CN113971717A - Microscopic three-dimensional reconstruction method based on Markov random field constraint - Google Patents
Microscopic three-dimensional reconstruction method based on Markov random field constraint Download PDFInfo
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Abstract
The invention discloses a microscopic three-dimensional reconstruction method based on Markov random field constraint, which comprises the following steps: scanning and shooting an object by using a microscope to obtain a plurality of images with different focusing degrees to form a multi-focusing image sequence; performing non-downsampling contourlet transformation on each image in the image sequence, and constructing a pyramid-shaped distributed low-pass filter set to process the non-downsampling contourlet transformation result; obtaining depth information and full focus information hidden in the image sequence by comparing different image processing results; correcting the depth information by using the prior constraint of the Markov random field; and constructing the three-dimensional form of the microscopic image by using the acquired depth information of the multi-focus image sequence. The algorithm is simple in realization principle, and can be effectively applied to the fields of fine structure detection, ultra-precision machining, medical surgery and the like. The method solves the problems that the focusing evaluation function in the prior art is difficult to balance the detection sensitivity and the noise robustness, and improves the reconstruction capability of the weak texture sample.
Description
Technical Field
The invention relates to the technical fields of digital image processing, computer vision and the like, in particular to a microscopic three-dimensional reconstruction method based on Markov random field constraint.
Background
The development of the precision machining technology puts higher requirements on the microscopic three-dimensional reconstruction technology. The key of the three-dimensional reconstruction technology is to accurately extract the depth information and the all-focus information of the microscopic sample. Under the condition, the focusing method has a large measurement range and low requirements on the surface smoothness of the sample to be detected, so that the method becomes a reliable method for detecting quality in the field of precision machining, and particularly for detecting the sample with a large-inclination-angle inclined plane, such as a cutting tool.
Although the focusing method has the capability of rapidly acquiring the surface depth information and the all-focus information of the sample, the focusing evaluation function, which is a key technology, still has some inherent problems, so that the expansion of the application range of the microscopic three-dimensional reconstruction algorithm is severely limited. First, to achieve accurate results, the focus merit function needs to be sensitive to high frequency information, but at the same time needs to be robust to noise, which is difficult to balance. Secondly, the upper limit expressed by the focusing evaluation function is still influenced by the richness of the texture information of the surface of the sample, and accurate focusing detection is difficult to be carried out on the sample with smooth surface and weak texture, so that the precision of three-dimensional reconstruction is limited. At present, the prior art mainly aims at improving the sensitivity and robustness of a Focus evaluation function, such as ydin T, Akgul Y S.A New Adaptive Focus Measure for Shape From Focus [ C ]// BMVC.2008: 1-10; and chinese patent publications CN108036739B, CN110443882B, CN111624756A and CN 111932677A.
From the above, it can be found that although the focusing method has certain advantages in the field of microscopic three-dimensional reconstruction compared with other three-dimensional reconstruction algorithms, the reconstruction algorithm still needs to be improved.
Disclosure of Invention
The invention aims to provide a microscopic three-dimensional reconstruction method based on Markov random field constraint, which solves the problems that the focusing evaluation function is difficult to balance detection sensitivity and noise robustness in the prior art, and improves the reconstruction capability of a weak texture sample.
In order to achieve the purpose of the invention, the technical scheme provided by the invention is as follows:
a microscopic three-dimensional reconstruction algorithm based on Markov random field constraint comprises the following steps:
(1.1) a microscope and a scanning platform are used for building a microscopic three-dimensional reconstruction system to carry out longitudinal scanning imaging on a sample to be detected, and a multi-focus image sequence reflecting focusing conditions of different depth areas on the surface of the sample is obtained;
(1.2) processing the multi-focus image sequence by means of a focusing evaluation function based on non-subsampled contourlet transformation to obtain a mask plate sequence which corresponds to the multi-focus image sequence and reflects an image focusing area;
(1.3) obtaining initial depth information and full focus information of the surface of the sample by means of a mask sequence;
(1.4) constructing an energy function by means of the Markov random field and the initial depth information, and solving the energy function to obtain an optimization result of the depth information;
and (1.5) performing three-dimensional reconstruction by using the extracted all-focus information and the optimized depth information.
