CN112116704B - Subcutaneous microvascular segmentation and three-dimensional reconstruction method based on optical coherence tomography - Google Patents
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Abstract
The invention relates to a subcutaneous microvascular segmentation and three-dimensional reconstruction method based on optical coherence tomography, which comprises the following steps: acquiring a two-dimensional image sequence through an FF-OCT system and preprocessing; grouping the acquired two-dimensional images, and carrying out robust principal component analysis on each group of images to obtain an image background and a high-response microvascular region; and (3) combining the image background with the high-response microvascular region, the position relation among the images of each group and the microvascular boundary distribution in each group of images, and carrying out microvascular segmentation and three-dimensional reconstruction. Compared with the prior art, the invention applies the global optical coherence tomography to the image recognition of venipuncture, which remarkably improves the imaging precision, not only ensures that the blood vessel positioning is more accurate, but also ensures that the clear imaging of the micro blood vessel is more reliable.
Description
Technical Field
The invention relates to the field of image recognition, in particular to a subcutaneous microvascular segmentation and three-dimensional reconstruction method based on optical coherence tomography.
Background
Subcutaneous microvascular imaging has specific requirements in occasions such as infant venipuncture, and infant venipuncture under 2 years old usually selects subcutaneous microvascular puncture at forehead to ensure the safety and stability of puncture. However, the existing vein puncture image identification method generally adopts ultrasonic vein imaging and near infrared vein imaging, so that the imaging precision is low, and the vein identification precision requirement at the forehead of the infant cannot be met.
Optical coherence tomography (Optical Coherence Tomography, OCT) is a technique for acquiring an image of a living organism tissue using a low coherence interference principle, and the OCT system obtains a series of interference patterns of the living organism tissue by combining a light beam reflected by the living organism tissue with a reference mirror light beam inside the OCT system, and can obtain the intensity and time delay of the reflected light of the living organism tissue by analyzing the interference patterns. The slice images of the biological tissue can be reconstructed by analyzing the reflected light intensity and the time delay. Meanwhile, the global optical coherence tomography (FF-Field Optical Coherence Tomography, FF-OCT) is taken as an improved OCT, has no artifact caused by the integral movement of the tissue along two transverse directions in OCT and has better sensitivity.
The invention combines the optical coherence tomography (Optical Coherence Tomography, OCT) technology and the venipuncture imaging technology, is used for fully and conveniently improving the accuracy of venipuncture and realizing the special requirements of occasions such as infant venipuncture and the like.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a subcutaneous microvascular segmentation and three-dimensional reconstruction method based on optical coherence tomography, which can meet the high-precision occasion of venipuncture.
The aim of the invention can be achieved by the following technical scheme:
a subcutaneous microvascular segmentation and three-dimensional reconstruction method based on optical coherence tomography comprises the following steps:
s1, acquiring a two-dimensional image sequence through an FF-OCT system and preprocessing;
S2, grouping the acquired two-dimensional images, and carrying out robust principal component analysis on each group of images to obtain an image background and a high-response microvascular region;
s3, dividing and three-dimensional reconstructing the micro blood vessels by combining the image background and the high-response micro blood vessel area and combining the position relation among the images and the micro blood vessel boundary distribution in each group of images.
Further, in the step S1, the preprocessing of the two-dimensional image includes logarithmic transformation, gray stretching, and smoothing of the image to attenuate the pretzel noise.
Further, the preprocessed logarithmic transformation includes:
calculating the converted normalized gray value s by comparing the change basic formula, wherein the calculation expression is as follows:
s＝c·logv+1(1+v·r)
Wherein c is a constant; v is a transformation factor for specifying the logarithmic transformation strength; r is the original gray value of the two-dimensional image, r is E [0,1];
the final gray value g after processing is obtained through calculation of the normalized gray value s after changing, and the calculation expression is as follows:
further, the calculation expression of gray stretching in the pretreatment is:
Wherein max p∈Imagefp (x, y) is the maximum gray value of the image, and min p∈Imagefp (x, y) is the minimum gray value of the image; f (x, y) is the pixel coordinate (x, y) gray value before transformation, and f' (x, y) is the pixel coordinate (x, y) gray value after transformation.
Further, in step S2, the grouping of the two-dimensional images specifically includes: the image sequence is expressed by an array D= [ v 1,v2,...,vl ], whereinThe column vectors are flattened by a single two-dimensional image array, and m and n are the pixel sizes of the original image; the image sequences of length l with pixel size m×n are grouped in step length l 0 to obtain a series of l 0 × (m·n) two-dimensional arrays.
