Prostate ultrasound image segmentation method using bidirectional exponentially weighted moving average algorithm

Abstract

This invention belongs to the field of medical imaging technology and discloses a prostate ultrasound image segmentation method based on a bidirectional exponentially weighted moving average algorithm. The specific steps are as follows: S1, preliminary localization: The transformation localization matrix is ​​obtained by using a set localization convolutional network to obtain the transformation localization matrix coefficients, and the average template is obtained by using a point distribution model and principal component analysis. The two are combined for preliminary localization. This invention improves upon the normal vector contour boundary operator proposed by Hodge, and uses a boundary operator that comprehensively considers the joint information of the neighborhood normal vector to segment the prostate. It also proposes a method based on bidirectional exponentially weighted moving average to segment the shape of the prostate. Based on the boundary operator, the normal vector index value is used as the data input. This method achieves better segmentation results with a single input of data than ordinary multi-iteration segmentation and can better preserve features in non-noise areas, enabling accurate and fast ultrasound image segmentation.

Description

Technical Field

[0001] This invention belongs to the field of medical imaging technology, specifically a prostate ultrasound image segmentation method based on a bidirectional exponentially weighted moving average algorithm. Background Technology

[0002] The prostate is an important part of the human body and the largest solid organ among the accessory glands of the male reproductive system. Composed of prostate tissue and muscle tissue, it is located between the bladder and the urogenital diaphragm, surrounding the root of the urethra. Its shape and size resemble a slightly flattened chestnut. It is broad at the upper end and tapering at the lower end, with a relatively flat posterior surface close to the rectum, and can be palpated via digital rectal examination. Its size and function largely depend on androgens, primarily affecting urinary control, sexual function, and reproduction. Abnormalities in prostate size or function can have adverse effects. For example, an enlarged prostate can compress the urethra, affecting urination; prostate removal can impair sexual function; and prostatitis can negatively impact quality of life. According to statistics from the International Health Center, approximately half of all men will experience prostatitis at some point in their lives. Prostate cancer can cause bone pain, spinal cord compression, and even threaten life. Therefore, the treatment of prostate issues is extremely important.

[0003] In medical research and practice, the shape, boundaries, and volume of the prostate are typically measured to obtain pathological information about the tissue, thus assisting doctors in making accurate diagnoses. Medical ultrasound is the routine clinical method for prostate imaging, and segmenting the prostate from ultrasound images is crucial for the diagnosis and treatment selection of prostate diseases. Transrectal ultrasound (TRUS) is a commonly used method for examining the prostate in clinical practice. It can obtain clearer images of the internal structures of the prostate than transabdominal ultrasound, facilitating detailed examination. However, due to the influence of imaging equipment, imaging principles, and individual differences, images inevitably contain noise. Furthermore, the accuracy of segmentation is affected by factors such as uneven grayscale and artifacts, making it difficult for doctors to manually mark boundary areas. They often have to rely on their own experience to depict these areas, a process that is not only lengthy and time-consuming but also significantly impacts the segmentation results. [2] Therefore, computer segmentation has become a hot topic.

[0004] Compared to manual segmentation, computer segmentation can be automated and is faster. Many algorithms are currently applicable to this work. Hodge proposed a semi-automatic 3D segmentation algorithm for prostate boundaries in ultrasound images based on a 2D Active Shape Model (ASM) and rotated slices, utilizing a point distribution model to segment the prostate boundaries, but this requires a large amount of prior knowledge. Bi et al. proposed a segmentation method based on an Active Shape Model and Rayleigh mixture model clustering. This model treats TRUS images as a mixture of Rayleigh distributions. Using the Rayleigh mixture model (RMM) to generate clustered images yields more uniform tissue information, reduces the inhomogeneity of ultrasound images, and improves the efficiency of shape deformation estimation, but at the cost of significant time investment. Deep learning has become increasingly popular in recent years, offering numerous solutions. Long's Fully Convolutional Networks (FCN) replaces the final fully connected layers with convolutional layers in traditional convolutional networks, enabling pixel-level image classification and solving semantic-level image segmentation. Wang et al. added a deep attention mechanism to convolutional networks to incorporate more prostate details into deep features, achieving more accurate segmentation. Yu et al. used an aggregation layer including semantics and details in the lightweight segmentation network BiSeNetV2 to enhance the connection and fusion of features, and designed training strategies to improve segmentation performance. However, its accuracy remains relatively low. U-net, through its encoding and decoding structure, combines low-level and high-level semantic features, resulting in good performance on small datasets of medical images. SegNet is very similar to U-net, but its encoder stores the max-pooling index position during pooling. However, its model size is large, computationally intensive, and time-consuming. DeepLabV3+ primarily uses a spatial pyramid module and an encoder-decoder structure for semantic segmentation, optimizing edge segmentation. See [link to relevant documentation] for details. Figure 11 However, pure deep learning often requires a lot of time and computing power for training, and once the accuracy reaches a certain level, further improvements become very costly. By combining convolutional base blocks with manually designed boundary operators, we can detect the corresponding boundary points more effectively, overcoming the drawbacks of time-consuming and costly training inherent in pure deep learning. Summary of the Invention

