CN102509353B - Block three-dimensional reconstruction method based on two-dimensional x-ray image sequential filtering back projection - Google Patents

Abstract

The invention discloses a partitioning three-dimensional reconstruction method based on two-dimensional x-ray image sequential filtering back projection, which comprises the following steps: firstly, cubic blocks are built according to the initial block number; secondly, a block reconstruction result is obtained through partial reconstruction of each cubic block; thirdly, the reconstruction results of all the blocks are combined; fourthly, the number set of all the blocks is calculated according to the block reconstruction results, the construction is performed according to the first three steps, the time complexity is fed back, and a feedback time complexity set can be obtained as long as all the elements of the block number set are calculated; and finally, the block number with the minimal time complexity is selected from the feedback time complexity set to serve as the optimal block number, the first three steps are carried out again, and the optimal block reconstruction result is obtained, thereby completing the three-dimensional reconstruction. Through the invention, the multithread programming technology can be fully used in the three-dimensional reconstruction field, thereby greatly improving the reconstruction speed.

Description

Piecemeal three-dimensional rebuilding method based on two-dimensional x-ray images sequential filtering back projection

Technical field

The present invention relates to a kind of piecemeal method for reconstructing based on filtered back projection, specifically relate to and a kind ofly based on the two-dimensional x-ray images sequence, carry out three-dimensional reconstruction speed technology three-dimensional imaging, based on filtered back projection.

Background technology

Three-dimensional reconstruction based on X ray has good observation dimensional information and the few advantage of radiation dose because of it, in fields such as industry, medical treatment, education, is paid attention to more and more in recent years.The X ray 3-D imaging system of movement-based C type arm is typical case's application of this three-dimensional reconstruction, its feature mainly is the thought based on filtered back projection, the two-dimensional x-ray images sequence of taking around object is carried out to three-dimensional reconstruction, but how the reconstruction efficiency of this technology is low, and can't reach the real-time reconstruction effect for the two-dimensional x-ray images sequence with high-resolution (as 1024 * 1000).Therefore existing three-dimensional reconstruction is furtherd investigate to exploitation, further the accelerated reconstruction process, realize that the real-time of three-dimensional reconstruction is very important.

Summary of the invention

Goal of the invention: the objective of the invention is in order to solve the deficiencies in the prior art, a kind of piecemeal three-dimensional rebuilding method based on filtered back projection is provided.

Technical scheme: in order to realize above purpose, the invention discloses a kind of piecemeal three-dimensional rebuilding method based on two-dimensional x-ray images sequential filtering back projection, comprise following steps:

Step 1, according to initial piecemeal number, set up the cube piecemeal: comprise and set up discrete coordinates system and determine each piecemeal coordinate district;

Step 2, carry out partial reconstruction to each cube piecemeal and obtain the piecemeal reconstructed results: comprise data normalization to be reconstructed, data pre-service to be reconstructed and the piecemeal backprojection reconstruction based on two-dimensional x-ray images;

Step 3, combine the reconstructed results of each piecemeal;

Step 4, calculate the set of all piecemeal numbers according to the reconstructed results of piecemeal, according to step 1 to step 3, rebuild and feed back its time complexity, until in the set of piecemeal number, each element all calculates completely, obtains the time complexity set of feedback;

Choose the piecemeal number with minimum time complexity from the time complexity set of feedback, using it as optimum piecemeal number, re-execute step 1 to step 3, obtain optimum piecemeal reconstructed results, complete three-dimensional reconstruction.

In step 1 of the present invention, each sub-step comprises:

(1) initialization piecemeal number N ₀=4 (the CPU numbers that can make its computing machine that equals to move three-dimensional rebuilding method have).