Further, after robust principal component analysis is performed on each group of image data, front Jing Shuzu with a pixel size of m×n can be obtainedWith background array/>Microvascular erythrocytes are dynamic in the image sequence and located in the foreground, while background tissue is static and located in the background, thus determining the microvascular boundary distribution of each group.
Further, the decomposition process of the robust principal component analysis can be expressed as the following convex optimization problem:
minA,E‖A‖*+θ‖E‖1,s.t.D＝A+E
Wherein II- * represents the core norm of the matrix, i.e. the sum of its singular values; II 1 represents the 1-norm of the matrix, i.e. the sum of the absolute values of the matrix elements; θ is a weighting parameter; d=a+e as a precondition;
Solving by adopting an imprecise augmented Lagrangian multiplier method, and recording X n×2m＝(A,E),f(X)＝‖A‖*+θ‖E‖1, h (X) =D-A-E, wherein the Lagrangian function of the convex optimization problem is as follows:
Wherein <. > is defined as: < a, B > = tr (a T B), tr (·) is the trace of the matrix, used to calculate the sum of the matrix diagonal elements; II- F represents the F-norm of the matrix, for A n×m A n×m⊙Bn×m is Hadamard product among the matrixes; f (X) is an objective function of the minimum to be calculated, h (X) is a conditional function, i.e., h (X) =0; y is the Lagrangian multiplier.
Further, the update process of a k and E k in the imprecise augmented lagrangian multiplier method includes the solutions of sub-problem 1, sub-problem 2, and the update of lagrangian multiplier Y k and parameter E k:
The expression of the sub-problem 1 is: a k+1＝argminAL(A,Ek,Yk,∈k);
the expression of the sub-problem 2 is: e k+1＝argminEL(Ak+1,E,Yk,∈k).
Further, in the foreground arrayIn determining vessel boundary points/>The coordinates, and simultaneously, the z-direction coordinates z i of the blood vessel are determined by combining the distance delta z of the foreground array in the z direction, and the three-dimensional point cloud coordinates (x, y, z) of any point on the micro-vessel boundary are obtained, wherein the general calculation expression of the three-dimensional point cloud coordinates is as follows:
Wherein b s,by,bz is the coordinate offset.
Further, the expression of the interval delta z of the foreground array in the z direction is as follows:
δz＝l0·δ0
Where δ 0 is the skin depth direction layered imaging interval and l 0 is the step size.
Compared with the prior art, the invention has the following beneficial effects:
1. The invention applies the whole-domain optical coherence tomography to the image recognition of venipuncture, which remarkably improves the imaging precision, not only ensures that the blood vessel positioning is more accurate, but also ensures that the clear imaging of micro blood vessels is more reliable.
2. The invention adopts the grouping robust principal component analysis to improve the identification speed and imaging quality of the vein blood vessel. Specifically: in a traditional RPCA analysis (robust principal component analysis) algorithm, in a two-dimensional image with a longer interval in the z direction, the boundary difference of micro blood vessels is larger, the image foreground changes obviously, the accuracy of the result is reduced, and the RPCA analysis is carried out on all image sequences, only a single foreground image, namely a two-dimensional result, is obtained; the grouping RPCA analysis of the invention utilizes the fact that the adjacent blood vessel boundaries in the z direction have small difference, the segmented foreground image can accurately reflect the blood vessel boundaries in the z direction, the imaging precision of the blood vessel boundaries is improved, and the grouping RPCA analysis is carried out to obtain a series of foreground images, namely three-dimensional boundary data of the micro blood vessels.
3. According to the invention, the resolution process of the robust principal component analysis is solved by adopting an inaccurate augmentation Lagrangian multiplier method, so that the resolution process is simplified, and the speed and efficiency of image recognition are obviously improved.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
Fig. 2 is a schematic diagram of an image filtering operation according to the present invention.
Fig. 3 is a schematic diagram of packet robustness principal component analysis according to the present invention.
Fig. 4 is a general process step diagram of the augmented lagrangian multiplier referred to in the present invention.
FIG. 5 is a step diagram of an imprecise augmented Lagrangian multiplier algorithm employed in the present invention.
FIG. 6 is a schematic representation of a three-dimensional reconstruction of microvasculature according to the present invention.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. The present embodiment is implemented on the premise of the technical scheme of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.
As shown in fig. 1, the present embodiment provides a subcutaneous microvascular segmentation and three-dimensional reconstruction method based on optical coherence tomography, which includes the following steps:
S1, acquiring a two-dimensional image sequence through an FF-OCT system and preprocessing; image preprocessing mainly comprises logarithmic transformation, gray stretching and image smoothing for weakening salt and pepper noise.
