CN101773395A - Method for extracting respiratory movement parameter from one-arm X-ray radiography picture - Google Patents

Abstract

A method for extracting respiratory motion parameters from a single-arm X-ray angiography image belongs to the cross field of digital signal processing and medical imaging, and the purpose is to separate respiratory motion from complex actual human heart motion. The present invention selects a group of structural feature points (including the head and tail points of the blood vessel segment) on the coronary blood vessel and tracks them in the sequence to obtain their motion curves over time, and then uses the method of Fourier series expansion and frequency domain filtering Two-dimensional respiratory motion curves are obtained by separation. In addition, in order to describe the respiratory movement more intuitively and effectively, the present invention reconstructs the two-dimensional expiratory movement obtained under two different angiographic viewing angles according to the three-dimensional reconstruction principle of the midpoint of the imaging system to obtain the three-dimensional respiratory movement. The invention can obtain better respiratory motion extraction results, has wider applicability and flexibility, and meets clinical requirements.

Description

A Method for Extracting Respiratory Motion Parameters from Single-arm X-ray Contrasting Images

technical field

The invention belongs to the intersecting field of digital signal processing and medical imaging, and in particular relates to a method for extracting respiratory motion parameters from a single-arm X-ray contrast image.

Background technique

Rhythmic expansion and contraction of the chest to complete inhalation and exhalation, which is breathing movement. Breathing movement will cause the overall translational movement of the human heart in three-dimensional space. In the X-ray contrast system, due to the influence of respiratory movement, the coronary blood vessels will undergo two-dimensional translational movement on the imaging surface.

Therefore, on the one hand, the coronary angiography image records the projection of the motion of the heart on the two-dimensional plane, and at the same time superimposes the two-dimensional translational movement of the coronary artery on the angiography plane caused by the respiratory movement of the human body. Then, in order to obtain a two-dimensional angiogram closer to the real situation and use it for three-dimensional reconstruction of blood vessels, it is necessary to separate the two kinds of motion information to analyze the heart motion and respiratory motion of the human body separately.

Many foreign literatures have to set marker points in advance when extracting human breathing motion, and then track them sequentially. Among them, it is more commonly used in X-ray angiography to directly manually track the non-cardiac structural feature points in the angiography. According to the characteristics of breathing movement, when a person breathes, he will drive other organs in the body to move together. It is generally believed that these organs will translate in three-dimensional space with the movement of the lungs, and their movements are all synchronized. Therefore, it can be assumed that the movement of the heart caused by respiratory movement is consistent with the movement of its adjacent organs on the plane of the contrast image, and some feature points on other tissues other than the heart can be found in the contrast image as marker points. These marker points are tracked throughout the sequence to obtain the motion of these marker points, and then the motion of these marker points is approximated to the breathing motion on this two-dimensional projection surface. Another method also uses these structural feature points that do not move with the heart, the difference is that it records the movement of these marker points while imaging. Therefore, it is required to select and mark each feature point before imaging. Obviously, both of these solutions are flawed. The former is mainly due to its poor applicability, because we cannot guarantee that there are marker points (feature points on other tissues other than the heart) that meet this condition in every frame of contrast images, and finding such points also requires Experience (a good understanding of human anatomy is required). Therefore, when the above feature points do not exist in the contrast image, it is difficult to extract the respiratory movement. The realization of the latter requires a lot of experimental control, which is not suitable for general clinical application.

At present, there is also a method to obtain respiratory motion parameters under the condition of double-arm X-ray contrast. The corresponding coronary vessels are three-dimensionally reconstructed to obtain the three-dimensional space distribution of the vessels at that moment. Then, after matching and reconstructing all contrast image pairs in a respiratory cycle, a set of three-dimensional structure sequences is obtained, and the spatial displacement vector between them is respiratory motion. Relatively speaking, this method can obtain more reliable respiratory motion estimation results, but it cannot be widely used in medical practice due to the constraints of dual-arm X-ray angiography conditions.

Contents of the invention

The purpose of the present invention is to propose a method for extracting respiratory motion parameters from a single-arm X-ray contrast image sequence, by selecting a group of feature points on the coronary vessels and tracking them in the sequence to obtain their motion curves over time, Then separate heart and respiration motion information by means of Fourier series expansion and frequency domain filtering. It has good clinical applicability.

A method for extracting human respiratory motion parameters based on frequency domain filtering, comprising the following steps:

(1) Obtain a single-arm X-ray contrast image sequence of coronary vessels, and determine the cardiac motion cycle N1;

(2) Select coronary vessel structural feature points;

(3) Extracting the respiratory motion curve, the specific method is:

(3.1) Automatically track the feature points of the coronary vessel structure in the image sequence of the contrast image, and obtain the feature point tracking sequence s(n), where n is the length of the feature point tracking sequence;

ns＝n-n％N1，其中，％为取余符号；(3.2) Select a segment in the feature point tracking sequence s(n) as the target sequence

ns=nn%N1, wherein, % is the remainder symbol;

进行离散傅立叶变换，得到目标频域响应S(k)，k＝0，...，ns-1；(3.3) For the target sequence

Carry out discrete Fourier transform, obtain target frequency domain response S (k), k=0,..., ns-1;

(3.4) Let the frequency domain response of respiratory motion

$R\left(k\right)=\left\{\begin{array}{cc}S\left(k\right),& (k\≠\frac{\mathrm{ns}}{N1}l,l=1,...,N1-1)\\ (S\left(k\right)+S(k+1))/2,& (k=\frac{\mathrm{ns}}{N1}l,l=1,...,N1-1)\end{array}\right.,$ Inverse discrete Fourier transform is performed on R(k) to obtain a respiratory motion curve r(ns), that is, respiratory motion parameters can be extracted.