(2) set up the cube partitioned organization: first build one and rebuild cube, take that to rebuild one of them summit of cube be true origin, right-handed coordinate system is set up as three coordinate axis of x, y, z respectively in three limits that are connected with initial point, with coordinate points (x, y, z) mean a voxel in arbitrary piecemeal, voxel coordinate point (x, y, z) meets arbitrarily, voxel refers to that the coordinate figure at a small cubes ，Yong Qi center in space means:

Wherein XDIM, YDIM, ZDIM mean respectively the maximal value of i, j, k axle,

mean the natural number set;

(3) determine each piecemeal coordinate district: keep j, k axle constant, the i axle is cut apart, first with following formula adjustment XDIM, be N ₀integral multiple:

$\mathrm{XDIM}=N_0\left[\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM}\right],$

Be the Range-partition of i axle [0, XDIM] N ₀part, its coordinate range is respectively:

$[0,\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM}-1],[\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM},\frac{2}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM}-1]\&CenterDot;\&CenterDot;\&CenterDot;[\frac{N_0-1}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM},\mathrm{XDIM}-1],$ N ₀individual x axial coordinate scope forms N in conjunction with j, k axle respectively ₀individual rectangular parallelepiped.

In step 2 of the present invention, comprise following sub-step:

(1) data to be reconstructed of standardizing: data at first to be reconstructed should be two-dimensional image sequence, it has stored several two-dimentional x ray images according to the order of sequence, and (picture numbers means with variable proj_num, the x ray image moves C type arm x ray imaging device by point source general on market and obtains), usually all there is one between adjacent image and take angle, be designated as θ.The order of obtaining image sequence according to imaging device deposits every width view data in one-dimensional sequence successively, and single image is according to the first row, the second row ... to the sequential storage of last column;

The pixel square probe unit length of side of stipulating mobile C type arm x ray imaging device is Δ, detector resolution is M * N, in imaging device, x ray emission source is D to the distance of detector, and in imaging device, x ray emission source is d to the distance of the geometric center of object to be reconstructed;

The x ray image geometric center of take is initial point, in image, a line direction to the right is x ' axle, the downward direction of one row is y ' axle, set up rectangular coordinate system, if i ', the ranks position of a pixel in j ' difference presentation video, set up the pixel column column position (i ', j ') to the mapping relations of rectangular coordinate system (x ', y '):

$\left\{\begin{array}{c}{x}^{\&prime;}=(j^{\&prime;}-\frac{N}{2})\&CenterDot;\mathrm{\&Delta;},j^{\&prime;}=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,N-1\\ y^{\&prime;}=(\frac{M}{2}-i^{\&prime;})\&CenterDot;\mathrm{\&Delta;},i^{\&prime;}=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,M-1\end{array}\right.---\left(1\right)$

M wherein, N, the Δ implication is consistent with narration above;

(2) treat data reconstruction and carry out pre-service:

Make the pixel value that P (i ', j ') is optional position in a width x ray image (i ', j '), by formula (2), revise weights

$\hat{P}(i^{\&prime;},j^{\&prime;})=\frac{P(i^{\&prime;},j^{\&prime;})D^2}{\sqrt{{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000110972610000021.png"\; state="\{\{state\}\}">D</figure-callout>}}^2+x^{\&prime;2}+y^{\&prime;2}}}=\frac{P(i^{\&prime;},j^{\&prime;})D^2}{\sqrt{{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000110972610000021.png"\; state="\{\{state\}\}">D</figure-callout>}}^2+{(j^{\&prime;}-N/2)}^2+{(M/2-i^{\&prime;})}^2}}---\left(2\right)$

D wherein, M, N and Δ are continued to use implication above.

The all pixel values of every a line to the x ray image after weighting (are designated as

) carry out filtering operation, suppose that wave filter is g, right

filtering operation be shown below

Wherein with

mean respectively Fourier transform and inverse transformation.

Because the cube after rebuilding finally need to be attributed to cube volume elements (also can be referred to as voxel, the numerical value of storage is called voxel value) of little storage numerical value, thus calculate again the size of each voxel of three-dimensional cube after reconstruction by following formula,

${\mathrm{\&Delta;}}_x^r=\frac{\mathrm{dN\&Delta;}}{\mathrm{XDIM}(D+0.5\mathrm{N\&Delta;})},{\mathrm{\&Delta;}}_y^r=\frac{\mathrm{dN\&Delta;}}{\mathrm{YDIM}(D+0.5\mathrm{N\&Delta;})},{\mathrm{\&Delta;}}_z^r=\frac{\mathrm{dM\&Delta;}}{\mathrm{YDIM}(D+0.5\mathrm{M\&Delta;})}---\left(4\right)$

One of them voxel is corresponding to a coordinate points in virtual cube in step 1, with

the size that means respectively voxel.

