CN112950690A - Multi-scale decomposition method based on wavelets - Google Patents
Multi-scale decomposition method based on wavelets Download PDFInfo
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- CN112950690A CN112950690A CN202110174579.3A CN202110174579A CN112950690A CN 112950690 A CN112950690 A CN 112950690A CN 202110174579 A CN202110174579 A CN 202110174579A CN 112950690 A CN112950690 A CN 112950690A
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Abstract
The invention discloses a multi-scale decomposition method based on wavelets, which comprises the following steps: (1) storing the point cloud data as 2.5D; (2) filtering in a wavelet mode to separate high frequency from low frequency; (3) projecting the 2.5D image to a scale function and a wavelet function; (4) performing low-pass filtering, namely, representing a frequency image by using wavelets in the step (3), and extracting the projection of the two parts on a scale function, namely, low-frequency data of the image; (5) after the filtering in the step (4), reserving low frequency, and performing projection on an inverse transformation kernel through a reserved low-frequency signal to perform image reconstruction; (6) the difference is reduced by down sampling and up sampling by a pyramid method; (7) and (5) repeating the steps (3) to (6) until the resolution of the microscopic measurement data is reduced to the specified requirement. The invention can reduce the difference between the microscopic measurement data quantity and the structured light measurement data quantity.
Description
Technical Field
The invention relates to the technical field of structured light measurement and microscopic measurement, in particular to a multi-scale decomposition method based on wavelets.
Background
The cross-scale measurement has wide application requirements in the fields of mechanical manufacturing, aerospace, cutter preparation, geoscience measurement and the like. With the continuous progress of modern precision manufacturing technology, manufactured products often have cross-scale topography. Therefore, a requirement is also placed on the measurement technique: the method ensures that the large-scale overall profile measurement is accurate, and simultaneously ensures that the small-scale local interested region has higher precision and richer details. However, due to the limitation of a single measurement mode, the requirements of both aspects cannot be met. The data measured by the large-field-of-view method is often low in resolution, and the local detail expression capability is limited; the high-resolution microscopic measurement method cannot represent the overall three-dimensional profile morphology due to the limitation of the measurement range. In this case, it is a feasible idea to combine two sets of measurement configurations with different scales or two measurement methods to measure the three-dimensional topography of the target. By using the cross-scale measurement method, the frequency domain bandwidth of measurement is expanded to a certain extent, so that the method has a large measurement range and simultaneously ensures the accuracy of local detail characteristics. Since the coordinate systems of the measured different scale data are not uniform, in order to ensure the integrity of the cross-scale data and the accuracy of the relative position in space, the measured different scale data need to be registered by means of stitching, and thus stitching of the cross-scale data is one of the most critical techniques. Different from three-dimensional data registration splicing under a single scale, the difference of information content, resolution and detail abundance of cross-scale data at corresponding overlapped parts often causes splicing errors and even failure. Therefore, the research on the multi-scale data processing method and the characterization technology of the scale parameters has important significance on the splicing of the cross-scale data, and more attention and investment must be obtained.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a multi-scale decomposition method based on wavelets, which utilizes wavelet decomposition to reduce the frequency of microscopic measurement data and the difference between the frequency of the microscopic measurement data and the frequency of structured light measurement data, reduces the data volume by means of pyramid down-sampling and up-sampling interpolation, and reduces the difference between the microscopic measurement data volume and the structured light measurement data volume.
In order to solve the above technical problems, the present invention provides a multi-scale decomposition method based on wavelets, comprising the following steps:
(1) storing the point cloud data into 2.5D, namely storing the Z coordinate of the point cloud data in a pixel value mode, and processing the point cloud data in a two-dimensional image processing mode;
(2) filtering in a wavelet mode to separate high frequency from low frequency;
(3) projecting the 2.5D image to a scale function and a wavelet function;
(4) performing low-pass filtering, namely, representing a frequency image by using wavelets in the step (3), and extracting the projection of the two parts on a scale function, namely, low-frequency data of the image;
(5) after the filtering in the step (4), reserving low frequency, and performing projection on an inverse transformation kernel through a reserved low-frequency signal to perform image reconstruction;
(6) the difference is reduced by down sampling and up sampling by a pyramid method;
(7) and (5) repeating the steps (3) to (6) until the resolution of the microscopic measurement data is reduced to the specified requirement.