In the step (1.1), the sample to be measured is longitudinally scanned and imaged by moving the Z axis of the microscope objective table at equal intervals by virtue of the imaging characteristic of small depth of field of the microscope.
Preferably, the specific method for processing the multi-focus image sequence by using the focus evaluation function based on the non-downsampling contourlet transform to obtain the mask plate sequence corresponding to the multi-focus image sequence and reflecting the image focus area includes:
1, converting a multi-focus image into a single-channel image, and converting each image in a focused image sequence by means of non-subsampled contourlet conversion;
2, processing the result of each image after conversion by using a pyramid low-pass filter bank to obtain a matrix with the same size;
3, constructing mask plate images with the same size and an initial value of 0 for each image in the multi-focus image sequence to form a mask plate sequence;
and 4, comparing the processing results (the matrix obtained in the step 2) between the images pixel by pixel, recording the pixel position and the channel number of the most value in the comparison results, and modifying the corresponding numerical value to be 1 in the mask plate sequence so as to update the mask plate sequence.
Preferably, the specific method for converting the multi-focus image into a single-channel image and transforming each image in the image sequence by means of non-downsampling contourlet transform comprises:
non-downsampling contourlet transformation is carried out on each image in the multi-focus image sequence, high-frequency information of 3 frequency bands is extracted, 2-level, 3-level and 4-level directional filter banks are sequentially constructed from a low frequency band to a high frequency band to carry out directional filtering, and texture distribution of 28 matrixes representing different frequency bands and different directions is obtained.
Preferably, the specific method for obtaining a matrix with the same size by processing the result of each image after transformation by using the pyramid low-pass filter bank includes:
1, constructing Gaussian filters with the sizes of 21, 13 and 5 from a low frequency band to a high frequency band according to parameter settings of the mean value mu being 0 and the variance sigma being 1 to form a pyramid low-pass filter bank;
2, carrying out absolute value summation processing on the direction coefficient matrixes under different scales, and processing the result by using a low-pass filter group of the corresponding scale after adding the absolute value of one coefficient matrix each time until the addition of all the direction coefficient matrixes under the scale is completed so as to obtain the processing results of different scales;
and 3, summing the processing results of different scales to obtain a matrix reflecting the focusing degree of each pixel in the image.
Preferably, the obtaining of the initial depth information and the through focus information of the sample surface by means of the reticle sequence includes:
1, multiplying the masks with different images by corresponding channels, and adding the multiplication results to obtain initial depth information estimated based on a focusing evaluation algorithm;
and 2, multiplying different images with corresponding masks, and adding the multiplication results to obtain a full-focus image reflecting the surface texture information of the sample.
Preferably, the constructing an energy function by means of the markov random field and the initial depth information, and obtaining the optimization result of the depth information by solving the energy function includes:
1, substituting initial depth information into an energy function frame based on maximum posterior probability to serve as a fidelity term of an energy function, and substituting a Markov random field on the surface of a sample to serve as a penalty term in the energy function;
and 2, expressing the energy function in the form of an undirected graph, and solving the undirected graph by means of an iterative optimization algorithm taking an alpha expansion graph cutting algorithm as a core to obtain the corrected depth information.
Preferably, the representing the energy function as an undirected graph, and solving the undirected graph by using an iterative optimization algorithm with an α -extended graph cut algorithm as a core to obtain the modified depth information includes:
1, taking an absolute value of a difference between a pixel and eight adjacent pixels as an n-links in an undirected graph, taking an absolute value of a difference between current depth information and a current channel as a t-links in the undirected graph, and taking energy of the undirected graph as initial minimum cut energy;
2, solving the current undirected graph based on the alpha expansion graph cut to obtain the minimum cut of the undirected graph;
and 3, calculating whether the minimum cut energy is reduced, if so, reconstructing t-links of the undirected graph by using the current minimum cut, and returning to the step 2, otherwise, outputting the minimum cut of the last iteration as an optimization result.
