Titanium alloy plate section deformation recognition method based on machine vision

Abstract

The present application relates to the technical field of image data processing, and more particularly to a titanium alloy plate cross-section deformation recognition method based on machine vision, which comprises the following steps: first, obtaining the actual profile and the standard profile of the plate cross-section to generate a deviation sequence; then, performing multi-scale wavelet transform on the sequence, calculating the coherent energy of each scale, and constructing a coherent energy sequence in scale order; then, based on the coherent energy sequence, extracting first and second characteristic values respectively quantifying the defect frequency attribute and the structural complexity; finally, identifying the deformation type according to the position of the two-dimensional feature point formed by the two characteristic values in the preset feature space. The present application realizes high-precision classification of various deformation defects such as burrs and waves, and improves the accuracy and reliability of automatic detection.

Description

Technical Field

[0001] This invention relates to the field of image data processing technology, and in particular to a machine vision-based method for recognizing cross-sectional deformation of titanium alloy plates. Background Technology

[0002] In aerospace, precision manufacturing and other fields, titanium alloy plates have become the core material for manufacturing key components due to their high strength, low density and excellent corrosion resistance. The accuracy of their cross-sectional profile is directly related to product performance and safety. Therefore, accurately detecting deformation defects in the plate cross-section has become a core link in the production process.

[0003] Currently, the commonly used inspection process involves comparing the actual profile of a titanium alloy plate cross-section with a standard profile to generate a deviation sequence, which clearly reflects the magnitude and location of the deformation. However, existing technologies have significant shortcomings in determining the type of deformation defect based on the deviation sequence: traditional methods rely heavily on manually designed feature engineering to extract discrete geometric features such as the maximum amplitude, width, and local gradient of the defect from the deviation sequence. This approach can only capture superficial information about the defect and cannot describe the complex internal morphology of the defect. Consequently, it is easy to confuse deformation defects with the same amplitude and width but different fundamental characteristics, ultimately leading to misjudgment.

[0004] To address these issues, multi-scale analysis tools such as Discrete Wavelet Transform (DWT) have been introduced into related technologies. The DWT algorithm can decompose the deviation signal into sub-bands of different frequencies, thereby allowing observation of the overall contour and local details of the defect separately. However, traditional DWT algorithms typically calculate and evaluate the energy of each scale sub-band independently, treating features at different scales as isolated information. This ignores the inherent correlation between the features of real structural defects, which are often coherently manifested across multiple adjacent scales. Consequently, it performs poorly in distinguishing between structural defects with complex internal textures and random noise that is only apparent at a single scale, directly affecting the accuracy of defect identification. Summary of the Invention

[0005] To address the technical problem of low defect recognition accuracy in the DWT algorithm due to its difficulty in distinguishing between complex internal texture defects and random noise, this invention provides a machine vision-based method for recognizing cross-sectional deformation of titanium alloy plates. This method includes the following steps:

[0006] The actual and standard profiles of the titanium alloy plate cross-section are obtained, and a deviation sequence is generated based on the actual and standard profiles. Multi-scale wavelet transform is performed on the deviation sequence to obtain detail coefficients at multiple scales. The coherence energy at each scale is calculated, and a coherence energy sequence is constructed in scale order. The coherence energy is positively correlated with the cumulative energy of the detail coefficients at the same scale and the energy of the detail coefficients at corresponding positions at adjacent scales. The cumulative energy of the detail coefficients is the sum of squares of the detail coefficients at the corresponding scale. Based on the coherence energy sequence, a first and second characteristic value of the deviation sequence are determined. The first characteristic value is positively correlated with the value of each element in the coherence energy sequence and the index of each element. The second characteristic value is positively correlated with the difference between the value of each element, the index of each element, and the first characteristic value. The first and second characteristic values ​​are used to construct a two-dimensional feature point, and the deformation type corresponding to the deviation sequence is identified based on the position of the two-dimensional feature point in a preset feature space.

