A multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform

Abstract

The present invention relates to the field of image processing technology. Aiming at the problems of fitting error, end effect and modal aliasing in the existing filtering methods, a multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform is disclosed. The method comprises the following steps: (1) generating a grayscale image; (2) obtaining a spectrum without global trend; (3) adaptive spectrum segmentation; (4) two-dimensional empirical wavelet decomposition; (5) empirical mode function merging; (6) surface component reconstruction. The present invention is based on adaptive scale space representation technology and Riesz transform, extends the original two-dimensional empirical wavelet transform, establishes the relationship between each extracted intrinsic mode function and its physical size, realizes multi-scale characterization and filtering of engineering surfaces, thereby indicating the irregularity of manufacturing process and part function, and provides a basis for the subsequent establishment of mapping relationship between surface components and processing technology system and part performance.

Description

Technical Field

[0001] The invention relates to the technical field of image processing, and in particular to an engineering surface multi-scale filtering method based on extended two-dimensional empirical wavelet transform. Background Art

[0002] Surface topography is an important link between a part and its intended functional behavior during the manufacturing process. In order to meet tighter tolerance requirements and higher performance standards, engineers often require the surface quality of parts to meet various surface functional attributes such as specified size, shape, and peak. The surface topography of engineering surfaces is multi-scale and consists of components in three wavelength ranges, where the longer wavelength component is the shape error, the shorter wavelength component is the roughness, and the waviness is a medium wavelength component, which is between the shape error and the roughness. Surface components of different scales have different sources and affect the function of parts in different ways, such as vibration, tool wear, chatter, and sealing. Therefore, realizing multi-scale filtering of the surface is of great significance for the analysis of engineering surface topography.

[0003] Filtering technology is the process of separating the surface into shape error, waviness and roughness, and has always been a hot topic in surface morphology analysis. 2RC filter and Gaussian filter are the earliest proposed filtering technologies, and Gaussian filter is still regarded as the current standard filter. As nonlinear and non-stationary signal processing tools, wavelet transform and empirical mode decomposition are gradually used in engineering surface analysis. Unlike traditional filtering methods, they have multi-scale geometric structures and can divide a given surface morphology into a series of frequency components, each of which matches its scale. The number of separated frequency components is more than three, which can better reflect finer surface information. In the existing technology, Jerome Gilles proposed the empirical wavelet transform (EWT) method in the paper “Empirical Wavelet Transform” (IEEE Transactions on Signal Processing. 2013; 61: 3999-4010), which inherits the filtering characteristics of wavelet transform and empirical mode decomposition. It not only overcomes the non-adaptive nature of wavelet filtering on the wavelet basis, but also fills the theoretical foundation of empirical mode decomposition and avoids the modal aliasing of empirical mode decomposition filtering. However, EWT lacks the characterization of surface components at various scales.

[0004] The high-definition measurement technology that has emerged in recent years combines the advantages of contact measurement technology with a large measurement range and non-contact measurement technology with a high sampling density, and can predict and reproduce a clearer surface morphology for the surface of parts. The Chinese patent number CN103544694A, entitled "Method for converting three-dimensional high-density point cloud data of part surface morphology into grayscale images", proposes a method for converting measured point clouds into grayscale images, providing a new data basis for subsequent surface multi-scale filtering. Summary of the invention

[0005] In order to overcome the shortcomings of fitting error, end effect and modal aliasing in traditional filtering methods and make up for the inability of EWT to characterize surface components, the present invention proposes a multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform (Extended Bi-dimensional Empirical Wavelet Transform, EBEWT). Based on adaptive scale space representation technology and Riesz transform, the present invention extends the original two-dimensional empirical wavelet transform, establishes the relationship between each extracted intrinsic mode function and its physical size, realizes the characterization and filtering of each scale component of the engineering surface, and thus indicates the irregularity of the manufacturing process and part function.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform, the method comprising the following steps:

[0008] (1) Generate grayscale image: Process the three-dimensional high-density point cloud data of the measured part surface morphology to generate a grayscale image that can reflect the height value of the surface morphology;

[0009] (2) Obtaining the spectrum without global trend: obtained by pseudo-extreme fast Fourier transform and polynomial fitting;

[0010] (3) Adaptive spectrum segmentation: Generate the scale space plane of the spectrum through scale space representation technology and find all meaningful modes;

[0011] (4) Two-dimensional empirical wavelet decomposition: Establish a two-dimensional wavelet filter bank to obtain the empirical mode function;

[0012] (5) EMF merging: merging the EMFs whose wavelengths match the specific surface components;

[0013] (6) Surface component reconstruction: The merged empirical mode functions are reconstructed separately using the inverse transform of the two-dimensional empirical wavelet, thereby separating the engineering surface into shape error F(x, y), waviness W(x, y), and roughness R(x, y).