[0005] To address the problems mentioned in the background art, this invention provides a prostate ultrasound image segmentation method based on a bidirectional exponentially weighted moving average algorithm, thereby resolving the issues raised in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a prostate ultrasound image segmentation method based on a bidirectional exponentially weighted moving average algorithm, the specific steps of which are as follows:

[0007] S1. Initial localization: The transformation localization matrix is ​​obtained by using the established localization convolutional network to obtain the transformation localization matrix coefficients, and the average template is obtained by using the point distribution model and principal component analysis. The two are combined to perform initial localization.

[0008] S2. Preliminary segmentation: Based on the preliminary localization, the first preliminary segmentation is performed using the boundary operator of the neighborhood information normal vector.

[0009] S3. Obtain the results. Use the improved two-way exponential weighted moving average method to input the normal vector row index values ​​of the segmentation points obtained from the initial segmentation to obtain the final set of segmentation points, and map it onto the TRUS image.

[0010] In the above technical solution, preferably, the specific steps of locating the convolutional network in step S1 are as follows: the network plays a localization role, and the transformation localization matrix is ​​obtained through the four output localization coefficients. The matrix locates the prostate region of the average template obtained later to the prostate region of the segmented image. The network consists of four convolutional blocks and three fully connected layers, and finally outputs four localization coefficients.

[0011] In the above technical solution, preferably, the point distribution model and principal component analysis in step S1 are as follows: the point distribution model is a concise expression of shape, using prior knowledge to represent the shape of the object through a shape description function, while principal component analysis reduces the dimensionality and redundancy of the data.

[0012] In the above technical solution, preferably, the neighborhood information normal vector contour boundary operator in step S2 specifically involves taking N points on the curve to construct normal vectors, and combining the neighborhood information of the normal vectors to obtain the segmentation points.

[0013] In the above technical solution, preferably, the bidirectional exponentially weighted moving average method in step S3 fully utilizes contextual information, uses future and present data, and assigns higher weights to data with more recent time series. Therefore, the bidirectional exponentially weighted moving average is more sensitive to changes in recent data.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0015] This invention improves upon the normal vector contour boundary operator proposed by Hodge, and uses a boundary operator that comprehensively considers the joint information of neighborhood normal vectors to segment the prostate. Experimental results show that compared with the traditional normal vector boundary operator, the improved operator has a better segmentation effect, a smoother boundary curve, and most boundary points have become stable, with only a few outliers requiring processing.

[0016] Furthermore, a method based on bidirectional exponentially weighted moving average is proposed to segment the shape of the prostate. Based on the boundary operator, the normal vector index value is used as the data input. This method achieves better segmentation results with a single input data than ordinary multi-iteration segmentation and can better preserve its features in non-noise areas, thus achieving accurate and fast ultrasound image segmentation. Attached Figure Description

[0017] Figure 1 This is a flowchart of the present invention;

[0018] Figure 2 This is a schematic diagram of the structure of the positioning convolutional network of the present invention;

[0019] Figure 3 This is a diagram showing the distribution model of repeated sampling in point distribution model and principal component analysis;