[0007] This invention generates a deviation sequence by obtaining the actual contour and standard contour of a titanium alloy sheet cross-section. After multi-scale wavelet transform processing, detail coefficients at multiple scales are obtained. Then, the coherence energy at each scale is calculated, and a coherence energy sequence is constructed. The coherence energy is defined by quantifying the energy correlation between the current scale and corresponding positions at adjacent scales, which enhances the continuous structural features across multiple scales while effectively suppressing isolated noise signals. Based on this coherence energy sequence, a first and second feature value are determined. These two feature values ​​more accurately reflect the intrinsic morphological characteristics of defects, such as high-frequency or low-frequency attributes and structural complexity. Finally, the two feature values ​​are used to construct two-dimensional feature points, and the deformation type is identified based on their position in a preset feature space. The entire process solves the problems of missed detections, misjudgments, and cumbersome operations associated with traditional detection methods. Furthermore, due to more precise feature extraction and clearer segmentation, it improves the accuracy and reliability of titanium alloy sheet cross-section deformation identification.

[0008] Preferably, the coherent energy satisfies the following relationship:

[0009] ;

[0010] in, It is the first Coherent energy at scale; It is the first The first of the scale detail coefficients One value; It is the first The detail factor of the scale One value; It is the floor function; It is the first Index value of scale detail coefficient; It is the first The total number of scale detail coefficients, It is the total number of scales.

[0011] This invention multiplies the energy at the current scale with the corresponding energy at its adjacent scales. This calculation method directly quantifies cross-scale correlation, ensuring that only features that exist simultaneously at the fine scale and its adjacent coarse scale are included in the effective energy sequence. This achieves enhancement of real structural defect signals and filtering of random noise at the algorithm level, laying a solid data foundation for subsequent accurate feature extraction.

[0012] Preferably, the first feature value satisfies the following relationship:

[0013] ;

[0014] in, It is the first eigenvalue; It is the total number of scales; It is the first Coherent energy at scale.

[0015] This invention constructs an index that can reflect the frequency bias of defect energy distribution. This feature value can quantify whether a defect is a high-frequency or low-frequency attribute, providing a key basis for distinguishing defects with different physical causes.

[0016] Preferably, the second eigenvalue satisfies the following relation: ;in, It is the second eigenvalue; It is the first eigenvalue; It is the total number of scales; It is the first Coherent energy at scale.

[0017] This invention can effectively distinguish between simple defects with energy concentrated on a few scales and complex defects with energy widely distributed across multiple scales by using a second eigenvalue. It adds a new dimension to the feature space, making it possible to distinguish between defects with similar shapes but different complexities, and further improving the precision of classification.

[0018] Preferably, generating the deviation sequence based on the actual contour and the standard contour includes: registering and aligning the actual contour and the standard contour using an iterative nearest point algorithm; calculating the normal distance from each point on the actual contour to the standard contour, and arranging all normal distances in their spatial order on the contour to form the deviation sequence.

[0019] This invention defines the specific method for generating the deviation sequence. Subsequent registration is performed using an iterative nearest-point algorithm, and the normal distance is calculated, ensuring the accuracy of the generated deviation sequence and its physical meaning. The ICP algorithm achieves more precise global optimal alignment, while the normal distance accurately reflects the actual deviation of each point on the contour, unaffected by the local tangent direction of the contour. This provides a high-quality, low-distortion input signal for subsequent wavelet analysis.

[0020] Preferably, obtaining the actual contour and standard contour of the titanium alloy plate cross-section includes: acquiring three-dimensional point cloud data of the titanium alloy plate cross-section using a line structured light vision system to obtain the actual contour; and extracting the standard contour from the CAD file of the titanium alloy plate.

[0021] Preferably, the multi-scale wavelet transform is a discrete wavelet transform based on the Daubechies wavelet basis function.

[0022] Preferably, identifying the deformation type corresponding to the deviation sequence based on the position of the two-dimensional feature point in the preset feature space includes: determining that the two-dimensional feature point falls into a preset region in the preset feature space; wherein each preset region corresponds to a deformation type.

