An Image Selective Segmentation Method Based on Convolution Kernel Approximation
Through the image selective segmentation method based on convolution kernel approximation, the thermonuclear convolution feature function and iterative convolution thresholding method are used to solve the problems of low image segmentation accuracy and slow speed in the prior art, and a more efficient image segmentation effect is achieved.
Patent Information
- Application Number
- CN202210741253.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-06-28
- Publication Date
- 2025-08-05
- Estimated Expiration
- 2042-06-28
AI Technical Summary
The existing image selective segmentation methods are not very accurate in processing complex images and have slow calculation speed, especially in medical imaging, which are not effective in extracting specific targets.
The image selective segmentation method based on convolution kernel approximation is adopted, and the boundary curve of the object to be segmented is represented by the thermonuclear convolution feature function. The energy functional is constructed and convexized is performed in combination with the RCI model. The iterative convolution thresholding method is used for solving, and the Dice similarity coefficient and Hausdorff distance are used as the segmentation accuracy evaluation index.
It improves the accuracy and speed of image segmentation, especially when processing complex images, which can more accurately extract specific targets, significantly improving the segmentation effect.
Smart Images
Figure CN115496766B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of image processing, and in particular to a method for selective image segmentation based on convolution kernel approximation, a readable storage medium and a terminal. Background Art
[0002] Image segmentation theory has important applications in fields such as image processing and computer vision. Image segmentation can be broadly categorized into two types: global segmentation, which separates all foreground objects from background objects in an image; and selective segmentation, which separates certain objects from the background and other objects. Currently, global segmentation has received widespread attention and extensive research, while selective segmentation has received relatively little research. The advantage of selective segmentation is that it extracts specific targets in an image that are of research value, thereby avoiding meaningless research on other objects. Selective segmentation is widely used in medical imaging.
[0003] The focus of this paper is the selective segmentation of images. In 2010, Badshah and Chen proposed the Badshah-Chen selective segmentation model, also known as the BC model. This model incorporates the new distance constraint of active contours into the CV model, constrains the intensity of the target area, and thus encourages the segmentation of homogeneous areas. In 2015, Spencer and Chen, based on the BC model, used the distance fitting penalty as an independent term in the energy functional, and used convex relaxation and exact penalty terms to reformulate the model into a convex form, and proposed the Spencer-Chen selective segmentation model, referred to as the SC model. In 2019, Roberts, Chen, and Irion introduced geodesic distance in the variational framework to replace the traditional Euclidean distance, and proposed a convex selective segmentation model, referred to as the RCI model. They improved the geodesic penalty term, improved the robustness to noise, and greatly improved the segmentation effect of images with blurred edges compared to other models.
[0004] In 1988, Osher and Sethian first proposed the level set method, drawing on ideas from fluid analysis. This method is an effective and computationally stable approach to solving curve evolution problems. While level set-based curve evolution has continued to develop since its inception, it still suffers from numerous drawbacks. In 1992, Merriman, Bench, and Osher (MBO) proposed the convolution kernel approximation, which aims to model and simulate curve motion using mean curvature. This approach involves iteratively convolving the characteristic function of the interior region of the curve with a heat kernel, followed by thresholding. The MBO scheme is applicable to piecewise constant "Mumford-Shah"-style image segmentation and general weighted image segmentation. In 2015, Esedoglu and Otto proposed a new formulation that interprets the MBO scheme as a motion minimization scheme for the Lyapunov functional of the characteristic function. This approach can be generalized to multiphase curvature motion with arbitrary surface tension. More recently, Ma, Wang, and others implicitly represented the evolution profile as a heat kernel convolution characteristic function, approximating the geodesic active contour functional. They also derived an iterative convolution thresholding method to minimize the energy functional. This paper combines the convolution kernel approximation method with a new perimeter approximation formula to further improve the RCI model and proposes an image selective segmentation algorithm based on convolution kernel approximation. Summary of the Invention
[0005] In order to solve the above problems, the present invention provides an image selective segmentation method based on convolution kernel approximation, which can improve the accuracy of image segmentation and has a fast calculation speed.
[0006] In order to achieve the above object, the present invention is implemented through the following technical solutions:
[0007] The present invention is a method for selective image segmentation based on convolution kernel approximation, comprising the following steps:
[0008] Step 1: Get the input initial image;
[0009] Step 2: Use the hot kernel convolution feature function to represent the evolution of the boundary curve of the object to be segmented in the image;
[0010] Step 3: Combine the RCI model to construct an energy functional expression based on the characteristic function, and convexify it to derive an equivalent minimization problem. Apply the iterative convolution thresholding method to solve the model and obtain the image segmentation result. Use the Dice similarity coefficient and Hausdorff distance as quantitative evaluation indicators of segmentation accuracy to test the image segmentation results.