[0014] The programming language of the entire method steps of the present invention is MATLAB. The present invention solves the problems of fitting error, end effect and modal aliasing in traditional filtering methods, realizes the accurate separation of various scale components of the engineering surface, and provides a basis for the subsequent establishment of mapping relationships between surface components and processing technology systems and part performance.

[0015] Preferably, in step (1), the specific process of generating the grayscale image is: by mapping the height values ​​reflecting the surface morphology of the part in the three-dimensional high-density point cloud data into the grayscale values ​​of the pixels, the high-definition measurement point cloud data is converted into a grayscale image.

[0016] Preferably, in step (2), the specific process of obtaining the spectrum without global trend is: by pseudo-extreme fast Fourier transform, the mean spectrum F of the grayscale image of the engineering surface is calculated. P (f)(|ω|) and half-mean spectrum HF P (ω), the global trend T(ω) of the semi-mean spectrum is generated by polynomial fitting, and the spectrum GF without the global trend is obtained after subtraction P (ω). Pseudo-extreme fast Fourier transform and polynomial fitting were performed based on MATLAB functions.

[0017] Preferably, in step (3), the specific process of the adaptive spectrum segmentation is: generating a spectrum GF by using a scale space representation technique. P (ω) scale space plane L(ω,t), in the scale space plane, find all meaningful modes, that is, satisfy L i >T's scale space curve L i , and obtain the spectrum boundary set Ω={ω n} n＝0,...,N , the number of divisions N is L i The number of clusters is , and T is the threshold. The threshold T is obtained by the Otsu clustering method.

[0018] As a preferred scale space plane, L(ω,t)=g(ω;t)*GF P (ω), g(ω; t) is the Gaussian kernel function.

[0019] Preferably, in step (4), the specific process of two-dimensional empirical wavelet decomposition is: according to the spectrum boundary set Ω={ω n} n＝0,...,N , establish a two-dimensional wavelet filter bank And calculate the approximate coefficient and detail factor Thus, a series of empirical mode functions f are obtained k (x,y)(k=0,1,...,N-1).

[0020] Preferably, φ1(x,y) is an empirical scaling function, is the empirical wavelet function, f k (x,y)(k=0,1,...,N-1) satisfies and

[0021] Preferably, in step (5), the process of merging the empirical mode functions is as follows: constructing a single-effect signal f of each empirical mode function through Riesz transformation. kM (x,y), and calculate the amplitude A of the single-shot signal in turn k (x,y), phase and frequency Thus, the wavelength λ of each empirical mode function is obtained k ; According to the cut-off wavelength λ of form error, waviness and roughness specified in the international standard ISO 4287 s , c and λ f (λ s <λ c <λ f ), merge the empirical mode functions whose wavelengths conform to the specific surface components; the merging of the empirical mode functions is done by judging the wavelength λ k At the cut-off wavelength λ s , c , f The interval in which it is located is realized.

[0022] Preferably, the Riesz transform is: the empirical mode function f k Riesz transform f of (x,y)(k=0,1,...,N-1) kR (x,y)=f k (x,y)*h(x,y), h(x,y) is the Riesz transform kernel, single signal f kM (x,y)=(f k (x,y),-f kR (x,y) T , Phase frequency wavelength

[0023] For each empirical mode function f k (x, y), the wavelength λ is calculated according to the following three cases k The empirical mode functions that belong to the same range are merged. Case 1: When λ0 ≥ λ f , then the shape error F(x,y)=f0(x,y)(k=0); Case 2: When λ k∈[λ c ,λ f ), then the waviness W(x,y)={f k (x,y)|k=1,2,…,i}; Case 3: When λ k ∈[λ s ,λ c ), then the roughness R(x,y)={f k (x,y)|k=i,...,N-1}.

