CN112950690B - Multi-scale decomposition method based on wavelet - Google Patents

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, and separating high frequency from low frequency; (3) Projecting the 2.5D image onto a scale function and a wavelet function; (4) Performing low-pass filtering, namely, using wavelets to represent frequency images in the step (3), and taking out projections of the two parts on a scale function, namely, low-frequency data of the images; (5) Filtering in the step (4), reserving low frequency, projecting the reserved low frequency signal onto an inverse transformation kernel, and reconstructing an image; (6) The difference is reduced by means of downsampling and upsampling by means of a pyramid method; (7) Repeating steps (3) - (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

A multi-scale decomposition method based on wavelet

Technical Field

The invention relates to the technical field of structured light measurement and microscopic measurement, and in particular to a multi-scale decomposition method based on wavelet.

Background technique

Cross-scale measurement has broad application needs in the fields of mechanical manufacturing, aerospace, tool preparation, and geospatial measurement. With the continuous advancement of modern precision manufacturing technology, the manufactured products often have cross-scale morphological features. Therefore, requirements are also put forward for measurement technology: while ensuring the accuracy of large-scale overall contour measurement, ensure that the small-scale local area of interest has higher accuracy and richer details. However, due to the limitations of a single measurement method, these two requirements cannot be taken into account. The data measured by the large field of view method often has low resolution and limited ability to express local details; while the high-resolution microscopic measurement method cannot characterize the overall three-dimensional contour morphology due to the limitation of the measurement range. In this case, it is a feasible idea to combine two sets of measurement configurations or two measurement methods of different scales to measure the three-dimensional morphology of the target. The use of cross-scale measurement methods has expanded the frequency domain bandwidth of the measurement to a certain extent, so that it has a larger measurement range while ensuring the accuracy of local detail features. Since the coordinate systems of the measured data of different scales are not unified, in order to ensure the integrity of the cross-scale data and the accuracy of the relative position in space, it is necessary to align them by splicing. Therefore, the splicing of cross-scale data is one of the most critical technologies. Different from the registration and stitching of 3D data at a single scale, the differences in information content, resolution, and detail richness of the corresponding overlapping parts of cross-scale data often lead to stitching errors or even failures. Therefore, the study of multi-scale data processing methods and scale parameter characterization technology is of great significance to the stitching of cross-scale data, and will surely receive more attention and investment.

Summary of the invention

The technical problem to be solved by the present invention is to provide a wavelet-based multi-scale decomposition method, which utilizes wavelet decomposition to reduce the frequency of microscopic measurement data, reduce the difference between the frequency of microscopic measurement data and the frequency of structured light measurement data, reduce the amount of data by pyramid downsampling and upsampling interpolation, and reduce the difference between the amount of microscopic measurement data and the amount of structured light measurement data.

In order to solve the above technical problems, the present invention provides a wavelet-based multi-scale decomposition method, comprising the following steps:

(1) The point cloud data is stored as 2.5D, that is, the Z coordinate of the point cloud data is stored in the form of pixel values, and the point cloud data is processed by processing two-dimensional images;

(2) Filtering by wavelet method to separate high frequency from low frequency;

(3) Project the 2.5D image onto the scaling function and the wavelet function;

(4) Perform low-pass filtering. The frequency image has been expressed by wavelet in step (3). The projections of both parts on the scale function are taken out, i.e., the low-frequency data of the image.

(5) After filtering in step (4), the low frequency is retained, and the image is reconstructed by projecting the retained low frequency signal onto the inverse transform kernel;

(6) Reducing the difference by downsampling and upsampling through the pyramid method;

(7) Repeat steps (3) to (6) until the resolution of the microscopic measurement data is reduced to the specified requirements.

Preferably, in step (2), the wavelet is selected according to the following rules: 1. Orthogonality: It is conducive to the accuracy of data reconstruction and avoids distortion of reconstructed data; 2. Support width: The length that decays from a finite value to 0. Too long a support length will increase the complexity of calculation time. The smaller the support width, the better the localization characteristics; 3. Symmetry: Good symmetry is conducive to avoiding distortion; 4. Regularity: It describes the smoothness of the function. The higher the regularity, the smoother the wavelet and the better the data compression effect; 5. Vanishing moment: The vanishing moment is conducive to having fewer non-zero wavelet coefficients, making as few wavelet coefficients as possible zero.

Preferably, in step (3), the 2.5D image is projected onto the scaling function and the wavelet function. Specifically, the image is represented by the scaling function and the wavelet function. The image is represented by the wavelet function in two steps, and the two dimensions are represented respectively, that is, the one-dimensional decomposition is performed twice. The one-dimensional decomposition is as follows:

Where f(x) is the function to be processed, N is the number of wavelet transform series, j ₀ is an arbitrary starting scale, k is the translation length of the wavelet transform, is the wavelet function of wavelet transform, /> is the scaling function of the wavelet transform, is the scale coefficient, and W _ψ (j,k) is the wavelet coefficient.

Preferably, in step (6), the difference is reduced by downsampling and upsampling by a pyramid method. First, the filtered data is downsampled, that is, the even rows and even columns of the image are retained. At this time, the amount of data has been reduced to one-fourth of the amount before downsampling. Then upsampling interpolation is performed, and the depth value 0 of the image is inserted into the even rows and even columns of the downsampled image. At this time, the resolution of the data is reduced.