Through the respiratory motion extraction method described above, the final obtained is a two-dimensional respiratory motion curve under a certain contrast angle. However, in order to describe the respiratory movement more intuitively and effectively, we can reconstruct the two-dimensional movement obtained under two different angiographic viewing angles according to the three-dimensional reconstruction principle of the midpoint of the imaging system to obtain the three-dimensional respiratory movement.

Specific steps are as follows:

Step1: Determine two contrast image sequences under different contrast angles, which are recorded as the left contrast map image sequence and the right contrast map image sequence, and then determine any corresponding reference point in the left and right contrast map image sequences, respectively recorded as p _l (x, y, t) and p _r (x, y, t), where (x, y) is the coordinates of any reference point in the image sequence, and t is the time, that is, the frame of the contrast image sequence serial number, t is an integer between 0 and 70, respectively select the coordinates (x _l , y _l ) and (x _r , y r ) at the time t _l in t _and t _r as the reference point p _l (x, y , t) and the initialization values of p _r (x, y, t), that is, p _l (x _l , y _l , t _l ) and p _r (x _r , y _r , t _r ), where t _l , t _r Corresponding to the same moment of the cardiac cycle, the end diastole is generally selected;

Step2: According to the above respiratory motion parameter extraction method, extract the respiratory motion curves of the left and right contrast image sequences, which are respectively recorded as curve _l (x, y, t) and curve _r (x, y, t), and then the two curves are respectively Corresponding to select the extreme point of the end-inspiration or the end-expiration in the breathing movement cycle as the breathing reference point, that is, select the extreme point of the end-inspiration or the extreme point of the end-expiration on both curves, record is curve _l (x _cl , y _cl , t _cl ) and curve _r (x _cr , y _cr , t _cr ), where t _cl and t _cr are the corresponding end-inspiration moments or expiratory At the final moment, (x _cl , y _cr ), (x _cr , y _cr ) are the coordinates of the corresponding time t _cl and t _cr on the curves curve _l (x, y, t) and curve _r (x, y, t) respectively ;

Step3: Perform respiratory motion compensation on the initialized point pairs p _l (x _l , y _l , t _l ) and p _r (x _r , y _r , t _r ) in the image sequence of the left and right contrast images, that is, t _l , t The breathing movement at time _r is compensated to the corresponding breathing reference time _tcl and _tcr , respectively:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; tl</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; tl</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; cl</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; cl</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; cl</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; tr</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; tr</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\end{array}\right.$

In the formula, curve _l (x _il , y _tl , t _l ), curve _r (x _tr , y _tr , t _r ) respectively represent t _l , t _r time curve curve _l (x, y, t) and curve _r ( Points on x, y, t), p′ _l (x′ _l , y′ _l , t′ _l ) and p′ _r (x′ _r , y′ _r , t _r ) are reference points after compensation. Then perform three-dimensional reconstruction on the two compensated reference points to obtain a three-dimensional point P(x _clr , y _clr , z _clr , t _clr ), where t _clr represents the end-spirit or expiratory phase corresponding to t _cl (or t _cr ). end of life;

Step4: It is reasonable to assume that the heart itself is at rest, and that only respiration causes the movement of the left coronary vascular tree. Then, the p′ _l (x′ _l , y′ _l , t _l ) and p′ _r (x′ _r , y′ _r , t _r ) obtained in Step3 can be further compensated to the respiratory Other moments in the motion cycle:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; cl</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; cl</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; cl</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\end{array}\right.$

Similarly, for the point pairs p′ _l (x′ _l+i , y′ _l+i , t _l+i ) and p′ _r (x′ _r+i , y′ _{r+i )} at other moments of the breathing cycle , t _r+i ) for 3D reconstruction to obtain a 3D point P(x _clr+i , y _clr+i , z _clr+i , t _clr+i ), where i represents relative to the breathing reference time t _l and t _r before (take a negative integer) or the number of frames after (take a positive integer);

Step5: Combining the results obtained in Step3 and Step4, the three-dimensional breathing motion can be obtained.

The technical effect of the present invention is embodied in: considering that under the condition of single-arm X-ray angiography, not all suitable feature points (like the intersection of ribs, etc.) can be found in all radiography images, so it is proposed to select the feature points of vascular structure and The new way of combining Fourier frequency domain filtering to extract respiratory motion has wider applicability and flexibility than pure manual tracking, and can be applied to almost all contrast sequences or two or more cardiac cycles). At the same time, this method has higher security and operability than the method of directly setting marker points in tissues near the heart and then tracking them by relevant imaging means. This is because the markers added to tissues in the body are generally invasive and will cause more or less damage to the human body itself, and the whole process of marker addition, imaging, exclusion, and respiratory motion extraction is complicated. Bring inevitable trouble and error in actual operation. In addition, the feature points selected by the method of the present invention relate to blood vessels at all levels of the left coronary artery, and comprehensively consider the movement information of the left coronary artery, thereby having better reliability and accuracy.