[0020] Figure 4 This is a partial schematic diagram of the strip diagram in the ordinary normal vector contour boundary operator;

[0021] Figure 5 This is a schematic diagram of the segmentation result of the ordinary normal vector contour boundary operator;

[0022] Figure 6 A schematic diagram of the improved contour boundary operator for neighborhood information normal vectors;

[0023] Figure 7 A schematic diagram of the segmentation result of the contour boundary operator for neighborhood information normal vectors;

[0024] Figure 8 A diagram showing the comparison of the number of iterations for the two-way exponentially weighted moving average method;

[0025] Figure 9 A schematic diagram of the segmentation results using the two-way exponentially weighted moving average method;

[0026] Figure 10 This is a schematic diagram comparing the segmentation effects of the present invention with those of other methods;

[0027] Figure 11 This is a schematic diagram comparing the method of the present invention with existing technical methods. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] like Figures 1 to 11 As shown, this invention provides a prostate ultrasound image segmentation method using a bidirectional exponentially weighted moving average algorithm. The specific steps of the prostate ultrasound image segmentation method using the bidirectional exponentially weighted moving average algorithm are as follows:

[0030] S1. Initial localization: The transformation localization matrix is ​​obtained by using a predefined localization convolutional network to obtain the transformation localization matrix coefficients, along with the average template obtained through the point distribution model and principal component analysis. These two are combined for initial localization. The structure diagram of the localization convolutional network is shown below. Figure 2 As shown;

[0031] S2. Preliminary segmentation: Based on the preliminary localization, the first preliminary segmentation is performed using the boundary operator of the neighborhood information normal vector.

[0032] S3. Obtain the results. Use the improved two-way exponential weighted moving average method to input the normal vector row index values ​​of the segmentation points obtained from the initial segmentation to obtain the final set of segmentation points, and map it onto the TRUS image.

[0033] like Figure 1 As shown, the workflow of this invention divides the entire segmentation process into three steps:

[0034] The first step is initial localization. The localization convolutional network outputs four transformation localization matrix coefficients to obtain the transformation localization matrix. Then, the average template obtained by the point distribution model (PDM) and principal component analysis (PCA) is combined to obtain the initial localization result through the transformation localization matrix and the average template.

[0035] The second step is to perform the first initial segmentation based on the initial localization using the Neighborhood Normal Vector Profile (NNVP) operator. After the initial segmentation, most of the segmentation points are already on the true boundary. Only a small number of segmentation points in areas where the prostate ultrasound image features are not obvious are not on the true boundary. These points are noise points.

[0036] The third step involves using the Bidirectional Exponentially Weighted Moving Average (BEWMA) method to input the row index values ​​of the normal vectors of the segmentation points obtained from the initial segmentation, thus obtaining the final set of segmentation points. This set is then mapped onto the TRUS image to obtain the final output result.

[0037] The specific working principle is explained below:

[0038] Application of localization convolutional networks: The network plays a localization role, and the transformation localization matrix is ​​obtained through the four output localization coefficients. The matrix locates the prostate region of the subsequently obtained average template to the prostate region of the segmented image; the network consists of four convolutional blocks, three fully connected layers, and finally outputs four localization coefficients.

[0039] Point distribution model and principal component analysis: The point distribution model is a concise representation of shape, using prior knowledge to represent the shape of an object through a shape description function;

[0040] In the point distribution model, the prostate contour shape is expressed by the following formula: x = [x1, x2, ..., x n ;y1,y2,…,y n ] T Each point set is obtained by sampling at equal intervals from the same location. Repeated sampling yields the point distribution model diagram shown below, as follows. Figure 3 As shown:

[0041] Building upon the above, principal component analysis is used to reduce data dimensionality and redundancy. Firstly, principal component analysis is used to obtain the global shape model. And calculate its covariance matrix. Calculate the eigenvalues ​​and eigenvectors Φ of the matrix, for the eigenvalues ​​(λ1, λ2, ..., λ). n Sort the data from largest to smallest, and select the t most significant feature vectors to form the average template. From the average template The model is initially located using the Transformed Localization Matrix (TLM).