The beneficial effects of the present invention are as follows: using wavelet decomposition to reduce the frequency of microscopic measurement data, thereby reducing the difference between the frequency of microscopic measurement data and the frequency of structured light measurement data; reducing the amount of data by pyramid downsampling and upsampling interpolation, thereby reducing the difference between the amount of microscopic measurement data and the amount of structured light measurement data.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic flow chart of the method of the present invention.

FIG. 2 is a schematic diagram of microscopic measurement point cloud data of the present invention.

FIG. 3 is a schematic diagram of a point cloud decomposed three times according to the present invention.

FIG. 4 is a schematic diagram of a point cloud decomposed 6 times according to the present invention.

Detailed ways

As shown in FIG1 , a wavelet-based multi-scale decomposition method includes the following steps:

(1) The point cloud data is stored as 2.5D, that is, the Z coordinate of the point cloud data is stored in the form of pixel values, and the point cloud data is processed by processing two-dimensional images;

(2) Filtering by wavelet method to separate high frequency from low frequency;

(3) Project the 2.5D image onto the scaling function and the wavelet function;

(4) Perform low-pass filtering. The frequency image has been expressed by wavelet in step (3). The projections of both parts on the scale function are taken out, i.e., the low-frequency data of the image.

(5) After filtering in step (4), the low frequency is retained, and the image is reconstructed by projecting the retained low frequency signal onto the inverse transform kernel;

(6) Reducing the difference by downsampling and upsampling through the pyramid method;

(7) Repeat steps (3) to (6) until the resolution of the microscopic measurement data is reduced to the specified requirements.

First, the 2.5D point cloud data is stored as image data, that is, the data is stored in the form of coordinates and pixel values in the pixel coordinate system of the two-dimensional image. The Z coordinate value in the microscopic measurement data is smoothed by simulating the filtering method in the two-dimensional image, that is, the Z coordinate value is treated as the pixel value in the two-dimensional image. According to the requirements of data processing, a suitable wavelet basis, DB4 wavelet basis, is selected, and the image is projected onto the scale function and wavelet function, that is, the scale function and wavelet function are used to represent the image, and filtering is performed to retain the low-frequency signal, that is, to retain the contour and remove the details. The low-frequency signal after filtering is reconstructed by the inverse transform kernel of the wavelet. Downsampling is performed by pyramid method, and the amount of data is reduced after downsampling, and the size of the image is also reduced; then the size of the image is restored by interpolation, and the inserted values are all 0, because the inserted values are all zero, they are not displayed in the point cloud data, thereby reducing the amount of data and the resolution.

Repeat the above steps to continuously reduce the resolution and data volume until correct cross-scale stitching can be performed. The decomposed point cloud data is shown in Figure 2.

The data processed by the above steps are stored in the form of text, and the text is imported into Geomagic software to display the point cloud decomposed 3 times as shown in Figure 3 and the point cloud decomposed 6 times as shown in Figure 4.

The present invention utilizes wavelet decomposition to reduce the frequency of microscopic measurement data, thereby reducing the difference between the frequency of microscopic measurement data and the frequency of structured light measurement data; and reduces the amount of data by pyramid downsampling and upsampling interpolation, thereby reducing the difference between the amount of microscopic measurement data and the amount of structured light measurement data.

Claims (4)

1. A wavelet-based multi-scale decomposition method, comprising the steps of:

(1) Storing the point cloud data as 2.5D, namely storing the Z coordinate of the point cloud data in the form of pixel values, and processing the point cloud data in a mode of processing a two-dimensional image;

(2) Filtering in a wavelet mode, and separating high frequency from low frequency;

(3) Projecting the 2.5D image onto a scale function and a wavelet function;

(4) Performing low-pass filtering, namely, using wavelets to represent frequency images in the step (3), and taking out projections of the two parts on a scale function, namely, low-frequency data of the images;

(5) Filtering in the step (4), reserving low frequency, projecting the reserved low frequency signal onto an inverse transformation kernel, and reconstructing an image;

(6) The difference is reduced by means of downsampling and upsampling by means of a pyramid method;

(7) Repeating steps (3) - (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. regularities; e. vanishing moment.

3. The wavelet-based multi-scale decomposition method according to claim 1, wherein in step (3), projecting 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 image is also divided into two steps by wavelet representation, and the two dimensions are respectively represented, namely, the two dimensions are decomposed in two dimensions, and the one-dimensional decomposition is represented by the following formula:

wherein f (x) is the function to be processed, N is the number of wavelet transform stages, j ₀ For any starting scale,k is the shift length of the wavelet transform,is a wavelet function of wavelet transformation, +.>For the scale function of the wavelet transform, +.>As a scale factor, W _ψ (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 means of downsampling and upsampling by means of a pyramid method, wherein the filtered data is downsampled first, i.e. the even rows and even columns of the image are preserved, and the amount of data is reduced to a quarter when not downsampled; and then up-sampling interpolation is carried out, and the depth value 0 of the inserted image is carried out on even lines and even columns of the down-sampled image, so that the resolution of the data is reduced.