Description of drawings

Fig. 1 is a block flow diagram of the present invention;

Figure 2(a) is the selected contrast image and its marked points in the respiratory motion extraction method, and the corresponding projection angle is (-26.8°, -27.2°);

Figure 2(b) is the selected contrast image and its marked points in the respiratory motion extraction method, and the corresponding projection angle is (50.8°, 30.2°);

Figure 3(a) is the original curve obtained by tracking the marker point 1 in Figure 2(a) in the contrast image sequence, where the solid line is the change of the horizontal coordinate (X-axis coordinate), and the dotted line is the vertical coordinate (Y-axis coordinate) change; Fig. 3(b) is the original curve obtained by tracking marker point 1 in Fig. Axis coordinates) change;

Fig. 3 (c) is the cardiac motion curve obtained by decomposing the original curve in Fig. 3 (a), wherein the solid line is the change of the horizontal coordinate (X-axis coordinate), and the dotted line is the change of the vertical coordinate (Y-axis coordinate);

Fig. 3 (d) is the cardiac motion curve obtained by decomposing the original curve in Fig. 3 (b), wherein the solid line is the change of the horizontal coordinate (X-axis coordinate), and the dotted line is the change of the vertical coordinate (Y-axis coordinate);

Fig. 3 (e) is the respiratory motion curve obtained by decomposing the original curve in Fig. 3 (a), wherein the solid line is the change of the horizontal coordinate (X-axis coordinate), and the dotted line is the change of the vertical coordinate (Y-axis coordinate);

Fig. 3 (f) is the respiratory motion curve obtained by decomposing the original curve in Fig. 3 (b), wherein the solid line is the change of the horizontal coordinate (X-axis coordinate), and the dotted line is the change of the vertical coordinate (Y-axis coordinate);

Figure 3(g) is the result of 6 curve fittings on the respiratory movement curve in Figure 3(e), where the solid line is the change of the horizontal coordinate (X-axis coordinate), and the dotted line is the change of the vertical coordinate (Y-axis coordinate) ;

Figure 3(h) is the result of 6 curve fittings on the respiratory movement curve in Figure 3(f), where the solid line is the change of the horizontal coordinate (X-axis coordinate), and the dotted line is the change of the vertical coordinate (Y-axis coordinate) ;

Figure 4(a) is the respiratory motion curve of all marked points under the projection angle of (-26.8°, -27.2°), where the solid line is the change of the horizontal coordinate (X-axis coordinate), and the dotted line is the vertical coordinate (Y-axis coordinate )The change;

Figure 4(b) is the breathing motion curve of all marked points under the projection angle of (50.8°, 30.2°), where the solid line is the change of the horizontal coordinate (X-axis coordinate), and the dotted line is the change of the vertical coordinate (Y-axis coordinate). Variety;

Figure 4(c) is the result of fitting the motion curves of all points in Figure 4(a), where the solid line is the change in the horizontal coordinate (X-axis coordinate), and the dotted line is the change in the vertical coordinate (Y-axis coordinate);

Figure 4(d) is the result of fitting the motion curves of all points in Figure 4(b), wherein the solid line is the change in the horizontal coordinate (X-axis coordinate), and the dotted line is the change in the vertical coordinate (Y-axis coordinate);

Fig. 5 is the three-dimensional results obtained after reconstructing the two-dimensional respiratory motion under contrast angles of (-26.8°, -27.2°) and (50.8°, 30.2°).

Detailed ways

The present invention will be further described below in conjunction with accompanying drawing:

The present invention proposes a method for extracting human respiratory motion parameters based on frequency domain filtering, as shown in Figure 1, comprising the following steps:

(1) Obtain a single-arm X-ray contrast image sequence of coronary vessels, and determine the cardiac motion cycle N1;

(2) Select the feature points of the vessel structure.

According to the guidance of physiological and anatomical knowledge, the feature points we mark need to be able to comprehensively reflect the movement information of the whole blood vessel. Therefore, the selected shape-specific points (ie structural feature points) generally include the starting point and ending point of each blood vessel segment. points, and each inflection point (the point with the greatest curvature) between the vessel segments. And in the sequence of contrast images under two different projection angles, all the feature points are numbered, and those corresponding to each other have the same name. As shown in Figure 2, there are 15 numbered shape-specific points in a pair of contrast images whose projection angles are (-26.8°, -27.2°) and (50.8°, 30.2°) respectively, and their relationship is One-to-one correspondence according to the number naming.

(3) Fourier series expansion method for separating heart and respiratory motion

Both the heart and the breathing movement of the human body are periodic movements, but the frequency of breathing movement is much smaller than that of heart movement. Generally speaking, the frequency of normal heart movement is 60 to 100 times per minute, and its period is 0.6 -1.0s, while the period of breathing movement is much longer, generally 3-6s, and it may be longer when it is quiet. On the other hand, the heart movement is relatively violent, while the breathing movement has a small amplitude, that is, the generated displacement is small, and it is a relatively smooth process.

According to these characteristics of heart motion and respiratory motion in contrast images, the present invention separates heart motion and respiratory motion through the method of Fourier series expansion combined with frequency domain filtering.

Let's first introduce the discrete Fourier series expansion.