S2, grouping the acquired two-dimensional images, and carrying out robust principal component analysis on each group of images to obtain an image background and a high-response microvascular region;
And S3, combining the image background and the high-response microvascular region, and carrying out microvascular segmentation and three-dimensional reconstruction by combining the position relation among the groups of images and the microvascular boundary distribution in each group of images.
In step S1, the preprocessing specifically includes:
(1) Logarithmic transformation
Calculating the converted normalized gray value s by comparing the change basic formula, wherein the calculation expression is as follows:
s＝c·logv+1(1+v·r)
Wherein c is a constant; v is a transformation factor for specifying the logarithmic transformation strength; r is the original gray value of the two-dimensional image, r is E [0,1]; notably, s.epsilon.0, 1 after transformation;
the final gray value g after processing is obtained through calculation of the normalized gray value s after changing, and the calculation expression is as follows:
The logarithmic transformation can enhance the image quality, expand the low gray-scale region, compress the high gray-scale region, and thereby suppress the high gray-scale response generated by the influence of melanin in the two-dimensional image to highlight the low gray-scale portion including the red cell image.
(2) Gray scale stretching
The gray scale stretching is to stretch an original low-contrast image into a high-contrast image in order to improve the gray scale value range of the image. Linear gray scale stretching is employed here, the basic expression of which is as follows:
Wherein max p∈Imagefp (x, y) is the maximum gray value of the image, and min p∈Imagefp (x, y) is the minimum gray value of the image; f (x, y) is the pixel coordinate (x, y) gray value before transformation, and f' (x, y) is the pixel coordinate (x, y) gray value after transformation.
(3) Image smoothing
Image smoothing is mainly to attenuate salt and pepper noise of two-dimensional images through median filtering. As shown in fig. 2, the median filtering operator M of the 7×7 image acts on the two-dimensional image area S, and the result is assigned to the center pixel K, which can be expressed as:
f′K(xK,yK)＝M{fp(x,y)；p∈S}
Wherein f' K (x, y) is the pixel value of the smoothed image of the central pixel coordinate (x K,yK), M is an operator for obtaining the median value of the pixel values in the specified region S, and f p (x, y) is the pixel value of the pixel point p before processing. Note that, limited to the operator M itself pixel size, the image boundary is not processed, and in this embodiment, the boundary pixel gradation value of the width Δd=3 remains unchanged.
In step S2 and step S3, as shown in fig. 3, the imaging z-direction is the skin depth direction, and the image sequence is expressed by an array d= [ v 1,v2,...,vl ], whereinAnd the column vectors are flattened by the array of the single two-dimensional image, and m and n are the pixel sizes of the original image. Firstly, an image sequence with the length of l and the pixel size of m multiplied by n is grouped by a step length of l 0 to obtain a series of l 0 multiplied by (m multiplied by n) two-dimensional arrays D 1,D2, performing Robust Principal Component Analysis (RPCA) on each group of image data D i to obtain a front Jing Shuzu/>, wherein the pixel sizes of the front Jing Shuzu/>, the pixel sizes of the front Jing Shuzu are all m multiplied by nWith background array/>Microvascular erythrocytes are dynamic in the image sequence, while background tissue is essentially static, microvascular is mainly in the foreground, while background tissue is mainly in the background. The boundary distribution of the microvessels of each group can be determined through the foreground and the background, and then the three-dimensional reconstruction of the microvessels can be performed by combining the position relationship on the z axis between the images of each group.
In step S2, robust principal component analysis is performed on each group of images to decompose the matrix D i, so as to recover a background portion with greater similarity, i.e. a low-rank matrixAnd a small range of moving objects or foreground parts, i.e. sparse matrix/>The specific process of decomposition by robust principal component analysis can be expressed as the following convex optimization problem:
minA,E‖A‖*+θ‖E‖1,s.t.D＝A+E
Wherein II- * represents the core norm of the matrix, i.e. the sum of its singular values; II 1 represents the 1-norm of the matrix, i.e. the sum of the absolute values of the matrix elements; θ is a weighting parameter; d=a+e as a precondition.
In this embodiment, the lagrangian multiplier method (Inexact Augmented Lagrange Multipliers, IALM) is used to solve, and record X n×2m＝(A,E),f(X)＝‖A‖*+θ‖E‖1, h (X) =d-a-E, and the lagrangian function of the convex optimization problem is:
Wherein <. > is defined as: < a, B > = tr (a T B), tr (·) is the trace of the matrix, the sum of the matrix diagonal elements is calculated; II- F represents the F-norm of the matrix, for A n×m F (X) is an objective function of the minimum to be calculated, h (X) is a conditional function, i.e., h (X) =0; y is the Lagrangian multiplier.