Preferably, the three-dimensional reconstruction by using the extracted all-focus information and the optimized depth information is to construct the three-dimensional graph by using the all-focus information as the bottom surface and the color of the three-dimensional graph and using the depth information as the height of the three-dimensional graph.
Compared with the prior art, the invention has the following technical effects:
the method of combining the non-downsampling contourlet transform and the pyramid low-pass filter is used for carrying out focusing evaluation, the advantages of multiscale and multidirectional extraction of texture information of the non-downsampling contourlet transform are exerted, low-pass processing of different degrees is carried out according to the transform results of different scales, and the sensitivity and the robustness of a focusing evaluation function are well balanced. The method has the advantages that the method has strong detection capability in the area with insufficient sample texture, and meanwhile, the strong detection capability cannot be excessively interfered in the area with rich sample texture.
In addition, in order to further eliminate the influence of weak texture on the estimated depth information result, the depth information result is corrected based on the prior constraint of the Markov random field. According to the Markov random field, the depth information is selectively subjected to smoothing operation so as to eliminate errors which are introduced by weak textures and do not meet the Markov random field, and the reconstruction capability of the weak texture sample is improved.
The method is simple in realization principle, and can be effectively applied to the fields of fine structure detection, ultra-precision machining, medical surgery and the like.
Drawings
Fig. 1 is a sample to be reconstructed in an embodiment.
FIG. 2 is a schematic diagram of a microscope scanning method for obtaining a sequence of multi-focus images of a surface of a sample to be measured in an embodiment.
FIG. 3 is a flowchart of the focusing evaluation in the examples.
FIG. 4 is a diagram illustrating non-downsampling contourlet transformation in an embodiment.
FIG. 5 is a flow chart of depth optimization in the embodiment.
FIG. 6 is an undirected graph of the graph cutting method in the embodiment.
FIG. 7 is a three-dimensional reconstruction result diagram in the embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the scope of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.
The embodiment provides a microscopic three-dimensional reconstruction algorithm based on Markov random field constraint, which comprises the following steps:
step 1: a sequence of multi-focus images was constructed for the sample shown in fig. 1.
Specifically, a microscope and a scanning platform are used for building a microscopic three-dimensional reconstruction system shown in fig. 2, and a scanning imaging characteristic of a small depth of field of the microscope is used for scanning and imaging a sample to be detected by moving the scanning platform at equal intervals, so that a multi-focus image sequence reflecting focusing conditions of different depth areas on the surface of the sample is obtained.
Step 2: as shown in fig. 3, the multi-focus image sequence is processed by a focus evaluation function based on non-downsampling contourlet transform, and a mask sequence corresponding to the multi-focus image sequence and reflecting the image focus area is obtained.
The specific process of the step 2 is as follows:
step 2.1: the multi-focus image is converted to a single-channel image, and each image in the image sequence is transformed by means of a non-subsampled contourlet transform.
Each image in the multi-focus image sequence is subjected to non-downsampling contourlet transformation as shown in fig. 4, high-frequency information of 3 frequency bands is extracted, 2-level, 3-level and 4-level directional filter banks are sequentially constructed from a low frequency band to a high frequency band to carry out directional filtering, and texture distribution of different frequency bands and different directions is represented by 28 matrixes.
Step 2.2: and processing the result of each image after transformation by using a pyramid low-pass filter bank to obtain a matrix with the same size.