[0042] Neighborhood information normal vector contour boundary operator:

[0043] Draw normal vectors at N points on the curve, specifying that the normal vectors point outwards from the curve. For ease of explanation, the contour curve is expanded into a strip-shaped region; the following figure shows a portion of the strip diagram:

[0044] like Figure 4 Let P(x,y) be a point on the k-th normal vector, and define a boundary operator. Each point on the normal vector has a corresponding row index value. A grayscale vector G of length l is defined in both the positive and negative directions at that point. The grayscale vector is represented as G based on the index of each point on the vector. out ={g i+l,k ,g i+l-1,k ......g i+1,k} and G in ={g i-l,k ,g i-l+1,k ......g i-1,k}, where the former represents the gray level of each point in the upper half of the region (outer part of the prostate) at point P, and the latter represents the gray level of each point in the lower half of the region (inner part of the prostate). g i+l,k This represents the gray value at point (i+l) on the k-th normal vector;

[0045] Therefore, the boundary operator at the i-th point on the k-th root normal vector can be expressed as: The formula calculates the cumulative grayscale difference between the upper and lower regions within the specified range of point i. In order to determine the boundary point here, the formula can be iterated repeatedly on this normal vector until the cumulative grayscale difference is maximized and the corresponding position is represented by the row index of the normal vector. This is the target boundary point.

[0046] Then, by iterating through each normal vector, the resulting segmentation is as follows:

[0047] Depend on Figure 5 It can be seen that the overall contour is relatively rough and does not achieve a good segmentation effect. These points are called noise points. The main reason for the above results is that the operator C only considers the gray level difference of the accumulated points on a single normal vector, and does not take into account the gray level information of adjacent regions, resulting in large differences between points before and after, and the contour points in some regions are relatively discrete and discontinuous.

[0048] To fit the segmentation points as closely as possible to the true boundary points, we combine the normal vectors of the adjacent regions of a point on the curve. The boundary operator C is improved as follows:

[0049] Figure 6 A normal vector of the boundary of a certain part of the prostate was drawn. and its adjacent normal vectors and To facilitate observation and description, we have created a magnified view of this local region. Taking a point on the k-th normal vector, if the row index of this point on the normal vector k is b, then this point can be represented as... The points corresponding to the same row indices on the other two normal vectors are already... Figure 4 Marked in the middle, respectively using and Let represent the improved boundary operator for the neighborhood information normal vector at point i on the k-th normal vector: The formula is equivalent to calculating the grayscale difference between the upper and lower half of the rectangular region on the boundary and taking the boundary point where the grayscale difference is the largest.

[0050] Boundary operator C neigh Compared to boundary operator C, which comprehensively considers neighborhood information, boundary points determined by the joint normal vector region are more convincing than those determined by a single normal vector, achieving noise reduction for the overall segmentation map. To consider even more neighborhood information, the value of m can be adjusted, resulting in an improved boundary operator effect as follows: Figure 7 As shown.

[0051] Two-way exponential weighted moving average method

[0052] Moving averages can predict future data based on historical and current time series data. In the field of image processing, it is essentially a low-pass filter, designed to filter out high-frequency disturbances in time series data while preserving low-frequency trends.

[0053] Simple Moving Average (SMA) directly calculates the equal-weighted average of a time series. However, because distorted and correct points are averaged together, the positions of correct points also become distorted, creating a vicious cycle of escalating distortion. To overcome this, while ensuring the algorithm's applicability to this model, and considering the different levels of importance of observations in the time series, we need to multiply the observations by weights before performing a local average. Therefore, we choose the Exponentially Weighted Moving Average (EWMA). EWMA assigns higher weights to more recent data in the time series and relatively lower weights to data further away. This ensures that the effects of these lower-weighted data points tend to have a smaller impact on the current position, but do not tend to zero. Therefore, EWMA is more sensitive to recent data changes than SMA. Here, the smoothing coefficient α∈(0,1) gives the following formula for the Exponentially Weighted Moving Average:

[0054] EWMA i =α*EWMA i-1 +(1-α)*X i (1)

[0055] In the formula, X i For the i-th input data; EWMA i Let be the predicted value of the i-th data point; EWMA i-1 α is the predicted value of the data preceding the i-th position; α is the smoothing coefficient.