Preferably, in step (2), the selection of the wavelet is performed according to the following rules: 1. orthogonality: the accuracy of data reconstruction is facilitated, and the distortion of reconstructed data is avoided; 2. supporting width: the length is reduced from a finite value to 0, the complexity of calculation time is improved when the support length is too long, and the smaller the support width is, the better the localization characteristic is; 3. symmetry: good symmetry is beneficial to avoiding distortion; 4. regularity: describing the smoothness of the function, wherein the higher the regularity, the smoother the wavelet and the better the data compression effect; 5. moment of disappearance: the vanishing moment is beneficial to fewer non-zero wavelet coefficients, so that the wavelet coefficients are zero as few as possible.
Preferably, in the step (3), the projecting the 2.5D image onto the scale function and the wavelet function specifically includes: the image is represented by a scale function and a wavelet function, the wavelet representation of the image is also divided into two steps, two dimensions are respectively represented, namely, two times of one-dimensional decomposition are carried out, and the one-dimensional decomposition is as follows:
where f (x) is the function to be processed, N is the number of levels of wavelet transform, j0At an arbitrary starting scale, k is the shift length of the wavelet transform,
is a function of a wavelet transform,
is a scale function of the wavelet transform,
is a scale factor, WψAnd (j, k) is a wavelet coefficient.
Preferably, in step (6), the difference is reduced by down-sampling and up-sampling with a pyramid method, and the filtered data is down-sampled first, that is, even rows and even columns of the image are retained, and the data amount is reduced to one fourth of the data amount when the data amount is not down-sampled; and then performing up-sampling interpolation, and performing depth value 0 insertion on even rows and even columns of the down-sampled image, wherein the resolution of the data is reduced at the moment.
The invention has the beneficial effects that: reducing the frequency of the microscopic measurement data by utilizing wavelet decomposition, and reducing the difference between the frequency of the microscopic measurement data and the frequency of the structured light measurement data; and the data volume is reduced by means of pyramid down-sampling and up-sampling interpolation, and the difference between the microscopic measurement data volume and the structured light measurement data volume is reduced.
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FIG. 1 is a schematic flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of point cloud data of microscopic measurement according to the present invention.
FIG. 3 is a schematic diagram of a point cloud that is decomposed 3 times according to the present invention.
FIG. 4 is a schematic diagram of a point cloud that is decomposed 6 times according to the present invention.
Detailed Description
As shown in fig. 1, a multi-scale decomposition method based on wavelets includes the following steps:
(1) storing the point cloud data into 2.5D, namely storing the Z coordinate of the point cloud data in a pixel value mode, and processing the point cloud data in a two-dimensional image processing mode;
(2) filtering in a wavelet mode to separate high frequency from low frequency;
(3) projecting the 2.5D image to a scale function and a wavelet function;
(4) performing low-pass filtering, namely, representing a frequency image by using wavelets in the step (3), and extracting the projection of the two parts on a scale function, namely, low-frequency data of the image;
(5) after the filtering in the step (4), reserving low frequency, and performing projection on an inverse transformation kernel through a reserved low-frequency signal to perform image reconstruction;
(6) the difference is reduced by down sampling and up sampling by a pyramid method;
(7) and (5) repeating the steps (3) to (6) until the resolution of the microscopic measurement data is reduced to the specified requirement.
Firstly, the 2.5D point cloud data is stored as image data, namely the data is stored in the form of coordinates and pixel values in a pixel coordinate system in the two-dimensional image. Smoothing the Z coordinate value in the microscopic measurement data by simulating a filtering mode in the two-bit image, namely processing the Z coordinate value as a pixel value in the two-bit image. Selecting proper wavelet base, DB4 wavelet base, according to the requirement of data processing, projecting the image onto the scale function and wavelet function, i.e. representing the image by the scale function and wavelet function, filtering, retaining the low-frequency signal, i.e. retaining the contour, and removing the details. And performing image reconstruction on the filtered low-frequency signal through an inverse wavelet transform kernel. The data volume is reduced after the down sampling is carried out in a pyramid mode, and meanwhile, the size of the image is also reduced; and then, the size of the image is restored in an interpolation mode, the inserted values are all 0, and the inserted values are all zero and are not displayed in the point cloud data, so that the data volume is reduced, and the resolution is reduced.