[0023] Preferably, the preset region is jointly defined by a threshold value of the first feature value and a threshold value of the second feature value, including: a region where the first feature value is greater than its threshold value and the second feature value is less than its threshold value, corresponding to burr defects; a region where the first feature value is less than its threshold value and the second feature value is less than its threshold value, corresponding to wave defects; a region where the first feature value is greater than its threshold value and the second feature value is greater than its threshold value, corresponding to complex burr defects; and a region where the first feature value is less than its threshold value and the second feature value is greater than its threshold value, corresponding to irregular wave defects.

[0024] Preferably, the threshold for the first feature value is the median of all first feature values ​​in the historical data; the threshold for the second feature value is the third quartile of all second feature values ​​in the historical data.

[0025] The beneficial effects of this invention are as follows: This invention proposes a coherent energy analysis method based on wavelet transform cross-scale correlation to solve the problem of cross-sectional deformation identification in titanium alloy plates. This invention effectively filters out random noise by quantifying the energy correlation of defect features across adjacent scales. Simultaneously, it constructs two eigenvalues ​​based on coherent energy, where the first eigenvalue reflects the high-frequency or low-frequency attributes of the defect, and the second eigenvalue measures the structural complexity of the defect. Finally, by using the positions of these two physically meaningful eigenvalues ​​in two-dimensional space, high-precision classification of various deformation defects such as burrs and waves is achieved, improving the accuracy and reliability of automated detection. Attached Figure Description

[0026] Figure 1 A flowchart of a machine vision-based method for recognizing cross-sectional deformation of titanium alloy plates provided in an embodiment of the present invention. Detailed Implementation

[0027] This invention provides a machine vision-based method for recognizing cross-sectional deformation of titanium alloy plates, such as... Figure 1 As shown, the method includes steps S100-S500:

[0028] Step S100: Obtain the actual profile and standard profile of the titanium alloy plate cross section, and generate a deviation sequence based on the actual profile and the standard profile.

[0029] It should be noted that the purpose of this step is to transform the geometric deformation of the plate cross-section in the physical world into a one-dimensional digital deviation sequence that can be analyzed by subsequent signal processing algorithms, thus laying a high-quality data foundation for subsequent feature extraction.

[0030] Specifically, firstly, high-precision 3D vision measurement equipment such as a line structured light vision system is used to project structured light stripes onto the cross-section of the titanium alloy plate to be measured. An industrial camera captures the deformation image of the stripes caused by the geometric undulations of the cross-section. Then, 3D reconstruction calculation is performed on the deformation image to generate 3D point cloud image data of the cross-section. This point cloud image data constitutes the actual contour image of the plate cross-section. At the same time, a 3D digital image of the ideal design contour is extracted from the computer-aided design (CAD) model file of the plate product. This 3D design contour image is the standard contour image used for comparison.

[0031] Subsequently, to eliminate systematic errors introduced by inconsistent workpiece positioning during measurement, it is necessary to precisely spatially align the 3D point cloud data points corresponding to the actual contour image with the 3D data points corresponding to the standard contour image. As a preferred implementation, an iterative nearest-point algorithm can be used to register the acquired actual contour point cloud to the standard contour. Understandably, the iterative nearest-point algorithm finds the optimal rigid body transformation matrix through iterative optimization, minimizing the sum of squared distances between the 3D points on the actual contour and their corresponding 3D points on the standard contour, thus achieving optimal alignment between the two contours. The iterative nearest-point algorithm is existing technology and will not be elaborated upon here.

[0032] After registration is completed, the normal distance from each 3D point on the actual contour to the registered standard contour is calculated. All these normal distance values ​​are arranged in spatial order on the contour to form a one-dimensional, ordered deviation sequence, which records the core deformation information of the actual contour relative to the standard contour.

[0033] At this point, the deviation sequence has been obtained.

[0034] Step S200: Perform multi-scale wavelet transform on the deviation sequence to obtain detail coefficients at multiple scales.