1) Discrete Fourier series expansion

Based on the principle of Fourier series expansion, continuous time periodic signals can be expressed by Fourier series, and correspondingly, periodic sequences can also be expressed by discrete Fourier series. If the period of the periodic sequence x _p (n) is N, then

x _p (n)=x _p (n+rN) (r is any integer) (1)

x _p (n) can be discrete Fourier series transform through formulas (2) and (3)

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; nk</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; nk</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

是周期序列的基频分量，就是k次谐波分量，X_p(k)为各次谐波的系数，也可认为是x_p(n)的频域响应；全部谐波分量只有N个是独立的，因为The formula (3) is explained as follows: in the formula

is the fundamental frequency component of the periodic sequence, It is the kth harmonic component, and X _p (k) is the coefficient of each harmonic, which can also be considered as the frequency domain response of x _p (n); only N of all harmonic components are independent, because

${\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; nk</span>}}<span\; class="notranslate">\; ,</span>$

Therefore, the number of items of the series sum is from k=0 to N-1, and there are N independent harmonic components in total. The formula (2) is exactly the summation formula of the coefficient X _p (k) determined by x _p (n).

2) Separation algorithm

Assume that the motion curve of the x-axis coordinates of a certain point P(x, y) on the coronary artery in the contrast image sequence is x(n) (n is the number of contrast frames), and the motion curve of the y-axis coordinates is y(n ), let s(n)=(x(n), y(n)), s(n) can be decomposed into the following formula:

s(n)=c(n)+r(n)+t(n)

Where c(n)=(x _c (n), y _c (n)) represents the movement of the blood vessel point caused by the movement of the heart, and r(n)=(x _r (n), y _r (n)) represents the respiration The motion caused by motion, t(n)=(x _t (n), y _t (n)) represents some other motions (including the movement of the human body during the radiography process, and the movement of the radiography equipment, etc.). For the convenience of representation, s(n) is used to represent the coordinate change curve of the extracted blood vessel point along the x-axis and y-axis, and c(n) represents the coordinate change curve of the blood vessel point along the x-axis and y-axis caused by heart movement. r(n) represents the coordinate change curve of the blood vessel point along the x-axis and y-axis caused by respiratory movement. Therefore, the operation on s(n) is the operation on x(n) and y(n) respectively, and the operation on c(n ) is the operation on x _c (n) and y _c (n) respectively, and the operation on r(n) is the operation on x _r (n) and y _r (n) respectively. Since t(n) is not measurable, it is ignored here and not considered, then we have

s(n)≈c(n)+r(n)

Assuming that the cycle of heart motion is N1 and the cycle of respiratory motion is N2, then c(n) and r(n) can be changed according to formula (3):

$\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; nk</span>}}$

$\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="N"\; filenames="H2009102735285E00013.png"\; state="\{\{state\}\}">N</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; nk</span>}}$

是心脏运动的谐波分量，是呼吸运动的谐波分量，C(k)、R(k)分别表示c(n)和r(n)的各次谐波系数。要使c(n)和r(n)完全分离，则其谐波分量不能发生重合(零频分量可以不予考虑，因为虽然呼吸运动的频率和心脏运动的频域分量在零频上面(直流分量)都存在，这里也没有办法能够将它们完全分开，但是由于零频分量变化到时域中是一个常数，因此它不会改变周期序列曲线的形状，也不会影响我们对心脏和呼吸运动的分析)，即in,

is the harmonic component of cardiac motion, is the harmonic component of respiratory motion, and C(k) and R(k) represent the harmonic coefficients of c(n) and r(n) respectively. To completely separate c(n) and r(n), their harmonic components cannot overlap (the zero frequency component can be ignored, because although the frequency of respiratory motion and the frequency domain component of cardiac motion are above zero frequency (DC components) exist, and there is no way to completely separate them here, but since the change of the zero-frequency component to the time domain is a constant, it will not change the shape of the periodic sequence curve, nor will it affect our understanding of heart and respiratory motion analysis), that is

$<span\; class="notranslate">\; \&ForAll;</span>\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>$

(8)

$\&Exists;\left(\frac{2\mathrm{\&pi;}}{N1}\right)\mathrm{no}1k1\&NotEqual;\left(\frac{2\mathrm{\&pi;}}{N2}\right)\mathrm{no}2\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="H2009102735285E00013.png"\; state="\{\{state\}\}">k</figure-callout>}2,$ (n1, n2 are time-domain independent variables, k1, k2 are frequency-domain independent variables)

To satisfy formula (8), N1 and N2 must be mutually prime. At the same time, to separate c(n) and r(n), it must also satisfy that the sequence length of s(n) is greater than or equal to a cycle of s(n), that is, greater than N1*N2.

However, the above requirements are difficult to meet. Even if N1 and N2 are mutually prime, the second condition cannot be satisfied. Because under normal circumstances, the contrast agent does not stay in the human body for too long, and a sequence of contrast images will only last for about 6s, and will not exceed 10s. Assuming that the frame rate is 80ms/frame (actually it may be smaller), then N1≈ 10, N2>30, N1*N2>300>10/0.08, so a sequence of one period cannot be obtained at all.

Although it is impossible to ideally separate the heart and respiratory motion, according to their respective motion characteristics, an approximate separation can be performed by means of Fourier series transformation and frequency domain filtering.