Repeating the above steps, continuously reducing the resolution and the data volume until correct cross-scale splicing can be performed, and obtaining the point cloud data after decomposition as shown in fig. 2.
And storing the data and text processed in the steps, importing the text into the Geomagic software, displaying the text as shown in figure 3, and decomposing the point cloud for 3 times and decomposing the point cloud for 6 times in figure 4.
The invention utilizes wavelet decomposition to reduce the frequency of microscopic measurement data and reduce the difference between the frequency of the microscopic measurement data and the frequency of the structured light measurement data; and the data volume is reduced by means of pyramid down-sampling and up-sampling interpolation, and the difference between the microscopic measurement data volume and the structured light measurement data volume is reduced.
Claims (4)
1. A multi-scale decomposition method based on wavelets is characterized by comprising the following steps:
(1) storing the point cloud data into 2.5D, namely storing the Z coordinate of the point cloud data in a pixel value mode, and processing the point cloud data in a two-dimensional image processing mode;
(2) filtering in a wavelet mode to separate high frequency from low frequency;
(3) projecting the 2.5D image to a scale function and a wavelet function;
(4) performing low-pass filtering, namely, representing a frequency image by using wavelets in the step (3), and extracting the projection of the two parts on a scale function, namely, low-frequency data of the image;
(5) after the filtering in the step (4), reserving low frequency, and performing projection on an inverse transformation kernel through a reserved low-frequency signal to perform image reconstruction;
(6) the difference is reduced by down sampling and up sampling by a pyramid method;
(7) and (5) repeating the steps (3) to (6) until the resolution of the microscopic measurement data is reduced to the specified requirement.
2. The wavelet based multi-scale decomposition method according to claim 1, wherein in step (2), the selection of the wavelet is performed according to the following rules: a. orthogonality; b. a support width; c. symmetry; d. regularity; e. moment vanishes.
3. The wavelet-based multi-scale decomposition method according to claim 1, wherein in the step (3), the projection of the 2.5D image onto the scale function and the wavelet function is specifically: the image is represented by a scale function and a wavelet function, the wavelet representation of the image is also divided into two steps, two dimensions are respectively represented, namely, two times of one-dimensional decomposition are carried out, and the one-dimensional decomposition is as follows:
where f (x) is the function to be processed, N is the number of levels of wavelet transform, j0At an arbitrary starting scale, k is the shift length of the wavelet transform,
is a function of a wavelet transform,
is a scale function of the wavelet transform,
is a scale factor, WψAnd (j, k) is a wavelet coefficient.
4. The wavelet-based multi-scale decomposition method according to claim 1, wherein in step (6), the difference is reduced by down-sampling and up-sampling by a pyramidal method, and the filtered data is down-sampled first, that is, even rows and even columns of the image are retained, when the data amount is reduced to one fourth of the data amount in the case of non-down-sampling; and then performing up-sampling interpolation, and performing depth value 0 insertion on even rows and even columns of the down-sampled image, wherein the resolution of the data is reduced at the moment.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5848193A (en) * | 1997-04-07 | 1998-12-08 | The United States Of America As Represented By The Secretary Of The Navy | Wavelet projection transform features applied to real time pattern recognition |
| CN105303535A (en) * | 2015-11-15 | 2016-02-03 | 中国人民解放军空军航空大学 | Global subdivision pyramid model based on wavelet transformation |
| CN111063027A (en) * | 2019-12-27 | 2020-04-24 | 河北工程大学 | Three-dimensional reconstruction data conduction system of digital holographic microscopic imaging equipment |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5848193A (en) * | 1997-04-07 | 1998-12-08 | The United States Of America As Represented By The Secretary Of The Navy | Wavelet projection transform features applied to real time pattern recognition |
| CN105303535A (en) * | 2015-11-15 | 2016-02-03 | 中国人民解放军空军航空大学 | Global subdivision pyramid model based on wavelet transformation |
| CN111063027A (en) * | 2019-12-27 | 2020-04-24 | 河北工程大学 | Three-dimensional reconstruction data conduction system of digital holographic microscopic imaging equipment |
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