[0011] A further improvement of the present invention is that: in step 2, the convolution kernel approximation method is used to evolve the boundary curve of the object to be segmented. The specific operation steps are: defining the characteristic function u(x) as:
[0012]
[0013] Use the characteristic function u to approximate the boundary integral:
[0014]
[0015] or
[0016]
[0017] in:
[0018]
[0019] Where τ is a positive parameter, * represents the convolution between two functions, and n is the dimension of the Euclidean space.
[0020] A further improvement of the present invention is that the energy functional expression based on the characteristic function in step 3 is:
[0021]
[0022] Where Ω is the target segmentation area, τ, λ1, λ2, θ are all given positive parameters, u represents the characteristic function, c1, c2 are the average intensities corresponding to functions u and 1-u, * represents the convolution between the two functions, and g is the integrand of the above boundary integral;
[0023] A further improvement of the present invention is that the derivation process of the equivalent minimization problem in step 3 is:
[0024] The energy functional minimization problem is expressed as:
[0025]
[0026] in
[0027] B:={u∈BV(Ω,R)|u={0,1}}
[0028] BV(Ω,R) represents a function space with bounded variation, and Ω is the target segmentation region.
[0029] Convexify B as follows:
[0030] K:={u∈BV(Ω,R)|u∈[0,1]}
[0031] And the following questions are derived:
[0032]
[0033] The further improvement of the present invention is that the specific operation of solving the model in step 3 is: a. Calculate E τ (u) at the kth iteration u k The first-order Taylor expansion at :
[0034]
[0035] in:
[0036]
[0037] The k+1th iteration u is obtained by solving the following linearization problem k+1 :
[0038]
[0039] Solve using the pointwise method, for Solved:
[0040]
[0041] Since the minimum value of a linear functional on a convex set must reach its minimum value on the boundary, we can get:
[0042]
[0043] c1, c2 are solved by the following alternating minimization formula:
[0044]
[0045] The present invention also provides a computer-readable storage medium having computer instructions stored thereon, which, when executed, execute the above-mentioned image selective segmentation algorithm based on convolution kernel approximation.
[0046] The present invention also provides a terminal comprising a memory and a processor, wherein the memory stores computer instructions that can be run on the processor, and when the processor runs the computer instructions, the steps of the above-mentioned image selective segmentation algorithm based on convolution kernel approximation are executed.
[0047] The beneficial effects of the present invention are:
[0048] 1. Based on the RCI model and its solution algorithm, the present invention uses the hot kernel convolution feature function u(x) to approximate the problem of processing the contour curve Γ, constructs a new energy functional expression, and uses the relevant optimization problem knowledge to give a convex relaxation form of the model, so that the model can more accurately segment the images that the original RCI model is good at analyzing.
[0049] 2. The present invention uses an iterative convolution thresholding method to design a numerical solution algorithm for the convex relaxation model, and the convergence speed is much faster than the solution of the original RCI model. BRIEF DESCRIPTION OF THE DRAWINGS
[0050] Figure 1 4 is a flow chart of an image selective segmentation algorithm based on convolution kernel approximation in an embodiment of the present invention.
[0051] Figure 2 The segmentation results of different methods on MR images.
[0052] Figure 3 The segmentation results of different methods on the synthetic image with offset field.
[0053] Figure 4 The segmentation results of CT images using different methods.
[0054] Figure 5 The segmentation results of grayscale uneven images using different methods are shown in Figure 2.
[0055] Figure 6 The segmentation results of different methods on real images. DETAILED DESCRIPTION
[0056] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments.
[0057] like Figure 1 As shown, the present invention is a method for selective image segmentation based on convolution kernel approximation, comprising the following steps:
[0058] Step 1: Get the input initial image;
[0059] Step 2: Use the hot kernel convolution feature function to represent the evolution of the boundary curve of the object to be segmented. You can select an object of interest in the initial image as the object to be segmented, and use the hot kernel convolution feature function to represent its boundary curve, that is, the outer contour. Define the feature function u(x) as:
[0060]
[0061] The general boundary integral can be approximated by the characteristic function u:
[0062]
[0063] or
[0064]
[0065] Here, τ is a free parameter and * represents the convolution between two functions.
[0066] The Gaussian function is defined as follows:
[0067]
[0068] Where n is the dimension of the Euclidean space. When n = 2, Γ can be an interface, and when n = 3, Γ can be a surface.
[0069] Step 3: Combine the RCI model to construct an energy functional expression based on the characteristic function, and convexify it to derive an equivalent minimization problem. Apply the iterative convolution thresholding method to solve the model and obtain the image segmentation result. Use the Dice similarity coefficient and Hausdorff distance as quantitative evaluation indicators of segmentation accuracy to test the image segmentation result.