As shown in FIG. 4, the general approach to such a problem requires solving the sub-problem 1.1 before updating Y k and gradually converging to near the optimal solution.
Sub-problem 1.1:
In this embodiment, inaccuracy refers to that the above sub-problem 1.1 does not need to be solved accurately in the solving process, and then Y k is updated, and only the a k、Ek needs to be updated continuously in the solving process, so that it is sufficient to converge to the optimal solution of the problem. The efficiency is higher than that of the method for accurately solving the sub-problem 1.1.
As shown in fig. 5, the update process of a k、Ek in the algorithm of this embodiment includes the solutions of the sub-problem 2.1 and the sub-problem 2.2, and the update of the lagrangian multiplier Y k and the parameter e k:
sub-problem 2.1:A k+1＝argminAL(A,Ek,Yk,∈k)
Sub-problem 2.2:E k+1＝argminEL(Ak+1,E,Yk,∈k)
Sub-problem 2.1 can be broken down into:
Wherein, thetaiII E k‖1 is constant in the current cycle, and has no influence on the result of the step; a n×m⊙Bn×m is Hadamard product (Hadamard product) between matrices; sum (·) is the operator that solves the sum of the elements of the matrix. And as shown in FIG. 5, there are And the formula is as follows:
Then in the current cycle there is:
wherein, Is also constant in the current loop,/>Is normal and has no influence on the result of the step; a n×m⊙Bn×m is Hadamard product (Hadamard product) between matrices; sum (·) is the operator that solves the sum of the elements of the matrix. Thus, there are/>Is in the same solution as the sub-problem 2.1, and can be used/>Update a k. As in fig. 5, row 4 performs singular value decomposition and row 5 performs a k update.
Likewise, sub-problem 2.2 can be broken down into:
Wherein, II A k+1‖* is constant in the current cycle, and has no effect on the result of this step; a n×m⊙Bn×m is Hadamard product (Hadamard product) between matrices; sum (·) is the operator that solves the sum of the elements of the matrix. And is composed of Then, as in fig. 6, in the current cycle there is:
wherein, Is also constant in the current loop,/>Is normal and has no influence on the result of the step; a n×m⊙Bn×m is Hadamard product (Hadamard product) between matrices; sum (·) is the operator that solves the sum of the elements of the matrix. Thus, there are/>Is in the same solution as the sub-problem 2.2, and can be usedUpdate E k. As in fig. 5, line 6 performs the E k update.
After the solution of the sub-problem 2.1 and the sub-problem 2.2 is completed, the updated a k+1、Ek+1 is used to update Y k:
Yk+1＝Yk+∈k(D-Ak+1-Ek+1)
The updating of epsilon k has the empirical formula:
Wherein epsilon 2＝10-5,τ＝1.6,∈0＝1.25/‖D‖2,‖·‖2 is taken according to the empirical value to represent the 2-norm of the matrix. From the above, the convergence result obtained using the imprecise augmented Lagrangian multiplier algorithm can be expressed as Wherein the set of foreground arrays is/>
In step S3, the boundary distribution of the microvessels of each group can be determined through the foreground array, and then the three-dimensional reconstruction of the microvessels can be performed by combining the position relationship of each group of images on the z axis. As shown in FIG. 6, the foreground arrays are equally spaced, and the FF-OCT imaging system determines the skin depth direction layered imaging interval delta 0, then the interval delta z＝l0·δ0 of the foreground arrays in the z direction. The section S is parallel to the yoz plane, vascular boundary points are distributed in the section, and a plurality of similar planes can be obtained through interval sampling in the x direction. In the foreground arrayThe sampling coordinates of the section S in the x direction are utilized/>Can determine the y-axis coordinate/>, corresponding to any point of the vascular boundaryMeanwhile, in the section S, the position z i of any point of the blood vessel boundary in the z direction can be determined by combining the interval delta z of the foreground array in the z direction, and finally, the three-dimensional coordinates of any point on the blood vessel boundary are obtained and expressed as follows:
wherein b x,by,bz is a coordinate offset, determined by the position of the imaging part in the world coordinate system; (x, y, z) is a general representation of the location of any point of the vessel boundary. Thus, three-dimensional point cloud data of the micro blood vessels are obtained, and the three-dimensional point cloud data can be used for positioning and puncture guiding.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (7)
1. The subcutaneous microvascular segmentation and three-dimensional reconstruction method based on optical coherence tomography is characterized by comprising the following steps of:
s1, acquiring a two-dimensional image sequence through an FF-OCT system and preprocessing;
S2, grouping the acquired two-dimensional images, and carrying out robust principal component analysis on each group of images to obtain an image background and a high-response microvascular region;