The separation step is based on the following assumptions:

上存在分量。这一点已经通过式(3)证明；(1) Heart movement is only at the frequency

There is weight on it. This has been proved by formula (3);

处平滑。由于呼吸运动具有平滑性，且

为呼吸运动基频分量的可能性较小，完全有理由这样假设。(2) The frequency domain component of respiratory motion is at the frequency

smooth. Due to the smoothness of breathing motion, and

It is less likely to be the fundamental frequency component of respiratory motion, and there is every reason to assume this.

The specific algorithm is as follows:

Step1: Determine the heart motion cycle N1 according to the sequence of contrast images observed by human eyes. In general, N1≈0.8/f, where N1 represents the number of frames of contrast images in one cardiac cycle, and 0.8 represents the time of one cardiac cycle, and the unit is seconds, f represents the frame rate, that is, the number of imaging images taken per second;

Step2: Track the feature points of the vascular structure selected in step (1) in the entire contrast image sequence to obtain the point tracking sequence s(n);

ns为N1的整数倍。若原始序列长度为n，则选取序列长度为ns＝n-n％N1，其中，％为取余符号；Step3: Select a sequence of length ns in the point tracking sequence s(n)

ns is an integer multiple of N1. If the original sequence length is n, then the selected sequence length is ns=nn%N1, where % is a remainder symbol;

Step4: will Decompose it into motion x(n) in the x direction and motion y(n) in the y direction, and then perform discrete Fourier transform on them respectively to obtain the harmonic coefficients X(k) and Y(k), k=0 ,...,ns-1;

Step5: Make the frequency domain response of respiratory movement

$R_x\left(k\right)=\left\{\begin{array}{cc}x\left(k\right),& (k\&NotEqual;\frac{\mathrm{ns}}{N1}l,l=1,...,N1-1)\\ (x\left(k\right)+x(k+1))/2,& (k=\frac{\mathrm{ns}}{N1}l,l=1,...,N1-1)\end{array}\right.,$ Inverse discrete Fourier transform is performed on R _x (k) to obtain respiratory motion r _x (n), and similarly, _ry (n) can be obtained.

Through the analysis of the contrast image sequence, it can be determined that the cardiac motion cycle N1 is 10 frames, and Fig. 3 is the result of separating respiratory motion and cardiac motion for the motion of marker 1 in Fig. 2 .

It can be seen from Figure 3 that the original motion curve of the marker points is greatly affected by respiratory motion and is messy, while the separated cardiac motion curve shows good periodicity, but there are still some glitches in the respiratory motion curve, which is also Reasons for insufficient separation. In order to remove the residual cardiac motion component in the respiratory motion, curve fitting is performed on the extracted original respiratory motion curve to remove the burrs on the respiratory motion curve, as shown in Figure 3(g) and 3(h). The combined breathing motion curves showed obvious periodicity.

Comparing the respiratory motion curves of all marked points together, it can be found that the respiratory motion curves of all points in the same imaging plane are not much different (as shown in Figure 4(a) and (b)), so we put all the marked points The respiratory motion of the coronary arteries is fitted into a curve as the respiratory motion curve of the coronary vessels in the angiographic plane (as shown in Figure 4(c) and (d)).

(3) Three-dimensional reconstruction of respiratory movement

Through the respiratory motion extraction method described above, the final obtained is a two-dimensional respiratory motion curve under a certain contrast angle, as shown in Fig. 4(c) and Fig. 4(d). However, it can be seen from the figure that this two-dimensional representation method obviously cannot express respiratory information clearly. Then, in order to describe the respiratory movement more intuitively and effectively, we can use the three-dimensional reconstruction principle of the midpoint of the imaging system to compare two different The two-dimensional motion obtained under the contrast angle is reconstructed to obtain the three-dimensional breathing motion. Specific steps are as follows:

Step1: Determine two contrast image sequences under different contrast angles, which are recorded as the left contrast map image sequence and the right contrast map image sequence, and then determine any corresponding reference point in the left and right contrast map image sequences, respectively recorded as p _l (x, y, t) and p _r (x, y, t), where (x, y) is the coordinates of any reference point in the image sequence, and t is the time, that is, the frame of the contrast image sequence serial number, t is an integer between 0 and 70, respectively select the coordinates (x _l , y _l ) and (x _r , y r ) at the time t _l in t _and t _r as the reference point p _l (x, y , t) and the initialization values of p _r (x, y, t), that is, p _l (x _l , y _l , t _l ) and p _r (x _r , y _r , t _r ), where t _l , t _r Corresponding to the same moment of the cardiac cycle, the end diastole is generally selected;

Step2: According to the above respiratory motion parameter extraction method, extract the respiratory motion curves of the left and right contrast image sequences, which are respectively recorded as curve _l (x, y, t) and curve _r (x, y, t), and then the two curves are respectively Corresponding to select the extreme point of the end-inspiration or the end-expiration in the breathing movement cycle as the breathing reference point, that is, select the extreme point of the end-inspiration or the extreme point of the end-expiration on both curves, record is curve _l (x _cl , y _cl , t _cl ) and curve _r (x _cr , y _cr , t _cr ), where t _cl and t _cr are the corresponding end-inspiration moments or expiratory At the final moment, (x _cl , y _cl ), (x _cr , y _cr ) are the coordinates of the corresponding time t _cl and t _cr on the curves curve _l (x, y, t) and curve _r (x, y, t) respectively ;