[0024] Preferably, in step (6), the shape error Waviness Roughness

[0025] The present invention has the beneficial effects:

[0026] (1) Based on adaptive scale space representation technology and Riesz transform, the present invention expands the original two-dimensional empirical wavelet transform, establishes the relationship between each extracted intrinsic mode function and its physical size, makes up for the deficiency of empirical wavelet transform in being unable to characterize surface components, realizes multi-scale characterization and filtering of engineering surfaces, and thus indicates the irregularities of manufacturing processes and part functions.

[0027] (2) The present invention proposes a multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform, which overcomes the shortcomings of fitting error, end effect and modal aliasing in traditional filtering methods, realizes the accurate separation of components of each scale on the engineering surface, and provides a basis for the subsequent establishment of mapping relationships between surface components and processing technology systems and part performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is the grayscale image of the original engineering surface in Example 1.

[0029] Figure 2 This is the spectrum segmentation diagram of Example 1.

[0030] Figure 3 It is the surface grayscale image of the empirical mode function of Example 1 (a represents the empirical mode function f0(x,y), b represents the empirical mode function f1(x,y), c represents the empirical mode function f2(x,y), d represents the empirical mode function f3(x,y), and e represents the empirical mode function f4(x,y)).

[0031] Figure 4 It is the original engineering surface sampled in Example 1 and the surface component diagram of each scale (a represents the original surface image, b represents the shape error, c represents the waviness, and d represents the roughness).

[0032] Figure 5 It is the grayscale image of the original engineering surface in Example 2.

[0033] Figure 6 This is the spectrum segmentation diagram of Example 2.

[0034] Figure 7 It is the surface grayscale image of the empirical modal function of Example 2 (a represents the empirical modal function f0(x,y), b represents the empirical modal function f1(x,y), c represents the empirical modal function f2(x,y), and d represents the empirical modal function f3(x,y)).

[0035] Figure 8 It is the original engineering surface sampled in Example 2 and the surface component diagram of each scale (a represents the original surface image, b represents the shape error, c represents the waviness, and d represents the roughness). DETAILED DESCRIPTION

[0036] The present invention is further described below in conjunction with specific implementation methods.

[0037] Overall embodiment

[0038] A multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform, the method comprising the following steps:

[0039] (1) Generate grayscale image: By mapping the height values ​​reflecting the surface morphology of the part in the three-dimensional high-density point cloud data into the grayscale values ​​of the pixels, the high-definition measurement point cloud data is converted into a grayscale image that can reflect the height values ​​of the surface morphology.

[0040] (2) Obtain the spectrum without global trend: Calculate the mean spectrum F of the grayscale image of the engineering surface through pseudo-extreme fast Fourier transform P (f)(|ω|) and half-mean spectrum HF P (ω), the global trend T(ω) of the semi-mean spectrum is generated by polynomial fitting, and the spectrum GF without the global trend is obtained after subtraction P (ω).

[0041] (3) Adaptive spectrum segmentation: The specific process of adaptive spectrum segmentation is: using scale space representation technology to generate spectrum GF P (ω) scale space plane L(ω,t), in the scale space plane, find all meaningful modes, that is, satisfy L i >T's scale space curve L i , and obtain the spectrum boundary set Ω={ω n} n＝0,...,N , the number of divisions N is L i The number of, T is the threshold; the scale space plane is L(ω,t)=g(ω;t)*GFP (ω), g(ω; t) is the Gaussian kernel function.