Similar with the image pixel principle, the voxel in cube metadata also can be expressed as (i, j, k) jointly with the relative position of three dimensions (meaning with i, j, k respectively).The geometric center of cube metadata of take is initial point, and take respectively i, j, tri-dimensions of k is x, y, the z axle is set up right hand rectangular coordinate system, when cube while being whole voxel location (i, j, k) to the mapping relations of rectangular coordinate system (x, y, z), can be expressed as,

$\left\{\begin{array}{c}x=(\mathrm{XDIM}/2-i)\&CenterDot;{\mathrm{\&Delta;}}_x^r\\ y=(j-\mathrm{YDIM}/2)\&CenterDot;{\mathrm{\&Delta;}}_y^r\\ z=(k-\mathrm{ZDIM}/2)\&CenterDot;{\mathrm{\&Delta;}}_z^r\end{array}\right.---\left(5\right)$

Wherein each symbol implication is consistent with narration above.

(3) backprojection reconstruction: in definite segmented areas, carry out respectively back projection in step 1, its corresponding process is as follows simultaneously,

Set up two-dimensional x-ray images (radioscopic image moves C type arm x-ray imaging device by point source general on market and obtains) pixel of the every width image of sequence and the relation of rebuilding voxel coordinate in cube for rebuilding: picture numbers means with proj_num, θ means the shooting angle between adjacent image, (obtain the order of image according to timer) successively every width view data deposited in to one-dimensional sequence that (single image is according to the first row, the second row ... sequential storage to last column), voxel coordinate is (x, y, z), the current shooting angle that will carry out the two-dimensional x-ray images of back projection is φ=proj_num θ, the coordinate of correspondence in the two-dimensional x-ray images that described voxel is proj_num in sequence number (x ' _p, y ' _p) be:

$(x_p^{\&prime;},y_p^{\&prime;})=(\frac{D(y\cos \mathrm{\&phi;}-x\sin \mathrm{\&phi;})}{d+x\cos \mathrm{\&phi;}+y\sin \mathrm{\&phi;}},\frac{D\&CenterDot;z}{d+x\cos \mathrm{\&phi;}+y\sin \mathrm{\&phi;}})---\left(6\right)$

Wherein, D is that in imaging device, the X ray emissive source is to the distance of detector, and d is the distance that in imaging device, the X ray emissive source arrives the geometric center of object to be reconstructed.

Make the pixel value that P (i ', j ') is arbitrary coordinate point in a width two-dimensional x-ray images (i ', j '), obtain corresponding to filtered correction pixel value with differential technique

Mean a voxel in cube metadata with the relative position (i, j, k) of three dimensions, the geometric center of cube metadata of take is initial point, and take respectively i, j, tri-dimensions of k is x, y, and the z axle is set up right hand rectangular coordinate system.Segmented areas separated based on the i axle for each, its i axle scope is respectively $[0,\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM}-1],[\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM},\frac{2}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM}-1]\&CenterDot;\&CenterDot;\&CenterDot;[\frac{N_0-1}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM},\mathrm{XDIM}-1],$ Be expressed as N in conjunction with j, k axle ₀the form of individual rectangular parallelepiped is expressed as with the form of tlv triple:

Wherein V means voxel value, and l is the piecemeal sequence number,

, for the arbitrary coordinate in each piecemeal (i, j, k), the x ray image series is at piecemeal V _lback projection on [i] [j] [k] is shown below

$V_l\left[i\right]\left[j\right]\left[k\right]=\underset{\mathrm{proj}\_\mathrm{num}=0}{\overset{\mathrm{NUM}}{\mathrm{\&Sigma;}}}{\hat{P}}_0{(i^{\&prime;},j^{\&prime;})}_{\mathrm{proj}\_\mathrm{num}}---\left(9\right)$

Wherein

in the x ray image that to be illustrated in sequence number be proj_num, the individual pixel of the i ' row j ' is through filtered correction pixel value, NUM means the maximum sequence number (the x ray image adds up to NUM+1) of x ray image, for each voxel in piecemeal, use (9) formula to carry out backprojection operation, just can obtain last piecemeal reconstructed results

In step 3 of the present invention, combination piecemeal reconstructed results step is as follows: utilize the piecemeal reconstructed results obtained in step 2 to carry out assembling combination, its formal description is:

Wherein

when (i, j, k) traversal in cube during all voxel, V[i] [j] [k] be reconstructed results.