Step3: Perform respiratory motion compensation on the initialized point pairs p _l (x _l , y _l , t _l ) and p _r (x _r , y _r , t _r ) in the image sequence of the left and right contrast images, that is, t _l , t The breathing movement at time _r is compensated to the corresponding breathing reference time _tcl and _tcr , respectively:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; tl</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; tl</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; cl</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; cl</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; cl</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; tr</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; tr</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\end{array}\right.$

In the formula, curve _l (x _il , y _tl , t _l ), curve _r (x _tr , y _tr , t _r ) respectively represent t _l , t _r time curve curve _l (x, y, t) and curve _r ( Points on x, y, t), p′ _l (x′ _l , y′ _l , t _l ) and p′ _r (x′ _r , y′ _r , t _r ) are reference points after compensation. Then perform three-dimensional reconstruction on the two compensated reference points to obtain a three-dimensional point P(x _clr , y _clr , z _clr , t _clr ), where t _clr represents the end-spirit or expiratory phase corresponding to t _cl (or t _cr ). end of life;

Step4: It is reasonable to assume that the heart itself is at rest, and that only respiration causes the movement of the left coronary vascular tree. Then, the p′ _l (x′ _l , y′ _l , t _l ) and p′ _r (x′ _r , y′ _r , t _r ) obtained in Step3 can be further compensated to the respiratory Other moments in the motion cycle:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; cl</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; cl</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; cl</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; curve</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\end{array}\right.$

Similarly, for the point pairs p′ _l (x′ _l+i , y′ _l+i , t _l+i ) and p′ _r (x′ _r+i , y′ _{r+i )} at other moments of the breathing cycle , t _r+i ) for 3D reconstruction to obtain a 3D point P(x _clr+i , y _clr+i , z _clr+i , t _clr+i ), where i represents relative to the breathing reference time t _l and t _r before (take a negative integer) or the number of frames after (take a positive integer);

Step5: Combining the results obtained in Step3 and Step4, the three-dimensional breathing motion can be obtained.

By analyzing the sequence of contrast images under contrast angles of (-26.8°, -27.2°) (left) and (50.8°, 30.2°) (right), the 22nd and 43rd frames, which are also in the end diastole, were selected respectively frame as the reference frame, and then select the starting point of the blood vessel as the reference point, and initialize it to (35, 62) and (303, 94), then analyze the respiratory motion curves extracted from the left and right imaging sequences, and determine the respiratory reference time respectively For frame 38 and frame 26. Then, according to the parameters selected above, the three-dimensional breathing motion can be obtained, as shown in FIG. 5 .

It can be seen from the figure that the overall trend of the three-dimensional breathing movement is to do translational movement back and forth, but there are still kinks in the local movement, which is not a simple linear movement. According to the analysis, the occurrence of the angle bending phenomenon should be caused by the incomplete separation of the effect of cardiac motion from respiratory motion. However, since the motion offset caused by the knuckle has little effect on the whole, under realistic conditions, the three-dimensional breathing motion can be reasonably assumed to be segmented linear motion.

Claims (2)

1. A human body respiratory motion parameter extraction method based on frequency domain filtering comprises the following steps:

(1) acquiring a single-arm X-ray radiography image sequence of coronary vessels, and determining a heart motion period N1;

(2) selecting coronary vessel structure characteristic points;

(3) extracting a respiratory motion curve in a specific mode:

(3.1) automatically tracking the coronary vessel structure characteristic points in the image sequence of the contrast map to obtain a characteristic point tracking sequence s (n), wherein n is characteristic point trackingThe length of the sequence; (3.2) selecting one section in the characteristic point tracking sequence s (n) as a target sequence

ns-N% N1, where% is the remainder symbol;

(3.3) to the target sequence

Performing discrete Fourier transform to obtain a target frequency domain response S (k), wherein k is 0.

(3.4) frequency-Domain response to respiratory motion

<math><mrow><mi>R</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mi>S</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>,</mo></mtd><mtd><mrow><mo>(</mo><mi>k</mi><mo>&NotEqual;</mo><mfrac><mi>ns</mi><mrow><mi>N</mi><mn>1</mn></mrow></mfrac><mi>l</mi><mo>,</mo><mi>l</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><mi>N</mi><mn>1</mn><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><mo>(</mo><mi>S</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>+</mo><mi>S</mi><mrow><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>)</mo></mrow><mo>/</mo><mn>2</mn><mo>,</mo></mtd><mtd><mrow><mo>(</mo><mi>k</mi><mo>=</mo><mfrac><mi>ns</mi><mrow><mi>N</mi><mn>1</mn></mrow></mfrac><mi>l</mi><mo>,</mo><mi>l</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><mi>N</mi><mn>1</mn><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mtd></mtr></mtable></mfenced><mo>,</mo></mrow></math>

And performing inverse discrete Fourier transform on the R (k) to obtain a respiratory motion curve r (ns), namely, extracting respiratory motion parameters.