[0042] (4) Two-dimensional empirical wavelet decomposition: The specific process of two-dimensional empirical wavelet decomposition is: according to the spectrum boundary set Ω = {ω n} n＝0,...,N , establish a two-dimensional wavelet filter bank And calculate the approximate coefficient and detail factor Thus, a series of empirical mode functions f are obtained k (x,y)(k=0,1,...,N-1); where φ1(x,y) is the empirical scaling function, is the empirical wavelet function; the obtained empirical mode function f k (x,y)(k=0,1,...,N-1) satisfies and

[0043] (5) EMF merging: The process of EMF merging is as follows: through Riesz transform, a single-shot signal f of each EMF is constructed. kM (x,y), and calculate the amplitude A of the single-shot signal in turn k (x,y), phase and frequency Thus, the wavelength λ of each empirical mode function is obtained k ; According to the cut-off wavelength λ of form error, waviness and roughness specified in the international standard ISO 4287 s , c and λ f (λ s <λ c <λ f ), merge the empirical mode functions whose wavelengths conform to the specific surface components; the merging of the empirical mode functions is done by judging the wavelength λ k At the cut-off wavelength λ s , c , f The interval in which the empirical mode function f k Riesz transform f of (x,y)(k=0,1,...,N-1) kR (x,y)=f k (x,y)*h(x,y), h(x,y) is the Riesz transform kernel, single signal f kM (x,y)=(f k (x,y),-f kR (x,y) T , Phase frequency wavelength

[0044] (6) Surface component reconstruction: Using the inverse transform of the two-dimensional empirical wavelet, the merged empirical mode functions are reconstructed separately, thereby separating the engineering surface into shape error Waviness Roughness

[0045] Example 1

[0046] A multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform, the method comprising the following steps

[0047] (1) Generate grayscale image: The surface of a ceramic gauge block is measured by using three-dimensional high-resolution surface morphology measurement technology to obtain three-dimensional high-density point cloud data. The sampling resolution in the X and Y directions is 0.1 mm, the measurement accuracy in the Z direction is 1 μm, the measurement surface size is 138.2 mm × 66.6 mm, and the total number of measurement points can reach 920,000 points. The height value reflecting the surface morphology of the part in the three-dimensional point cloud data is mapped to the pixel grayscale value to generate a grayscale image of the gauge block surface, such as Figure 1 shown.

[0048] (2) Obtain the spectrum without global trend: Calculate the mean spectrum F of the generated grayscale image P (f)(|ω|)(matrix of size 1384×1) and half-mean spectrum HF P (ω) (a matrix of size 692×1), and the global trend of the half-mean spectrum is generated by polynomial fitting T(ω)=4.36×10 -9 ω 5 -9.86×10 -6 ω 4 +0.009ω 3 +802ω 2 -7.94×10 4 ω+2.82×10 6 , after subtraction, we get the spectrum GF without global trend P (ω) (a matrix of size 692×1).

[0049] (3) Adaptive spectrum segmentation: generating spectrum GF P The scale space plane L(ω,t) of (ω) (a sparse matrix of size 692×232). In the scale space plane, the scale space curve L = {232, 10, 107, 24, 6, 6, 232, 23, 232, 232}, the threshold T = 167, and the spectrum boundary set Ω = {0.08, 1.05, 2.42, 3.12}, the number of divisions N = 4, and the spectrum segmentation diagram is as follows Figure 2 shown.

[0050] (4) Two-dimensional empirical wavelet decomposition: According to the spectrum boundary set and the number of partitions, a two-dimensional wavelet filter bank B is established. εLP ={φ1(x,y),{ψ1(x,y),ψ2(x,y),ψ3(x,y),ψ4(x,y)}}(5×1 cell array, each subcell is a 334×692 size matrix), and calculate the approximate coefficients (334×692 size matrix) and detail coefficients (4×1 cell array, each subcell is a 334×692 size matrix), thus obtaining the empirical mode function {f0(x,y),f1(x,y),f2(x,y),f3(x,y),f4(x,y)}, as shown in Figure 3.

[0051] (5) EMF merging: Perform Riesz transform on each EMF to construct a single-shot signal set of EMFs {f 0M (x,y),f 1M (x,y),f 2M (x,y),f 3M (x,y),f 4M (x, y)}, thus obtaining the wavelength set of the empirical mode function {λ0=11.2,λ1=2.12,λ2=0.84,λ3=0.24,λ4=0.15}. According to the surface tolerance requirements Ra=0.1um and Rz=0.5um, the cut-off wavelengths are λ s =0.0025mm,λ c =0.25mm and λ f =2.5mm, so the empirical modal function f0(x,y) is the shape error, the combined empirical modal function {f1(x,y),f2(x,y)} is the waviness, and the combined empirical modal function {f3(x,y),f4(x,y)} is the roughness.