[0070] The present invention uses the RCI model combined with the outer contour characteristic function u(x) obtained in step 2 to construct an energy functional;
[0071] Among them, the expression of the original RCI model is:
[0072]
[0073] The contour curve Γ in (5) is implicitly represented by the characteristic function u(x), and the following energy functional form is obtained:
[0074]
[0075] Where Ω is the target segmentation area, τ, λ1, λ2, θ are all given positive parameters, u represents the characteristic function, c1, c2 are the average intensities corresponding to functions u and 1-u, * represents the convolution between the two functions, and g is the integrand of the above boundary integral;
[0076] By performing convex optimization on the above energy functional, an equivalent minimization problem is derived; the specific process is as follows:
[0077] The solution of the model of the present invention can be regarded as the following energy functional minimization problem:
[0078]
[0079] in
[0080] B:={u∈BV(Ω,R)|u={0,1}} (8)
[0081] From the above, we can see that the energy functional minimization problem of formula (7) is non-convex. In order to solve this problem, the present invention convexifies B as follows:
[0082] K:={u∈BV(Ω,R)|u∈[0,1]} (9)
[0083] And the following questions are derived:
[0084]
[0085] The energy functional minimization problems (7) and (10) are equivalent, and the energy functional is concave. By using the property that the image of the concave functional is always lower than its linear approximation, the energy functional E can be obtained. τ The problem of minimizing (u) is transformed into finding the minimum value of its linearized functional. The present invention designs an iterative convolution thresholding method to solve equation (10), which is as follows:
[0086] Calculate E τ (u) at the kth iteration u k The first-order Taylor expansion at :
[0087]
[0088] in:
[0089]
[0090] Next, we solve the following linearization problem to obtain u for the k+1th iteration: k+1 :
[0091]
[0092] It can be solved in a point-wise manner. It can be solved:
[0093]
[0094] Since the minimum of a linear functional on a convex set must reach its minimum on the boundary, we have:
[0095]
[0096] And c1, c2 can be solved by the following alternating minimization formula:
[0097]
[0098] The optimal solution obtained through the above calculations is the optimal solution to the initial image segmentation problem. The iterative convolution thresholding method designed in this paper solves the energy functional minimization problem and provides a fast numerical solution algorithm for the model. Compared with traditional algorithms, this algorithm has significantly improved usability, image segmentation speed, and accuracy.
[0099] In the implementation process, once the variational selective segmentation model for segmenting images with uneven intensity is constructed, the model can be used to segment complex images with uneven intensity to obtain the corresponding image segmentation results and evaluate them. The present invention uses DSC and HD as evaluation indicators for different algorithms. The indicators DSC and HD are defined as follows:
[0100]
[0101]
[0102] Here, S1 represents the area of the target object after segmentation, S2 represents the corresponding ground-truth area, n refers to the total number of segmented target boundary sets, A is the binary image after segmentation, and B is the corresponding ground-truth binary image. Obviously, higher DSC values and lower HD values indicate more accurate segmentation results.
[0103] The specific assessment is as follows:
[0104] First, the algorithm of the present invention, BC algorithm, SC algorithm, and RCI algorithm based on AOS were used to perform segmentation experiments on three MR brain images (a), (b), and (c). The segmentation results are shown in Tables 1 and Figure 2 shown. Figure 2 The first column is the original image with the labeled set (blue line) and the groundtruth (red line), based on Figure 2 From the segmentation result images, it can be seen that the BC model and the SC model still have a lot of white matter not segmented out when segmenting the MR images. In comparison, the RCI model and the model of the present invention segment the MR images very well. Figure 2 The DSC and HD values of the segmentation results are shown in Table 1:
[0105] Table 1 is Figure 2 DSC and HD values of segmentation results
[0106]
[0107] The numerical results presented in Table 1 show that the algorithm of the present invention achieves the best DSC and HD values for segmenting three MR brain images compared to other models. Furthermore, the algorithm of the present invention achieves convergence in significantly fewer steps and in significantly less time than other algorithms.
[0108] The segmentation effect of the algorithm of the present invention on the synthetic image with offset field is as follows: Figure 3 As shown in Table 2, Figure 3The segmentation results of three synthetic images with offset fields (d), (e), and (f) using different algorithms are given. The first column in the figure shows the original image with the label set (blue line) and the groundtruth (red line). It can be seen from the figure that as the synthetic image has more sharp corners, the BC algorithm, SC algorithm, RCI algorithm, and the algorithm of the present invention can still obtain good segmentation results. It can be seen that the algorithm of the present invention is as robust to segmentation targets with many sharp edges as other algorithms. Table 2 Figure 3 The DSC, HD value, iterative convergence steps and convergence time (s) of the segmentation results are as follows:
[0109]
[0110]
[0111] The bold font in the table refers to the optimal value in each column. From Table 2, it can be seen that the DSC value and HD value of the algorithm of the present invention are second only to the BC algorithm, and are better than the SC algorithm and the RCI algorithm. However, the BC algorithm does not converge, while the algorithm of the present invention achieves the expected effect in terms of numerical value. In terms of the number of iterations and convergence time, it is undoubtedly the fastest.