2. A method for three-dimensional reconstruction of the respiratory motion curve of claim 1 to obtain three-dimensional respiratory motion, comprising the steps of:

(I) determining two contrast image sequences under different contrast angles, recording as a left contrast image sequence and a right contrast image sequence, determining any corresponding reference point in the left contrast image sequence and the right contrast image sequence, respectively recording as p_l(x, y, t) and p_r(x, y, t), where (x, y) is the coordinate of the reference point in the image sequence, t is time, i.e. the frame number of the contrast image sequence, and t is an integer between 0 and 70, the time t in t is selected respectively_l，t_rCoordinates of lower (x)_l，y_l)、(x_r，y_r) As reference point p_l(x, y, t) and p_rInitialization value of (x, y, t), i.e. p_l(x_l，y_l，t_l) And p_r(x_r，y_r，t_r) Wherein t is_l，t_rThe same time corresponding to the cardiac cycle in the left and right angiogram sequences;

(II) extracting respiratory motion curves of left and right contrast image sequences according to the respiratory motion parameter extraction method of claim 1, and respectively recording the curves as curve_l(x, y, t) and cure_r(x, y, t), then correspondingly selecting an extreme point of an inspiratory end or an expiratory end in the respiratory motion period as a respiratory reference point on the two curves respectively, namely selecting an extreme point of the inspiratory end or selecting an extreme point of the expiratory end on the two curves respectively, and marking as curve_l(x_cl，y_cl，t_cl) And curve_r(x_cr，y_cr，t_cr) Wherein t is_cl，t_crThe time of the end of inspiration or expiration corresponding to the left and right contrast images in the sequence, (x)_cl，y_cl)、(x_cr，y_cr) Are respectively curved_l(x, y, t) and cure_rAt (x, y, t) corresponding to time t_cl、t_crThe coordinates of (a);

(III) for initialized point pairs p in left and right contrast image sequences_l(x_l，y_l，t_l) And p_r(x_r，y_r，t_r) Performing respiratory motion compensation, i.e. t_l，t_rThe respiratory motion at the moment is respectively compensated to the corresponding respiratory reference moment t_cl，t_crThe following steps:

<math><mfenced open='{' close=''><mtable><mtr><mtd><msubsup><mi>p</mi><mi>l</mi><mo>&prime;</mo></msubsup><mrow><mo>(</mo><msubsup><mi>x</mi><mi>l</mi><mo>&prime;</mo></msubsup><mo>,</mo><msubsup><mi>y</mi><mi>l</mi><mo>&prime;</mo></msubsup><mo>,</mo><msub><mi>t</mi><mi>l</mi></msub><mo>)</mo></mrow><mo>=</mo><msub><mi>p</mi><mi>l</mi></msub><mrow><mo>(</mo><msub><mi>x</mi><mi>l</mi></msub><mo>,</mo><msub><mi>y</mi><mi>l</mi></msub><mo>,</mo><msub><mi>t</mi><mi>l</mi></msub><mo>)</mo></mrow><mo>-</mo><mrow><mo>(</mo><msub><mi>curve</mi><mi>l</mi></msub><mrow><mo>(</mo><msub><mi>x</mi><mi>tl</mi></msub><mo>,</mo><msub><mi>y</mi><mi>tl</mi></msub><mo>,</mo><msub><mi>t</mi><mi>l</mi></msub><mo>)</mo></mrow><mo>-</mo><msub><mi>curve</mi><mi>l</mi></msub><mrow><mo>(</mo><msub><mi>x</mi><mi>cl</mi></msub><mo>,</mo><msub><mi>y</mi><mi>cl</mi></msub><mo>,</mo><msub><mi>t</mi><mi>cl</mi></msub><mo>)</mo></mrow><mo>)</mo></mrow></mtd></mtr><mtr><mtd><msubsup><mi>p</mi><mi>r</mi><mo>&prime;</mo></msubsup><mrow><mo>(</mo><msubsup><mi>x</mi><mi>r</mi><mo>&prime;</mo></msubsup><mo>,</mo><msubsup><mi>y</mi><mi>r</mi><mo>&prime;</mo></msubsup><mo>,</mo><msub><mi>t</mi><mi>r</mi></msub><mo>)</mo></mrow><mo>=</mo><msub><mi>p</mi><mi>r</mi></msub><mrow><mo>(</mo><msub><mi>x</mi><mi>r</mi></msub><mo>,</mo><msub><mi>y</mi><mi>r</mi></msub><mo>,</mo><msub><mi>t</mi><mi>r</mi></msub><mo>)</mo></mrow><mo>-</mo><mrow><mo>(</mo><msub><mi>curve</mi><mi>r</mi></msub><mrow><mo>(</mo><msub><mi>x</mi><mi>tr</mi></msub><mo>,</mo><msub><mi>y</mi><mi>tr</mi></msub><mo>,</mo><msub><mi>t</mi><mi>r</mi></msub><mo>)</mo></mrow><mo>-</mo><msub><mi>curve</mi><mi>r</mi></msub><mrow><mo>(</mo><msub><mi>x</mi><mi>cr</mi></msub><mo>,</mo><msub><mi>y</mi><mi>cr</mi></msub><mo>,</mo><msub><mi>t</mi><mi>cr</mi></msub><mo>)</mo></mrow><mo>)</mo></mrow></mtd></mtr></mtable></mfenced></math>

in the formula, curve_l(x_tl，y_tl，t_l)、curve_r(x_tr，y_tr，t_r) Respectively represent t_l，t_rCurve at time_l(x, y, t) and cure_rPoint on (x, y, t), p'_l(x′_l，y′_l，t_l) And p'_r(x′_r，y′_r，t_r) Is a compensated reference point. Then, three-dimensional reconstruction is carried out on the two compensated reference points to obtain a three-dimensional point P (x)_clr，y_clr，z_clr，t_clr) Wherein t is_clrRepresents the sum of t_clOr t_crCorresponding to a consistent end of inspiration or end of expiration;