Constructing Gaussian filters with the sizes of 21, 13 and 5 from a low frequency band to a high frequency band according to parameter settings of the mean value mu being 0 and the variance sigma being 1 to form a pyramid low-pass filter bank; carrying out absolute value summation processing on the direction coefficient matrixes under different scales, and processing the result by using a low-pass filter group of the corresponding scale after adding an absolute value of a coefficient matrix each time until all the direction coefficient matrixes under the scale are added to obtain processing results of different scales; the processing results at different scales are summed to obtain a matrix reflecting the degree of focus of the different pixels of the image.
Step 2.3: and constructing a mask plate image with the same size and an initial value of 0 for each image in the multi-focus image sequence.
Step 2.4: and comparing the processing results between the images pixel by pixel, recording the pixel position and the channel number of the most value in the comparison results, and modifying the corresponding numerical value to be 1 in the mask plate sequence to update the mask plate sequence.
And step 3: and obtaining initial depth information and full focus information of the surface of the sample by means of the mask plate sequence.
The specific process of the step 3 is as follows:
step 3.1: and multiplying the masks with different images by corresponding channels, and adding the multiplication results to obtain initial depth information estimated based on a focusing evaluation algorithm.
Step 3.2: and multiplying different images by corresponding masks, and adding the multiplication results to obtain a full-focus image reflecting the surface texture information of the sample.
And 4, step 4: as shown in fig. 5, an energy function is constructed by using the markov random field and the initial depth information, and the optimization result of the depth information is obtained by solving the energy function.
The specific process of the step 4 is as follows:
step 4.1: substituting initial depth information into an energy function framework based on the maximum posterior probability as a fidelity term of an energy function, and substituting a Markov random field on the surface of a sample as a penalty term in the energy function;
step 4.2: expressing the energy function as an undirected graph form shown in FIG. 6, and solving the undirected graph by means of an iterative optimization algorithm taking an alpha expansion graph cut algorithm as a core to obtain modified depth information;
taking the absolute value of the difference between the pixel and the eight adjacent pixels as n-links in the undirected graph, taking the absolute value of the difference between the current depth information and the current channel as t-links in the undirected graph, and taking the energy of the undirected graph as initial minimum cut energy; solving the current undirected graph based on the alpha expansion graph cut to obtain the minimum cut of the undirected graph; and calculating whether the minimum cut energy is reduced, if so, reconstructing t-links of the undirected graph by using the current minimum cut, and performing a new iteration, otherwise, outputting the minimum cut of the previous iteration as an optimization result.
The specific process of the step 5 is as follows:
the three-dimensional graph is constructed by using the all-focus information as the bottom surface and the color of the three-dimensional graph and the optimized depth information as the height of the three-dimensional graph, and the result of the three-dimensional reconstruction is shown in fig. 7. The method is constrained by the Markov random field, the noise on the surface of the sample is less, and the boundary between regions with different depths is obvious, so that a good three-dimensional reconstruction effect is achieved.
Claims (8)
1. A microscopic three-dimensional reconstruction method based on Markov random field constraint is characterized by comprising the following steps:
(1.1) a microscope and a scanning platform are used for building a microscopic three-dimensional reconstruction system to carry out longitudinal scanning imaging on a sample to be detected, and a multi-focus image sequence reflecting focusing conditions of different depth areas on the surface of the sample is obtained;
(1.2) processing the multi-focus image sequence by means of a focusing evaluation function based on non-subsampled contourlet transformation to obtain a mask plate sequence which corresponds to the multi-focus image sequence and reflects an image focusing area;
(1.3) obtaining initial depth information and full focus information of the surface of the sample by means of a mask sequence;
(1.4) constructing an energy function by means of the Markov random field and the initial depth information, and solving the energy function to obtain an optimization result of the depth information;
and (1.5) performing three-dimensional reconstruction by using the extracted all-focus information and the optimized depth information.