In step 4 of the present invention, comprise following sub-step:

Step 41, the definition comprehensive contribution factor: piecemeal number N ₀in fact be subject to the constraint of x axle number of dimensions XDIM, make α=XDIM mod N ₀.α under ideal situation=0, if time complexity is unsatisfactory, available constraint

feed back by reconstruction time, further adopt strategy to obtain optimum piecemeal number N ₀ ^*.

Consider reconstruction precision and performance optimization degree, define a comprehensive contribution factor:

$\mathrm{\&eta;}=\mathrm{\&lambda;}(1-\frac{t}{t_0})+(\mathrm{\&lambda;}-1)\frac{\mathrm{\&alpha;}}{\mathrm{XDIM}}---\left(11\right)$

λ is a parameter that is used for characterizing precision and performance, can be set according to actual conditions (λ ∈ [0,1], when λ gets 0,0.5 and at 1 o'clock, can mean respectively that precision is preferential, precision property be equal to consider and performance preferential); t ₀mean respectively N with t ₀while getting initial value 4 and the reconstruction time while getting current numerical value.

Step 42, determine the piecemeal number: choose all block counts that meet parameter alpha=0, generate set corresponding reconstruction time be designated as

then from

in choose the minimum and piecemeal number of reconstruction time also minimum block count be designated as

corresponding reconstruction time is t _k, define the set of optimum piecemeal number calculate

in the corresponding comprehensive contribution factor of each piecemeal number η _i:

${\mathrm{\&eta;}}_i=\mathrm{\&lambda;}\&CenterDot;(1-\frac{t_{(i+N_k)}}{t_{N_k}})+(\mathrm{\&lambda;}-1)\&CenterDot;\frac{{\mathrm{\&alpha;}}_{(i+N_k)}}{\mathrm{XDIM}},i=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,(N_{(k+1)}-N_k),$

Wherein, with

mean that respectively the piecemeal number is (i+N _k) and N _kthe time reconstruction time,

${\mathrm{\&alpha;}}_{(i+N_k)}=\mathrm{XDIM}\mathrm{mod}(i+N_k).$

Obtain the set of optimum piecemeal number

in comprehensive contribution factor η corresponding to each block count _iafter, the block count of getting this value minimum and piecemeal minimum number is optimum piecemeal number N ₀ ^*.

Beneficial effect: a kind of piecemeal three-dimensional rebuilding method based on filtered back projection provided by the invention, compared with prior art have the following advantages: because partitioned organization of the present invention is rebuild thought and the multithreading unity of thinking, and can also provide feasible algorithm and determine optimum block count, thereby can realize that efficient multiple programming technology is to accelerate whole three-dimensional reconstruction process, and then can carry out real-time three-dimensional imaging to all kinds of high-resolution two-dimensional x-ray images sequences, make the three-dimensional reconstruction of two-dimensional x-ray images really practical.

The accompanying drawing explanation

Fig. 1 is one-piece construction figure of the present invention.

Fig. 2 sets up the schematic diagram of partitioned organization in the embodiment of the present invention.

Fig. 3 is piecemeal backprojection reconstruction process flow diagram.

Fig. 4 is for determining optimum block count purpose process flow diagram.

Embodiment:

Below in conjunction with the drawings and specific embodiments, further illustrate the present invention, should understand these embodiment only is not used in and limits the scope of the invention for the present invention is described, after having read the present invention, those skilled in the art all fall within the application's claims limited range to the modification of the various equivalent form of values of the present invention.Before adopting the present invention, acquiescence those skilled in the art have grasped the three-dimensional reconstruction based on filtered back projection.

