to obtain analytic solutions of phi and zeta, the iterative computation method of the evolution curve and the lagrangian multiplier is provided by the method, which specifically includes:
wherein,in the form of an evolution equation of a curve,an iterative equation that is a lagrange multiplier. By alternately calculating these two equations until φ and ζ stabilize, the final evolution curve can be obtained.
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.
In the first stage, let α be 2.5; in the second stage, let α be 0.2;
and fifthly, if the Lagrange multiplier zeta and the level set function phi are stable, a segmentation result can be obtained.
The technical effects of the embodiment are demonstrated by starfish segmentation detection, left ventricle segmentation detection in a heart ultrasonic image, pedestrian segmentation detection and terracotta warriors segmentation detection under observation of different viewpoints. In addition, in the left ventricle segmentation detection in the cardiac ultrasound image, the segmentation effect of the embodiment is compared with that of the conventional C-V model to show the significant advantages of the embodiment.
The purpose of the starfish segmentation test is to segment the starfish in fig. 2 (a) using a priori shape library of three different shaped templates as shown in fig. 2 (b), (c), (d), where fig. 2 (b) and fig. 2 (c) are two different a priori starfish shapes, respectively, and fig. 2 (d) is a hand shape. The starfish segmentation results are shown in fig. 3, where fig. 3 (b) is the result of the first stage segmentation (corresponding to 75 iterations), and fig. 3 (c) - (f) are the segmentation and registration results. The starfish is separated from the image background and the starfish's own shadow, and its tentacles, which are obscured by the beach, are also reconstructed. Fig. 3.(d) and 3.(e) show: the shape template of the shape of the sea star can be matched with the evolution curve, but the shape template of the shape of the hand cannot. Fig. 4 (a) shows that the lagrangian multiplier is calculated adaptively in the two stages of the method of the present embodiment and finally converges to a steady state. Fig. 4 (b) shows values of partial hausdorff distances. The shape templates in fig. 2.(c) can be seen in fig. 4.(b) as having the greatest similarity to the evolution curve. Even if the target object has partial shielding or is influenced by clutter and noise, the proper shape template can be selected from the prior shape set by using the Hausdorff distance.
The purpose of left ventricle segmentation detection in cardiac ultrasound images is to segment the left ventricle from the cardiac ultrasound images. The left ventricle prior shape template library used for detection is shown in fig. 5. FIG. 6 is a segmentation result using the method of the present embodiment, wherein FIG. 6 (e) shows the detection result using only the C-V model without the prior shape analysis, in which the evolution curve has a leakage problem at the weak boundary; also, since the C-V model represents the M-S model in the form of a piecewise constant, it is apparent that the C-V model cannot cope with the case where the center room target gray distribution is not uniform, for example, in FIG. 6 (e). The segmentation method using the method can reconstruct the missing shape in the area with non-uniform gray scale distribution, as shown in fig. 6 (d). The registration results are shown in fig. 6 (f) - (j). The registration is done in a first stage, the result of which is projected onto the segmentation result of the second stage. In fig. 6.(j), the shape template of fig. 5.(e) is mismatched with the evolution curve, which is the effect of the boundary leakage in fig. 6.(c), and its corresponding partial hausdorff distance (curve labeled e) is relatively large as can be seen in fig. 7. (a). Fig. 7 shows part of the hausdorff distance and lagrange multiplier for this detection. In fig. 7.(a), the curve labeled "d" has a relatively small fractional hausdorff distance after several iterations, so its corresponding shape template (fig. 5.(d)) is selected to guide the curve evolution in fig. 6.
The purpose of pedestrian segmentation detection is to segment a pedestrian in an image. This embodiment selects 11 images from the continuous images of a person walking as a prior shape library and superimposes these 11 images on the initial evolution curve in fig. 8. (b). Although the target object is dressed, the pedestrian can be still separated by the separation method of the embodiment, as shown in fig. 8 (d). Fig. 9 shows a partial hausdorff distance and lagrange multiplier for pedestrian segmentation detection. The steady state of the curves labeled (e) - (o) in fig. 9 (a) correspond to the partial hausdorff distances in fig. 8 (e) - (o). After 329 iterations, the values of the lagrange multipliers will also stabilize, as in fig. 9 (b). It is to be noted in particular that: in the present embodiment, the first stage α is 2.5, p1=p20.8; considering that the registration result of the first stage is relatively rough and some partial Hausdorff distance values are relatively close, the parameters are not set as fixed values once in the second stage of detection, but are gradually changed from the value of the first stage to alpha being 0.3, and p is gradually changed from the value of the first stage to alpha being 0.31=p2This allows for the identification of process and shape templates ═ 0.95The selection is more accurate.
The segmentation detection of the terracotta soldiers under different viewpoint observation selects 25 shape templates shown in figure 10 to form a priori shape template library of the terracotta soldiers, and the shape templates are 2D images obtained by multi-viewpoint observation of the 3D terracotta soldiers. In fig. 11, gaussian noise is artificially added to the original image to be segmented, and partial occlusion is added to terracotta soldiers and horses. The partial Hausdorff distance value is set to 0.6 in the first stage because such occlusion will cause a severe disturbance in the selection of shape templates using partial Hausdorff distances. For the conventional 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 the embodiment.
The results of the above examples demonstrate that: the method of the method can still identify and segment the target object even if the images are observed from different viewpoints as long as enough prior shape templates are provided.
Claims (9)
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 LinThe outer edge is LoutWithin C and not at LinPoint in (B) is CinOutside C and not LoutPoint in (B) is CoutThen 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 LoutThe 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 Lout。
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: eS(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; eSIs the shape energy, f is a rigid transformation function, specificallyIncluding a translation term Tx,TyRotation term θ and scaling term s, (T)x,TyRepresenting 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,Ty,θ,s}。
2.3) according to the translation term Tx,TyThe 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: hLK(A,B)=max(hL(A,B),hK(B, A)), wherein:for the improved directed hausdorff distance,representing the Kth value in the distance set, point set A ═ a1,...,amIs all points on the evolution curve, m denotes the number of points in a, and the set of points B ═ B1,...,bnIs 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:
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:
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