[0052] (6) Surface component reconstruction: Use the inverse transform of the two-dimensional empirical wavelet to reconstruct the shape error Waviness and roughness like Figure 4 As shown, multi-scale filtering of the engineering surface is achieved.

[0053] Example 2

[0054] A multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform, the method comprising the following steps

[0055] (1) Generate grayscale image: The top surface of a brake rotor is measured by using three-dimensional high-resolution surface morphology measurement technology to obtain three-dimensional high-density point cloud data. The sampling resolution in the X and Y directions is 0.1 mm, the measurement accuracy in the Z direction is 1 μm, the measurement surface size is 275.4 mm × 268.3 mm, and the total number of measurement points can reach 7 million points. The height value reflecting the surface morphology of the part in the three-dimensional point cloud data is mapped to the pixel grayscale value to generate a grayscale image of the cylinder top surface processing process. Combined with computational economy, a partial area of ​​30 mm × 30 mm is selected as an example for analysis, such as Figure 5 shown.

[0056] (2) Obtain the spectrum without global trend: Calculate the mean spectrum F of the generated grayscale image P (f)(|ω|)(600×1 matrix) and half-mean spectrum HF P (ω) (a 300×1 matrix), using polynomial fitting to generate the global trend of the half-mean spectrum T(ω) = 0.031ω 4 -20.82ω 3 +4707ω 2 -4.08×10 5 ω+1.05×10 7 , after subtraction, we get the spectrum GF without global trend P (ω) (a matrix of size 300×1).

[0057] (3) Adaptive spectrum segmentation: generating spectrum GF P (ω) scale space plane L(ω,t) (300×101 sparse matrix). In the scale space plane, the scale space curve L = {101,101,101}, the threshold T = 45, and the spectrum boundary set Ω = {0.08,1.78,3.08}, the number of divisions N = 3, the spectrum segmentation diagram is as follows Figure 6 shown.

[0058] (4) Two-dimensional empirical wavelet decomposition: According to the spectrum boundary set and the number of partitions, a two-dimensional wavelet filter bank B is established. εLP ={φ1(x,y),{ψ1(x,y),ψ2(x,y),ψ3(x,y),ψ4(x,y)}}(4×1 cell array, each subcell is a 300×300 matrix), and calculate the approximate coefficients (300×300 size matrix) and detail coefficients (3×1 cell array, each subcell is a 300×300 matrix), thus obtaining the empirical mode function {f0(x,y),f1(x,y),f2(x,y),f3(x,y)}, such as Figure 7 shown.

[0059] (5) EMF merging: Perform Riesz transform on each EMF to construct a single-shot signal set of EMFs {f 0M (x,y),f 1M (x,y),f 2M (x,y),f 3M (x, y)}, thus obtaining the wavelength set of the empirical mode function {λ0=35.5,λ1=1.67,λ2=0.68,λ3=0.56}. According to the surface tolerance requirements Ra=0.8um and Rz=6.3um, the cut-off wavelengths are λ s =0.0025mm,λ c =0.8mm and λ f =8mm, so the empirical modal function f0(x,y) is the shape error, the combined empirical modal function {f1(x,y),f2(x,y)} is the waviness, and the combined empirical modal function {f3(x,y),f4(x,y)} is the roughness.

[0060] (6) Surface component reconstruction: Use the inverse transform of the two-dimensional empirical wavelet to reconstruct the shape error Waviness and roughness like Figure 8 As shown, multi-scale filtering of the engineering surface is achieved.

[0061] Conclusion: It can be seen from the above Examples 1-2 that the multi-scale filtering method of the present invention overcomes the shortcomings of fitting error, end effect and modal aliasing in traditional filtering methods, realizes the accurate separation of various scale components of the engineering surface, and provides a basis for establishing the mapping relationship between surface components and processing technology systems and part performance.

[0062] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent transformation made to the above embodiment based on the technical essence of the present invention still falls within the protection scope of the technical solution of the present invention.