(IV) reacting p 'obtained in step (III)'_l(x′_l，y′_l，t_l) And p'_r(x′_r，y′_r，t_r) Further compensation to other moments of the respiratory motion cycle without the influence of cardiac motion:

<math><mfenced open='{' close=''><mtable><mtr><mtd><msubsup><mi>p</mi><mi>l</mi><mo>&prime;</mo></msubsup><mrow><mo>(</mo><msubsup><mi>x</mi><mrow><mi>l</mi><mo>+</mo><mi>i</mi></mrow><mo>&prime;</mo></msubsup><mo>,</mo><msubsup><mi>y</mi><mrow><mi>l</mi><mo>+</mo><mi>i</mi></mrow><mo>&prime;</mo></msubsup><mo>,</mo><msub><mi>t</mi><mrow><mi>l</mi><mo>+</mo><mi>i</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><msubsup><mi>p</mi><mi>l</mi><mo>&prime;</mo></msubsup><mrow><mo>(</mo><msubsup><mi>x</mi><mi>l</mi><mo>&prime;</mo></msubsup><mo>,</mo><msubsup><mi>y</mi><mi>l</mi><mo>&prime;</mo></msubsup><mo>,</mo><msub><mi>t</mi><mi>l</mi></msub><mo>)</mo></mrow><mo>+</mo><mrow><mo>(</mo><msub><mi>curve</mi><mi>l</mi></msub><mrow><mo>(</mo><msub><mi>x</mi><mrow><mi>l</mi><mo>+</mo><mi>i</mi></mrow></msub><mo>,</mo><msub><mi>y</mi><mrow><mi>l</mi><mo>+</mo><mi>i</mi></mrow></msub><mo>,</mo><msub><mi>t</mi><mrow><mi>l</mi><mo>+</mo><mi>i</mi></mrow></msub><mo>)</mo></mrow><mo>-</mo><msub><mi>curve</mi><mi>l</mi></msub><mrow><mo>(</mo><msub><mi>x</mi><mi>cl</mi></msub><mo>,</mo><msub><mi>y</mi><mi>cl</mi></msub><mo>,</mo><msub><mi>t</mi><mi>cl</mi></msub><mo>)</mo></mrow><mo>)</mo></mrow></mtd></mtr><mtr><mtd><msubsup><mi>p</mi><mi>r</mi><mo>&prime;</mo></msubsup><mrow><mo>(</mo><msubsup><mi>x</mi><mrow><mi>r</mi><mo>+</mo><mi>i</mi></mrow><mo>&prime;</mo></msubsup><mo>,</mo><msubsup><mi>y</mi><mrow><mi>r</mi><mo>+</mo><mi>i</mi></mrow><mo>&prime;</mo></msubsup><mo>,</mo><msub><mi>t</mi><mrow><mi>r</mi><mo>+</mo><mi>i</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><msubsup><mi>p</mi><mi>r</mi><mo>&prime;</mo></msubsup><mrow><mo>(</mo><msubsup><mi>x</mi><mi>r</mi><mo>&prime;</mo></msubsup><mo>,</mo><msubsup><mi>y</mi><mi>r</mi><mo>&prime;</mo></msubsup><mo>,</mo><msub><mi>t</mi><mi>r</mi></msub><mo>)</mo></mrow><mo>+</mo><mrow><mo>(</mo><msub><mi>curve</mi><mi>r</mi></msub><mrow><mo>(</mo><msub><mi>x</mi><mrow><mi>r</mi><mo>+</mo><mi>i</mi></mrow></msub><mo>,</mo><msub><mi>y</mi><mrow><mi>r</mi><mo>+</mo><mi>i</mi></mrow></msub><mo>,</mo><msub><mi>t</mi><mrow><mi>r</mi><mo>+</mo><mi>i</mi></mrow></msub><mo>)</mo></mrow><mo>-</mo><msub><mi>curve</mi><mi>r</mi></msub><mrow><mo>(</mo><msub><mi>x</mi><mi>cr</mi></msub><mo>,</mo><msub><mi>y</mi><mi>cr</mi></msub><mo>,</mo><msub><mi>t</mi><mi>cr</mi></msub><mo>)</mo></mrow><mo>)</mo></mrow></mtd></mtr></mtable></mfenced></math>

similarly, point pairs p 'for other times of the respiratory motion cycle'_l(x′_l+i，y′_l+i，t_l+i) And p'_r(x′_r+i，y′_r+i，t_r+i) Performing three-dimensional reconstruction to obtain a three-dimensional point P (x)_clr+i，y_clr+i，z_clr+i，t_clr+i) Where i denotes at the time t_lAnd t_rThe number of previous or subsequent frames, i is a negative integer when the number of previous frames is the number of previous frames, and i is a positive integer when the number of subsequent frames is the number of subsequent frames;

and (V) integrating the results obtained in the step (III) and the step (IV) to obtain the three-dimensional respiratory motion.

Images