[0056] Relying entirely on historical data for prediction will inevitably cause a lag in the predicted data, which will be reflected in the graph as a rightward shift of the curve. The moving average method trades the time lag for a smoother predicted curve.

[0057] Through experiments, we found that using a small smoothing coefficient α will result in an insignificant filtering effect on data noise, failing to achieve the expected results; while a large α value will cause the future predicted data to be excessively shifted to the right and lagged. Therefore, it is necessary to correct the bias to correct the lag and increase the robustness of the algorithm.

[0058] Formula (4) dynamically sets the size of α through iteration rounds, thereby avoiding the situation where there is less data in the early stage of algorithm iteration and a large difference from the original data;

[0059] Formula (5) reduces the significant lag between the predicted curve and the actual data as the algorithm iterates further, while keeping the initial impact of the exponentially weighted moving average algorithm minimal. This is achieved by using the smoothing coefficient α and the iteration number i.

[0060]

[0061]

[0062] Where: EWMA i Let α be the predicted value of the i-th normal vector; new is the smoothing coefficient; i is the iteration number.

[0063] For the classic exponentially weighted moving average method, the filtering effect near noise points will become better and better as the number of iterations increases. However, for most of the segmentation points that are already located on the true boundary, these points will deviate from the original true boundary, resulting in the shape of the constraint not being accurate enough, and the segmentation accuracy will actually decrease.

[0064] Building upon the classic exponentially weighted moving average method, we further improve upon it. First, the contour point data used in the iterations employs the row index values ​​of the normal vectors described earlier. Second, considering the characteristics of prostate shape data, in the second calculation, we use the shape data already obtained from the positive input of the EWMA in the first round—the predicted data—to back-calculate the shape data of the current image. From the aforementioned, let idx... i Let I be the row index of the initial segmentation result on the i-th normal vector, from which the vector IDX can be obtained. i This vector consists of the index values ​​of the first i normal vector rows, i.e., IDX. i ={idx1,idx2,idx3,…,idx i}, i∈(1,N), is used to represent the row index value of the normal vector of the initial segmentation result. The improved formula is as follows:

[0065]

[0066] In the formula, N is the total number of normal vectors; EWMA k This is the predicted value of the k-th normal vector; EWMA k-1 This is the predicted value of the preceding normal vector at the k-th position; IDX N-k+1 The future normal vector row index value needed to back-calculate the current data is the existing predicted value; α new This is the smoothing coefficient.

[0067] Unlike the classic exponentially weighted moving average method, our improved exponentially weighted moving average method, by using contextual information related to the prostate contour in the image bidirectionally and performing only two data processing steps, surpasses the segmentation effect of multi-iteration algorithms, while already constraining lag. Furthermore, for most excellent segmentation points, this method can better preserve the shape features of the true boundary and improve segmentation accuracy.

[0068] In comparison, we use the row index values ​​of the normal vector from the first part as data input. Compared to ordinary coordinate point input, changing the two-dimensional coordinate input to one-dimensional row index value input results in less computation and higher accuracy. Secondly, for general prediction, using past and present data to predict future data only uses data forward. However, for prostate data, we use data backward—that is, using the predicted prostate shape data to infer the current prostate shape data. Experiments show that this backward data usage has better segmentation results and shorter segmentation time compared to multiple forward data usages. Figure 6 The diagram illustrates the effect of different forward iterations and compares it with the method presented in this paper.

[0069] Figure 7 The denoising performance of the classic exponentially weighted moving average method under two and five forward iterations was compared. Figure 7 The data displayed are the normal vector row indices of 100 labeled feature points. The green line represents the denoising effect of the proposed method. Comparing the results of two iterations, a smoother denoising effect is achieved. Compared to the results of five iterations, more salient features are preserved, and the denoising effects in both comparisons are very significant.

[0070] against Figure 8 , 9 As shown in Figure 10, in order to measure the performance of the method, all the prostate ultrasound images used in this experiment were from real clinical examination data of a certain hospital. The real boundaries of the prostate in all images were marked by professional doctors as the ground truth of the target boundary, which was used for subsequent segmentation performance evaluation.