[0035] It should be noted that the deformation information contained in the deviation sequence has different scale characteristics in the frequency domain. For example, sharp burrs exhibit high-frequency components due to their abrupt changes in edge, while gentle waves exhibit low-frequency components due to their slow changes in contour. To simultaneously capture and distinguish these deformation features at different scales, multi-scale analysis techniques are required. Discrete wavelet transform (DWT) is a tool for achieving this goal. Through convolution operations between wavelet basis functions and the signal, it can decompose the deviation sequence into different scale spaces, effectively separating features at different frequency scales while fully preserving its temporal location information. Therefore, this invention employs multi-scale wavelet transform to decompose the one-dimensional deviation sequence into a set of coefficients that simultaneously reflect the macroscopic contours and microscopic details of the deformation, laying a data foundation for subsequent feature extraction and recognition.

[0036] Specifically, for the deviation sequence, a specific wavelet basis function is selected, and a discrete wavelet transform is performed on it.

[0037] As a preferred implementation, the wavelet basis function can be the dbN wavelet from the Daubechies wavelet family, such as db4. This type of wavelet is chosen because it possesses excellent properties of tight support and orthogonality. Tight support ensures that the wavelet basis function has non-zero values ​​only within a finite interval, which effectively reduces edge distortion during the decomposition process, thus enabling more accurate analysis of local defects on the titanium alloy cross-sectional profile. Orthogonality ensures that the coefficients decomposed at different scales are independent, avoiding feature redundancy and improving the accuracy of subsequent energy calculations.

[0038] The determination of the number of decomposition layers M requires consideration of the typical size of the defect and the sampling resolution of the deviation sequence. Generally, when the defect size is small and the sampling resolution is high, the number of decomposition layers can be appropriately increased to capture finer details; when the deformation is mainly macroscopic contours, the number of layers can be appropriately reduced. In this embodiment, considering the common micron-level defects in titanium alloy plates and the high-resolution point cloud acquisition scenario, the number of decomposition layers is preferably 3. If the sampling resolution is low or larger-scale deformation needs to be analyzed, the number of decomposition layers can be adjusted to 5 to 10 layers. Implementers can adjust the number of decomposition layers according to their needs.

[0039] After M-level discrete wavelet transform, the deviation sequence is decomposed into two parts: first, an approximation coefficient vector, representing the low-frequency information of the deviation sequence, reflecting the overall trend of deformation, such as the macroscopic undulations of the cross-sectional profile; second, a set of detail coefficient vectors, representing the high-frequency information of the deviation sequence at various scales. There is a corresponding relationship between the level of detail: the smaller the scale, the higher the corresponding frequency, and the more microscopic the details represented, capable of capturing minute surface textures or measurement noise; the larger the scale, the lower the frequency, and the more macroscopic the details, capable of capturing gentle wave profiles. Discrete wavelet transform is an existing technology and will not be elaborated upon here.

[0040] This completes the multi-scale decomposition of the bias sequence and yields detail coefficients at multiple scales.

[0041] Step S300: Calculate the coherent energy at each scale and construct a coherent energy sequence in scale order.

[0042] It should be noted that the morphological characteristics of a structural, real physical defect do not exist in isolation at a single scale, but are coherently reflected across multiple adjacent scales; while random noise typically exhibits energy only at one or a few discontinuous scales. Therefore, the purpose of calculating coherent energy is to capture and amplify this cross-scale characteristic correlation, thereby enhancing the ability to characterize structural defects while suppressing the interference of random noise.

[0043] Specifically, this invention multiplies the detail coefficients at each scale with the detail coefficients corresponding to their spatial positions at adjacent scales point by point, and then sums the absolute values ​​of all products to obtain the coherent energy at the corresponding scale; in this way, the coupling strength of energy between adjacent scales can be quantified.