s3, dividing and three-dimensional reconstructing the micro-blood vessels by combining the image background and the high-response micro-blood vessel area and combining the position relation among the images and the micro-blood vessel boundary distribution in each group of images;
In step S2, the grouping of the two-dimensional images specifically includes: the image sequence is expressed by an array D= [ v 1,v2,...,vl ], wherein The column vectors are flattened by a single two-dimensional image array, and m and n are the pixel sizes of the original image; grouping an image sequence with a pixel size of m multiplied by n and a length of l by a step length of l 0 to obtain a series of l 0 multiplied by (m multiplied by n) two-dimensional arrays;
After the robustness principal component analysis is carried out on each group of image data, the front Jing Shuzu with the pixel size of m multiplied by n can be obtained With background array/>The microvascular red blood cells are dynamic in the image sequence and are positioned in the foreground, and the background tissues are static and are positioned in the background, so that the microvascular boundary distribution of each group is determined;
The decomposition process of the robust principal component analysis can be expressed as the following convex optimization problem:
minA,E||A||*+θ||E||1，s.t.D＝A+E
Wherein I * represents the core norm of the matrix, i.e., the sum of its singular values; and 1 represents the 1-norm of the matrix is used, i.e. the sum of the absolute values of the matrix elements; θ is a weighting parameter; d=a+e as a precondition;
Solving by adopting an imprecise augmented Lagrangian multiplier method, and recording X n×2m＝(A,E),f(X)＝||A||*+θ||E||1, h (X) =D-A-E, wherein the Lagrangian function of the convex optimization problem is as follows:
Wherein <. > is defined as: < a, B > = tr (a T B), tr (·) is the trace of the matrix, used to calculate the sum of the matrix diagonal elements; and F represents the F-norm of the matrix is used, for A n×m have A n×m⊙Bn×m is Hadamard product among the matrixes; f (X) is an objective function of the minimum to be calculated, h (X) is a conditional function, i.e., h (X) =0; y is the Lagrangian multiplier.
2. The method for subcutaneous microvascular segmentation and three-dimensional reconstruction based on optical coherence tomography according to claim 1, wherein the preprocessing of the two-dimensional image in step S1 comprises logarithmic transformation, gray stretching and smoothing of the image to attenuate pretzel noise.
3. The method of subcutaneous microvascular segmentation and three-dimensional reconstruction based on optical coherence tomography according to claim 2, wherein the preprocessed logarithmic transformation comprises:
calculating the converted normalized gray value s by comparing the change basic formula, wherein the calculation expression is as follows:
s＝c·logv+1(1+v·r)
Wherein c is a constant; v is a transformation factor for specifying the logarithmic transformation strength; r is the original gray value of the two-dimensional image, r is E [0,1];
the final gray value g after processing is obtained through calculation of the normalized gray value s after changing, and the calculation expression is as follows:
4. The method for subcutaneous microvascular segmentation and three-dimensional reconstruction based on optical coherence tomography according to claim 1, wherein the calculation expression of gray stretching in the pretreatment is:
Wherein max p∈Imagefp (x, y) is the maximum gray value of the image, and min p∈Imagefp (x, y) is the minimum gray value of the image; f (x, y) is the pixel coordinate (x, y) gray value before transformation, and f' (x, y) is the pixel coordinate (x, y) gray value after transformation.
5. The method of claim 1, wherein the updating of a k and E k in the imprecise augmented lagrangian multiplier method comprises solving sub-problem 1 and sub-problem 2, and updating lagrangian multiplier Y k and parameter E k:
the expression of the sub-problem 1 is: a k+1＝arg minAL(A,Ek,Yk,∈k);
The expression of the sub-problem 2 is: e k+1＝arg minEL(Ak+1,E,Yk,∈k).
6. The method for subcutaneous microvascular segmentation and three-dimensional reconstruction based on optical coherence tomography according to claim 1, wherein in the foreground arrayIn determining vessel boundary points/> And simultaneously determining a vessel z-direction coordinate z i by combining the distance delta z of the foreground array in the z-direction to obtain a three-dimensional point cloud coordinate (x, y, z) of the micro-vessel, wherein the three-dimensional point cloud coordinate has the following calculation expression:
Wherein b x,by,bz is the coordinate offset.
7. The method for subcutaneous microvascular segmentation and three-dimensional reconstruction based on optical coherence tomography according to claim 6, wherein the expression of the interval delta z of the foreground array in the z direction is:
δz＝l0·δ0
Where δ 0 is the skin depth direction layered imaging interval, l 0 is the step size, and δ z is explained.
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