[0112] The segmentation effect of the algorithm of the present invention on CT images with blurred edges is as follows: Figure 4 As shown in Table 3, Figure 4 The segmentation results of three CT images with blurred edges (g), (f), and (i) using different algorithms are shown. As can be seen, the BC and SC models exhibit over-segmentation, with this defect being particularly pronounced in the BC model. The RCI model and the proposed model achieve better results. To more intuitively demonstrate the advantages and disadvantages of the different algorithms, Table 3 lists metrics such as DSC and HD for each algorithm, as shown below:
[0113]
[0114] The bold font in the table refers to the best value in each column. As can be seen from Table 3, the segmentation of these three images by the proposed algorithm is optimal in many indicators, indicating that the proposed algorithm has high segmentation accuracy and fast convergence speed.
[0115] The segmentation performance of the algorithm of the present invention for grayscale non-uniform images is as follows: Figure 5 As shown in Table 4, Figure 5 The results of selective segmentation of grayscale inhomogeneous images by different algorithms are given. From the segmentation results in the figure, it can be seen that for grayscale inhomogeneous images with simple edges, the segmentation results of several models meet expectations. However, for grayscale inhomogeneous images with complex edges such as (l), it is obvious that the segmentation effects of BC and SC models are poor, while the segmentation results of RCI model and the model of the present invention are better. Table 4 shows Figure 5The DSC, HD value, iterative convergence steps and convergence time (s) of the segmentation results are as follows:
[0116]
[0117] The bold font in the table refers to the optimal value of each column. It can be seen from the numerical results given in Table 4 that the algorithm of the present invention can well segment grayscale uneven images with simple edges, and the segmentation effect of grayscale uneven images with complex edges also meets expectations. What is more noteworthy is that it is easy to find that the convergence iteration speed of the algorithm of the present invention is still the fastest.
[0118] Figure 6 This is the segmentation result diagram of the algorithm of the present invention for the real images (m), (n), (o), and (p). It can be seen from the figure that the algorithm of the present invention can better identify the edges of the target to be segmented in the real image and achieve the expected effect.
[0119] The basic principles, main features and advantages of the present invention are shown and described above. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and improvements may be made to the present invention without departing from the spirit and scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims, the description and their equivalents.
Claims
1. A method for selective image segmentation based on convolution kernel approximation, characterized by: The steps include: Step 1: Get the input initial image; Step 2: Use the hot kernel convolution feature function to represent the evolution of the boundary curve of the object to be segmented in the image; Define the characteristic function for: ； Using characteristic function To approximate the boundary integral: ； or ； in: ； in, is a positive parameter, represents the convolution between two functions, is the dimension of the Euclidean space Step 3: Combine the RCI model to construct an energy functional expression based on the characteristic function, and convexify it to derive an equivalent minimization problem. Apply the iterative convolution thresholding method to solve the model, obtain the image segmentation result, and verify the image segmentation result. The energy functional expression based on the characteristic function is: ； in, is the target segmentation region, are all given positive parameters, represents the characteristic function, is a function and The corresponding average intensity, represents the convolution between two functions, is the integrand of the above boundary integral.
2. The method for selective image segmentation based on convolution kernel approximation according to claim 1, characterized in that: The derivation process of the equivalent minimization problem in step 3 is: The energy functional minimization problem is expressed as: ； in, ; Convexify B as follows: ； And the following questions are derived: ； in, represents the space of functions with bounded variation, is the target segmentation region.
3. The method for selective image segmentation based on convolution kernel approximation according to claim 2, characterized in that: The specific operations for solving the model in step 3 are: a, calculation In the Iterations The first-order Taylor expansion at : ； in: ; By solving the following linearization problem, we can obtain Iteration : ； Solve using the pointwise method, for , solve: ； Since the minimum value of a linear functional on a convex set must reach its minimum value on the boundary, we can get: ； Solved by the following alternating minimization formula: 。 4. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the computer instructions are executed, the steps of the image selective segmentation method based on convolution kernel approximation according to any one of claims 1 to 3 are executed.
5. A terminal comprising a memory and a processor, characterized in that: The memory stores computer instructions that run on the processor, and when the processor runs the computer instructions, the steps of the image selective segmentation method according to any one of claims 1 to 3 are performed.