[0044] Based on the above logic, the first The coherent energy at different scales satisfies the following relation:

[0045] ;

[0046] in, It is the first Coherent energy at scale; It is the first The first of the scale detail coefficients One value; It is the first The detail factor of the scale values, of which The operation achieves spatial alignment of adjacent scale coefficients due to the downsampling characteristics of wavelet transform; It is the floor function; It is the first Index value of scale detail coefficient; It is the first The total number of scale detail coefficients, It is the total number of scales, determined by the original length of the bias sequence and the wavelet transform downsampling characteristics, and usually satisfies... , It is the length of the deviation sequence; This is the current analytical scale, with values ​​ranging from 2 to... .

[0047] The core of this relationship lies in the product term. Only when the deformation characteristics are at two adjacent scales and The corresponding positions of these features all exhibit high energy, meaning their detail coefficients are all large, and only then will their product contribute to the coherent energy. Conversely, if a feature has high energy only at a fine scale and its energy decays at a coarser scale, its product term will be small, and its contribution to the coherent energy will be effectively suppressed. Therefore, coherent energy can amplify signals from structural deformations while also possessing good noise robustness.

[0048] After calculating the coherent energy at each scale, they are constructed into a coherent energy sequence according to the scale from high frequency to low frequency, for example... .

[0049] Thus, the coherent energy sequence was obtained.

[0050] Step S400: Based on the coherent energy sequence, determine the first characteristic value and the second characteristic value of the deviation sequence.

[0051] It should be noted that although coherent energy sequences contain rich morphological information, they are still multidimensional vectors, making direct and intuitive comparison and classification difficult. This step further refines and reduces the dimensionality of this multidimensional energy distribution information, generating two scalar eigenvalues ​​with clear physical meaning based on the statistical characteristics of coherent energy sequences: the first eigenvalue and the second eigenvalue. The first eigenvalue quantifies the concentrated location of deformation energy on the scale axis, reflecting whether the energy is mainly concentrated at high-frequency or low-frequency scales. The second eigenvalue quantifies the dispersion of deformation energy distribution on the scale axis, i.e., whether the energy is concentrated at a few adjacent scales or dispersed across multiple discontinuous scales.

[0052] For the first eigenvalue, the construction approach is achieved through energy-weighted averaging. Specifically, the coherent energy at each scale is first normalized to eliminate the interference of differences in the total energy of different defects on the calculation results, ensuring that the coherent energy at each scale reflects its proportion in the overall energy. Then, a frequency-related value is assigned to each scale. In this embodiment, we select... , As the scale index, this function decreases as the scale index increases, meaning that higher frequency scales correspond to larger values ​​and lower frequency scales correspond to smaller values. This effectively distinguishes the frequency attributes of the scale without requiring additional adjustable parameters, thus meeting the fast calculation needs of engineering scenarios.

[0053] Then, using the proportion of coherent energy at each scale as weights, a weighted average is calculated on the corresponding frequency correlation values, yielding the first eigenvalue. The first eigenvalue is positively correlated with the sum of the products of the values ​​of each element in the coherent energy sequence and their corresponding indices. This is because the essence of weighted averaging is... and The product of these factors is summed, with the proportion of coherent energy as the weight. It increases as the scale index decreases, therefore or The larger either one is, the more significant its contribution to the first eigenvalue.

[0054] Based on the above logic, the first eigenvalue satisfies the following relation:

[0055] ;

[0056] in, It is the first eigenvalue; It is the total number of scales; It is the first Coherent energy at scale.

[0057] In this relationship, if the deformation energy is mainly concentrated at the high-frequency scale, the value of the correlation between the scale and frequency will be larger, and the weight of its coherent energy proportion will be higher, resulting in a larger final first eigenvalue. This represents sharp deformations such as burrs. Conversely, if the energy is mainly concentrated at the low-frequency scale, the first eigenvalue will be smaller, representing gentle deformations such as waves.

[0058] The calculation of the first eigenvalue has been explained above. The method for obtaining the second eigenvalue will be described below.