Fig. 1 has provided one-piece construction figure of the present invention.As shown in Figure 1, the piecemeal three-dimensional rebuilding method based on two-dimensional x-ray images sequential filtering back projection in the present invention, comprise following steps: step 1, according to initial piecemeal number, set up the cube piecemeal: comprise and set up discrete coordinates system and determine each piecemeal coordinate district; Step 2, carry out partial reconstruction to each cube piecemeal and obtain the piecemeal reconstructed results: comprise data normalization to be reconstructed, data pre-service to be reconstructed and the piecemeal backprojection reconstruction based on two-dimensional x-ray images; Step 3, combine the reconstructed results of each piecemeal; Step 4, calculate the set of all piecemeal numbers according to the reconstructed results of piecemeal, according to step 1 to step 3, rebuild and feed back its time complexity, until in the set of piecemeal number, each element all calculates completely, obtains the time complexity set of feedback; Choose the piecemeal number with minimum time complexity from the time complexity set of feedback, using it as optimum piecemeal number, re-execute step 1 to step 3, obtain optimum piecemeal reconstructed results, complete three-dimensional reconstruction.

Step 1 comprises the steps:

Initialization piecemeal number N ₀=4, partitioned organization as shown in Figure 2.

Set up the cube partitioned organization: first build one and rebuild cube, take that to rebuild one of them summit of cube be true origin, right-handed coordinate system is set up as three coordinate axis of x, y, z respectively in three limits that are connected with initial point, with coordinate points (x, y, z) mean a voxel in arbitrary piecemeal, voxel coordinate point (x arbitrarily, y, z) meet:

, wherein parameter X DIM, YDIM, ZDIM mean respectively the maximal value of x, y, z axle,

mean the natural number set.

Determine each piecemeal coordinate district: keep y, z axle constant, the x axle is cut apart, adjust parameter X DIM by following formula and be the piecemeal number N ₀integral multiple:

$\mathrm{XDIM}=N_0\left[\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM}\right].$

The scope of x axle [0, XDIM] on average is divided into to N ₀individual coordinate range, that is:

$[0,\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM}-1],[\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM},\frac{2}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM}-1]\&CenterDot;\&CenterDot;\&CenterDot;[\frac{N_0-1}{{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HDA0000110972610000031.png"\; state="\{\{state\}\}">N</figure-callout>}}_0}\mathrm{XDIM},\mathrm{XDIM}-1].$

N ₀individual x axial coordinate scope forms N in conjunction with y, z axle respectively ₀individual cube piecemeal.

Fig. 3 is piecemeal backprojection reconstruction process flow diagram:

Step 1 is the pretreated x radiographic image data of input;

Step 2 arranges timer in order to record reconstruction time;

The x ray image sequence number that step 3 is obtained is proj_num, by φ=proj_num θ, calculates and obtains its shooting angle;

Step 4 for the first time circulation time according to N ₀set up partitioned organization, and in each circulation according to formula

$V_l\left[i\right]\left[j\right]\left[k\right]=V_l\left[i\right]\left[j\right]\left[k\right]+{\hat{P}}_0{(i^{\&prime;},j^{\&prime;})}_{\mathrm{proj}\_\mathrm{num}}$ Carry out piecemeal back projection;

Step 5 judges the x ray image, and whether back projection is complete;

Step 6 sequence number variable adds 1;

The all x ray images of step 7 back projection is complete;

Step 8 is rebuild textural association to each piecemeal and is assembled into an individual data items V[i] [j] [k];

Step 9 is obtained reconstruction time t;

Step 10 output reconstructed results.