2. A markov random field constraint based microscopic three-dimensional reconstruction method according to claim 1, wherein said (1.2) is achieved by the sub-steps of:
(2.1) converting the multi-focus image into a single-channel image, and transforming each image in the multi-focus image sequence by means of non-downsampling contourlet transformation;
(2.2) processing the result of each image after transformation by using a pyramid low-pass filter bank to obtain a matrix with the same size;
(2.3) constructing mask plate images with the same size and an initial value of 0 for each image in the multi-focus image sequence to form a mask plate sequence;
and (2.4) comparing the processing results between the images pixel by pixel, recording the pixel position and the channel number of the most value in the comparison results, and modifying the corresponding numerical value to be 1 in the mask plate sequence so as to update the mask plate sequence.
3. A method for microscopic three-dimensional reconstruction based on markov random field constraints according to claim 2, wherein said step (2.1) is carried out by:
non-downsampling contourlet transformation is carried out on each image in the multi-focus image sequence, high-frequency information of 3 frequency bands is extracted, 2-level, 3-level and 4-level directional filter banks are sequentially constructed from a low frequency band to a high frequency band to carry out directional filtering, and texture distribution conditions of 28 matrixes representing different frequency bands and different directions are obtained.
4. A method of markov random field constraint based microscopic three-dimensional reconstruction according to claim 2, wherein said step (2.2) is carried out by the following sub-steps:
(2.2.1) constructing Gaussian filters with the sizes of 21, 13 and 5 from a low frequency band to a high frequency band according to parameter settings of the mean value mu being 0 and the variance sigma being 1 to form a pyramid low-pass filter bank;
(2.2.2) carrying out absolute value summation processing on the direction coefficient matrixes under different scales, and processing the result by using a low-pass filter group of the corresponding scale after adding the absolute value of one coefficient matrix each time until all the direction coefficient matrixes under the scale are added to obtain processing results of different scales;
(2.2.3) summing the results of the different scales to obtain a matrix reflecting the degree of focus of each pixel in the image.
5. A markov random field constraint based microscopic three-dimensional reconstruction method according to claim 1, wherein said (1.3) is achieved by the sub-steps of:
(3.1) multiplying the masks with different images by corresponding channels, and adding the multiplication results to obtain initial depth information estimated based on a focusing evaluation algorithm;
and (3.2) multiplying different images with corresponding masks, and adding the multiplication results to obtain a full-focus image reflecting the sample surface texture information.
6. A markov random field constraint based microscopic three-dimensional reconstruction method according to claim 1, wherein said (1.4) is achieved by the sub-steps of:
(4.1) substituting initial depth information into an energy function framework based on the maximum posterior probability to serve as a fidelity term of the energy function, and substituting a Markov random field on the surface of the sample to serve as a penalty term in the energy function;
and (4.2) representing the energy function in the form of an undirected graph, and solving the undirected graph by means of an iterative optimization algorithm taking an alpha expansion graph cutting algorithm as a core to obtain the corrected depth information.
7. A method for microscopic three-dimensional reconstruction based on Markov random field constraints according to claim 6, characterized in that said step (4.2) is carried out by the following sub-steps:
(4.2.1) taking the absolute value of the difference between the pixel and the eight adjacent pixels as n-links in the undirected graph, taking the absolute value of the difference between the current depth information and the current channel as t-links in the undirected graph, and taking the energy of the undirected graph as initial minimum cut energy;
(4.2.2) solving the current undirected graph based on an alpha extended graph cut algorithm to obtain the minimum cut of the undirected graph;
(4.2.3) calculating whether the minimum cut energy is reduced, if so, reconstructing t-links of the undirected graph by using the current minimum cut, and returning to the step (4.2.2), otherwise, outputting the minimum cut of the last iteration as an optimization result.
8. The three-dimensional reconstruction using the extracted all-focal information and the optimized depth information as claimed in claim 1, wherein the (1.5) reconstructs a microscopic three-dimensional shape with the all-focal information as a bottom surface and a color and the depth information as a height.
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