[0059] The second eigenvalue is calculated based on differences in energy distribution: first, the concentration locations of coherent energy at all scales are determined; then, the squared distance between the coherent energy at each scale and this concentration location is calculated; finally, the proportion of coherent energy at each scale is used as a weight to sum these squared distance values, and the result is the second eigenvalue. This value measures the differences in the distribution of coherent energy across different scales, reflecting whether the energy is more concentrated in a few scales near the concentration location or more dispersed across multiple scales.

[0060] Based on the above logic, the second eigenvalue satisfies the following relation:

[0061] ;

[0062] in, It is the second eigenvalue; It is the first eigenvalue; It is the total number of scales; It is the first Coherent energy at scale.

[0063] This relationship shows that if the deformation is of a single type, such as an ideal regular burr, its coherent energy will be highly concentrated on a few adjacent scales. In this case, the frequency correlation values ​​at these scales... The location of energy concentration, also known as the first eigenvalue. The difference is very small, making and The distance squared term is also extremely small, and after combining it with the weighted calculation based on the proportion of coherent energy, the final second eigenvalue will also be very small. Conversely, if the deformation morphology is complex or contains mixed defects, such as many small burrs superimposed on a large wave, its energy will be dispersed across multiple non-adjacent scales. The frequency correlation values ​​of these scales... The location of energy concentration, also known as the first eigenvalue. The difference is significant, leading to and The large value of the squared distance term means that even if the energy proportion of some scales is not high, the large squared distance term will still increase the overall weighted result, ultimately resulting in a large value for the second eigenvalue. This characteristic allows the second eigenvalue to effectively distinguish between single defects and mixed defects, providing a key basis for subsequent titanium alloy defect classification.

[0064] Thus, the first and second eigenvalues, which can quantify the morphological characteristics of the deviation sequence, have been determined.

[0065] Step S500: Construct a two-dimensional feature point from the first feature value and the second feature value, and identify the deformation type corresponding to the deviation sequence based on the position of the two-dimensional feature point in the preset feature space.

[0066] It should be noted that each deformation to be analyzed is uniquely described by a first eigenvalue and a second eigenvalue. This step uses these two eigenvalues ​​to construct a two-dimensional feature space, in which different types of deformation will naturally cluster in different regions, thereby determining the deformation type.

[0067] Specifically, a two-dimensional feature point is constructed by using the first feature value as the horizontal axis and the second feature value as the vertical axis. The position of this two-dimensional feature point simultaneously reflects the frequency concentration attribute of the deformation, i.e., high frequency or low frequency, and the complex morphological attribute, i.e., single or mixed.

[0068] Then, based on the position of the two-dimensional feature point in the preset feature space, its corresponding deformation type is identified. The preset feature space is divided into regions by setting a first threshold for the first feature value and a second threshold for the second feature value: the first threshold divides the horizontal axis (i.e., the first feature value) into two parts: above the threshold (high frequency concentration) and below the threshold (low frequency concentration); the second threshold divides the vertical axis (i.e., the second feature value) into two parts: above the threshold (complex shape) and below the threshold (simple shape). These two thresholds intersect to form four recognition regions. Based on the two-dimensional feature points of the deformation to be measured... The deformation types of the different regions into which the object fell were identified as follows:

[0069] The region in which the two-dimensional feature point falls corresponds to a burr defect, where the first feature value is greater than its threshold and the second feature value is less than its threshold.

[0070] The region in which the two-dimensional feature point falls is a wave defect, where the first feature value is less than its threshold and the second feature value is less than its threshold.

[0071] The region in which the two-dimensional feature point falls corresponds to a complex burr defect, where the first feature value is greater than its threshold and the second feature value is greater than its threshold.

[0072] The region where the first eigenvalue is less than its threshold and the second eigenvalue is greater than its threshold corresponds to an irregular wave defect.

[0073] In a preferred embodiment, the first threshold and the second threshold can be determined by extracting features from a large number of known type samples and then based on their statistical distribution. For example, the first threshold can be set to the 50th percentile of the first feature value of all training samples to effectively distinguish between deformations where energy is mainly concentrated in high-frequency and low-frequency areas; the second threshold can be set to the 75th percentile of the second feature value of all training samples to effectively distinguish between deformations with pure morphology and those with complex morphology.