[0071] A total of 670 unenhanced data images were used in the experiment, of which 132 images were used for testing. Each image had a resolution of 576×768 pixels, and each pixel was 0.138mm×0.138mm in size. In the experiment, the parameters of the exponentially weighted moving average method used in this invention were set as follows: initial smoothing coefficient α = 0.9, N = 100;

[0072] Figure 9The image shows the segmentation results of test images randomly numbered 157, 256, 144, 24, 801, and 356 using this invention. The green segmentation represents the segmentation results achieved by the method described in this paper, while the red segmentation represents the set of ground truth points.

[0073] Figure 10 This is a comparison of the segmentation results of the proposed method with those of some other networks. The network hyperparameters were set as follows: Batch_size = 8, LR = 0.01, Momentum = 0.9, Scheduler = PolynomialDecay, Weight_decay = 4.0e-5. All networks were configured with dynamic rounds until model convergence. The experimental platform relied on PaddlePaddle, and all networks used were those proposed in the original paper without modification. The relevant platform parameters are as follows: platform: Linux, Python: 3.7.4, GPU: Tesla V100-SXM2-32GB. All networks were configured with dynamic rounds until model convergence.

[0074] Compared to previous methods for processing prostate noise, deep learning networks share a drawback: in TRUS images, due to low image quality, some segmentation results may exhibit outlier regions and erroneous segmentation effects, such as... Figure 11 The U-net segmentation results for images 24 and 356, and the SegNet segmentation results for images 157 and 24;

[0075] The method proposed in this invention does not achieve such results and has the following three characteristics: (1) It uses the exponentially weighted moving average method to process the shape features of the prostate. It predicts the position of the next shape point based solely on the shape features of the prostate ultrasound image itself, thereby obtaining the shape features of the entire prostate. Therefore, it has a good adaptability to different prostate shape features; (2) It uses future prostate data to backtrack the current data, making full use of contextual information. Near noise points, it only needs two data inputs to achieve a smoother segmentation effect than the classic multiple iterations, showing good performance in both time and space; (3) It can effectively preserve features for well-segmented parts that are already at the real boundary, while the classic moving average method cannot preserve its features at the real boundary to achieve a similar excellent segmentation effect near noise points.

[0076] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0077] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for prostate ultrasound image segmentation using a bidirectional exponentially weighted moving average algorithm, characterized in that, The specific steps are as follows: S1, preliminary positioning, obtaining a transformation positioning matrix through a set positioning convolution network to obtain a transformation positioning matrix coefficient and an average template obtained through a point distribution model and principal component analysis, combining the two for preliminary positioning; wherein the positioning convolution network in the S1 step is specifically as follows: the network has a positioning function, and four positioning coefficients are obtained through the output to obtain a transformation positioning matrix The matrix positions the prostate region of the average template obtained later to the prostate region of the segmented image, and the network is composed of four convolution blocks and three fully connected layers, and finally outputs four positioning coefficients. S2, preliminary segmentation, on the basis of preliminary positioning, the first preliminary segmentation is carried out according to the neighborhood information normal vector edge operator, wherein the neighborhood information normal vector contour edge operator in the S2 step is specifically that the normal vector is taken at N points on the curve, and the segmentation point is taken in combination with the neighborhood information of the normal vector; S3, get the result, the normal vector row index value of the segmentation point obtained by the initial segmentation is input using the improved bidirectional exponential weighted moving average method, the final segmentation point set is obtained, and it is mapped to the TRUS picture, wherein the bidirectional exponential weighted moving average method in the S3 step is specifically that the context information is fully utilized, the future and present data are utilized, and the data close in time sequence is given a higher weight, so the bidirectional exponential weighted moving average is more sensitive to the change of recent data.

2. The method of claim 1, wherein the method is a bidirectional exponentially weighted moving average algorithm for prostate ultrasound image segmentation. The point distribution model and principal component analysis in the S1 step are specifically as follows: the point distribution model is a brief expression of shape, which uses prior knowledge to express the shape of the object through a shape description function, and the principal component analysis reduces the dimension and redundancy of data.

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