Claims

1. A multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform, characterized in that: Includes steps: (1) Generate grayscale image: Process the measured three-dimensional high-density point cloud data of the part surface morphology to generate a grayscale image that can reflect the height value of the surface morphology; (2) Obtain the spectrum without global trend: Calculate the mean spectrum F of the grayscale image of the engineering surface by pseudo-extreme fast Fourier transform P (f)(|ω|) and half-mean spectrum HF P (ω), use polynomial fitting to generate the global trend T(ω) of the semi-mean spectrum, and make a difference to get the spectrum GF without the global trend P (ω); Pseudo-polar fast Fourier transform and polynomial fitting are completed based on MATLAB functions; (3) Adaptive spectrum segmentation: Generate spectrum GF through scale space representation technology P (ω) scale space plane L(ω,t), find all meaningful modes in the scale space plane, that is, satisfy L i >T's scale space curve L i , and obtain the spectrum boundary set Ω={ω n } n＝0,……,N , the number of divisions N is L i The number of, T is the threshold; (4) Two-dimensional empirical wavelet decomposition: Establish a two-dimensional wavelet filter bank to obtain the empirical mode function; (5) EMF merging: merging the EMFs whose wavelengths match the specific surface composition; (6) Surface component reconstruction: The merged empirical mode functions are reconstructed separately using the inverse transform of the two-dimensional empirical wavelet, thereby separating the engineering surface into shape error F(x, y), waviness W(x, y), and roughness R(x, y).

2. The multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform according to claim 1 is characterized in that: In the step (1), the specific process of generating the grayscale image is: by mapping the height values ​​reflecting the surface morphology of the part in the three-dimensional high-density point cloud data into the grayscale values ​​of the pixels, the high-definition measurement point cloud data is converted into a grayscale image.

3. The multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform according to claim 1 is characterized in that: In step (2), the specific process of obtaining the spectrum without global trend is as follows: by pseudo-extreme fast Fourier transform, the mean spectrum F of the grayscale image of the engineering surface is calculated. P (f)(ω) and half-mean spectrum HF P (ω), the global trend T(ω) of the semi-mean spectrum is generated by polynomial fitting, and the spectrum GF without the global trend is obtained after subtraction P (ω).

4. The multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform according to claim 1 is characterized in that: The scale space plane is L(ω,t)=g(ω;t)*GF P (ω), g(ω; t) is the Gaussian kernel function.

5. The multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform according to claim 1 is characterized in that: In step (4), the specific process of two-dimensional empirical wavelet decomposition is: according to the spectrum boundary set Ω = {ω n } n＝0,...,N , establish a two-dimensional wavelet filter bank φ1(x,y) is the empirical scaling function, is the empirical wavelet function, and calculates the approximate coefficients and detail factor Thus, a series of empirical mode functions f are obtained k (x, y), where k = 1, 2, ..., N-1, and N is the number of partitions.

6. The multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform according to claim 5, characterized in that: f k (x, y), where k = 0, 1, ..., N-1, where N is the number of partitions, satisfying and In the formula, k = 1, 2, ..., N-1, where N is the number of divisions.

7. The multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform according to claim 1, characterized in that: In step (5), the process of merging the empirical mode functions is as follows: constructing the single-effect signal f of each empirical mode function through Riesz transformation kM (x,y), and calculate the amplitude A of the single-shot signal in turn k (x,y), phase and frequency Thus, the wavelength λ of each empirical mode function is obtained k ; According to the cut-off wavelength λ of form error, waviness and roughness specified in the international standard ISO 4287 s , c and λ f ,λ s <λ c <λ f , merge the empirical mode functions whose wavelengths conform to the specific surface components; the merging of the empirical mode functions is done by judging the wavelength λ k At the cut-off wavelength λ s , c , f The interval in which it is located is realized.

8. The multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform according to claim 7 is characterized in that: The Riesz transform is: The empirical mode function f k (x, y) (where k = 0, 1, ..., N-1, where N is the number of partitions), the Riesz transform f kR (x,y)=f k (x,y)*h(x,y), h(x,y) is the Riesz transform kernel, single signal f kM (x,y)=(f k (x,y),-f kR (x,y) T , Phase frequency 9. The multi-scale filtering method for engineering surfaces based on extended two-dimensional empirical wavelet transform according to claim 1, characterized in that: In step (6), the shape error F(x, y) = F -1 {F{f0(x,y)}}, waviness Roughness

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