[0074] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for recognizing cross-section deformation of a titanium alloy plate based on machine vision, characterized in that, The method comprises the steps of: obtaining an actual profile and a standard profile of a titanium alloy plate section, and generating a deviation sequence based on the actual profile and the standard profile; performing multi-scale wavelet transform on the deviation sequence to obtain detail coefficients at multiple scales; calculating the coherent energy at each scale and constructing a coherent energy sequence in order of scale; the coherent energy is positively correlated with the cumulative energy of the detail coefficients at the same scale and the energy of the detail coefficients at the corresponding position at the adjacent scale; the cumulative energy of the detail coefficients is the sum of squares of the detail coefficients at the corresponding scale; determining a first characteristic value and a second characteristic value of the deviation sequence based on the coherent energy sequence; the first characteristic value is positively correlated with the values of the elements in the coherent energy sequence and the indexes corresponding to the elements; the second characteristic value is positively correlated with the values of the elements, the indexes of the elements and the difference between the first characteristic value; constructing a two-dimensional feature point with the first characteristic value and the second characteristic value, and identifying the deformation type corresponding to the deviation sequence according to the position of the two-dimensional feature point in a preset feature space; The coherent energy satisfies the relationship: ; wherein, is the coherent energy of the th scale; is the th value of the detail coefficient of the th scale; is the th value of the detail coefficient of the th scale; is a floor function; is an index value of the detail coefficient of the th scale; is a total number of the detail coefficient of the th scale, is a total number of scales; The first eigenvalue satisfies a relationship: ; wherein, is the first eigenvalue; is the first eigenvalue; is the coherence energy of the scale; The second eigenvalue satisfies a relationship: ; wherein, is the second eigenvalue.

2. The machine vision-based titanium alloy plate cross-section deformation recognition method according to claim 1, characterized in that, The method comprises the steps of: aligning the actual profile and the standard profile using an iterative closest point algorithm; calculating the normal distance of each point on the actual profile to the standard profile, and arranging all the normal distances in the spatial order on the profile to form the deviation sequence.

3. The machine vision-based titanium alloy plate cross-section deformation recognition method according to claim 1, characterized in that, The method comprises the steps of: using a line structured light vision system to collect three-dimensional point cloud data of the titanium alloy plate section to obtain the actual profile; extracting the standard profile from the CAD file of the titanium alloy plate.

4. The machine vision-based titanium alloy plate cross-section deformation recognition method according to claim 1, characterized in that, The multi-scale wavelet transform is a discrete wavelet transform based on a Daubechies wavelet basis function.

5. The machine vision-based titanium alloy plate cross-section deformation recognition method according to claim 1, characterized in that, The method comprises the steps of: determining whether the two-dimensional feature point falls into a preset region in the preset feature space; wherein each preset region corresponds to a deformation type.

6. The machine vision-based titanium alloy plate cross section deformation recognition method according to claim 5, characterized in that, The preset region is jointly defined by a threshold value of the first characteristic value and a threshold value of the second characteristic value, and comprises: a region where the first characteristic value is greater than the threshold value and the second characteristic value is less than the threshold value, corresponding to a burr defect; a region where the first characteristic value is less than the threshold value and the second characteristic value is less than the threshold value, corresponding to a wave defect; a region where the first characteristic value is greater than the threshold value and the second characteristic value is greater than the threshold value, corresponding to a complex burr defect; a region where the first characteristic value is less than the threshold value and the second characteristic value is greater than the threshold value, corresponding to an irregular wave defect.

7. The machine vision-based titanium alloy plate cross section deformation recognition method according to claim 6, characterized in that, The threshold value of the first characteristic value is the median of all first characteristic values in historical data; the threshold value of the second characteristic value is the third quartile of all second characteristic values in historical data.

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