Fig. 4 is for determining optimum block count purpose process flow diagram:

Step 11 initialization α=XDIM mod N ₀=0;

Step 12 is tried to achieve the piecemeal number set met the demands

Step 13 is obtained corresponding reconstruction time set by experiment

Step 14 is obtained minimum reconstruction time and find corresponding piecemeal number N _k;

Step 15 judgement N _kwhether only, go to step if not 16; If go to step 17;

Step 16 makes N _kget minimum value;

Step 17N _kvalue remains unchanged;

Step 18 is according to N _kobtain the set of optimum piecemeal number

Step 19 is obtained corresponding reconstruction time set by experiment

Step 20 is according to formula

${\mathrm{\&eta;}}_i=\mathrm{\&lambda;}\&CenterDot;(1-\frac{t_{(i+N_k)}}{t_{N_k}})+(\mathrm{\&lambda;}-1)\&CenterDot;\frac{{\mathrm{\&alpha;}}_{(i+N_k)}}{\mathrm{XDIM}},i=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,(N_{(k+1)}-N_k)$

Try to achieve corresponding comprehensive contribution factor set

Step 21 is obtained minimum comprehensive contribution factor η _i, and find corresponding piecemeal number

Step 22 judgement

whether only, go to step if not 23; If go to step 24;

Step 23 order

get minimum value;

Step 24

value remains unchanged;

Step 25 is tried to achieve optimum block count

The invention provides the piecemeal three-dimensional rebuilding method based on two-dimensional x-ray images sequential filtering back projection; method and the approach of this technical scheme of specific implementation are a lot; the above is only the preferred embodiment of the present invention; should be understood that; for those skilled in the art; under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.In the present embodiment not clear and definite each ingredient all available prior art realized.

Claims (1)

1. the piecemeal three-dimensional rebuilding method based on two-dimensional x-ray images sequential filtering back projection, is characterized in that, comprises following steps:

Step 1, according to initial piecemeal number, set up the cube piecemeal: comprise and set up discrete coordinates system and determine each piecemeal coordinate district;

Step 2, carry out partial reconstruction to each cube piecemeal and obtain the piecemeal reconstructed results: comprise data normalization to be reconstructed, data pre-service to be reconstructed and the piecemeal backprojection reconstruction based on two-dimensional x-ray images;

Step 3, combine the reconstructed results of each piecemeal;

Step 4, calculate the set of all piecemeal numbers according to the reconstructed results of piecemeal, according to step 1 to step 3, rebuild and feed back its time complexity, until in the set of piecemeal number, each element all calculates completely, obtains the time complexity set of feedback;

Choose the piecemeal number with minimum time complexity from the time complexity set of feedback, using it as optimum piecemeal number, re-execute step 1 to step 3, obtain optimum piecemeal reconstructed results, complete three-dimensional reconstruction;

Step 1 comprises the steps:

Initialization piecemeal number N ₀=4;

Set up the cube partitioned organization: first build one and rebuild cube, take that to rebuild one of them summit of cube be true origin, right-handed coordinate system is set up as three coordinate axis of x, y, z respectively in three limits that are connected with initial point, with coordinate points (x, y, z) mean a voxel in arbitrary piecemeal, voxel coordinate point (x arbitrarily, y, z) meet: , wherein parameter X DIM, YDIM, ZDIM mean respectively the maximal value of x, y, z axle,

mean the natural number set;

Determine each piecemeal coordinate district: keep y, z axle constant, the x axle is cut apart, adjust parameter X DIM by following formula and be the piecemeal number N ₀integral multiple:

$\mathrm{XDIM}=N_0\left[\frac{1}{N_0}\mathrm{XDIM}\right];$

The scope of x axle [0, XDIM] on average is divided into to N ₀individual coordinate range, that is:

$[0,\frac{1}{N_0}\mathrm{XDIM}-1],[\frac{1}{N_0}\mathrm{XDIM},\frac{2}{N_0}\mathrm{CDIM}-1]\&CenterDot;\&CenterDot;\&CenterDot;[\frac{N_0-1}{N_0}\mathrm{XDIM},\mathrm{XDIM}-1];$

N ₀individual x axial coordinate scope forms N in conjunction with y, z axle respectively ₀individual cube piecemeal;

Piecemeal backprojection reconstruction based on two-dimensional x-ray images in step 2 comprises the steps:

Set up the pixel of the every width image of two-dimensional x-ray images sequence for rebuilding and the relation of rebuilding voxel coordinate in cube: picture numbers means with proj_num, θ means the shooting angle between adjacent image, successively every width view data is deposited in to one-dimensional sequence, voxel coordinate is (x, y, z), the current shooting angle that will carry out the two-dimensional x-ray images of back projection is φ=proj_num θ, the coordinate of correspondence in the two-dimensional x-ray images that described voxel is proj_num in sequence number (x ' _p, y ' _p) be:

$(x_p^{\&prime;},y_p^{\&prime;})=(\frac{D(y\cos \mathrm{\&phi;}-x\sin \mathrm{\&phi;})}{d+x\cos \mathrm{\&phi;}+y\sin \mathrm{\&phi;}},\frac{D\&CenterDot;z}{d+x\cos \mathrm{\&phi;}+y\sin \mathrm{\&phi;}})$

Wherein, D is that in imaging device, the X ray emissive source is to the distance of detector, and d is the distance that in imaging device, the X ray emissive source arrives the geometric center of object to be reconstructed;

Make the pixel value that P (i ', j ') is arbitrary coordinate point in a width two-dimensional x-ray images (i ', j '), obtain corresponding to filtered correction pixel value with differential technique

Mean a voxel in cube metadata with the relative position (i, j, k) of three dimensions, the geometric center of cube metadata of take is initial point, and take respectively i, j, tri-dimensions of k is x, y, and the z axle is set up right hand rectangular coordinate system;

Segmented areas separated based on the i axle for each, its i axle scope is respectively $[0,\frac{1}{N_0}\mathrm{XDIM}-1],[\frac{1}{N_0}\mathrm{XDIM},\frac{2}{N_0}\mathrm{CDIM}-1]\&CenterDot;\&CenterDot;\&CenterDot;[\frac{N_0-1}{N_0}\mathrm{XDIM},\mathrm{XDIM}-1],$ Be expressed as N in conjunction with j, k axle ₀the form of individual rectangular parallelepiped is expressed as with the form of tlv triple:

Wherein V means voxel value, and l is the piecemeal sequence number;

For voxel (i, j, k) in each piecemeal, the two-dimensional x-ray images sequence is at piecemeal V _lback projection on [i] [j] [k] is shown below:

$V_l\left[i\right]\left[j\right]\left[k\right]=\underset{\mathrm{proj}\_\mathrm{num}}{\overset{\mathrm{NUM}}{\mathrm{\&Sigma;}}}{\hat{P}}_0{(i^{\&prime;},j^{\&prime;})}_{\mathrm{proj}\_\mathrm{num};}$

Wherein

in the two-dimensional x-ray images that to be illustrated in sequence number be proj_num, the individual pixel of the i ' row j ' is through filtered correction pixel value, NUM means the maximum sequence number of two-dimensional x-ray images, two-dimensional x-ray images adds up to NUM+1, with carrying out backprojection operation, obtain last piecemeal reconstructed results for each voxel in piecemeal

In step 3, combination piecemeal reconstructed results step is as follows:

Utilize the piecemeal reconstructed results obtained in step 2 to carry out assembling combination, be described as:

Wherein

when (i, j, k) traversal in cube during all voxel, V[i] [j] [k] be reconstructed results;

Calculating optimum piecemeal number according to the time complexity set of feedback in step 4 comprises the steps:

Step 41, the definition comprehensive contribution factor: piecemeal number N ₀by x axle maximal value XDIM constraint, make parameter alpha=XDIMmodN ₀;

Definition comprehensive contribution factor η:

$\mathrm{\&eta;}=\mathrm{\&lambda;}\&CenterDot;(1-\frac{t}{t_0})+(\mathrm{\&lambda;}-1)\&CenterDot;\frac{\mathrm{\&alpha;}}{\mathrm{XDIM}}$

λ is for characterizing the parameter of precision and performance, λ ∈ [0,1]; t ₀mean respectively the piecemeal number N with t ₀while getting initial value 4 and the reconstruction time while getting current numerical value;

Step 42, determine the piecemeal number: first choose all piecemeals that meet parameter alpha=0, and to add up its number be m, generate set

corresponding reconstruction time be designated as then from set

in choose the minimum and piecemeal number of reconstruction time also minimum block count be designated as

, corresponding reconstruction time is t _k, define the set of optimum piecemeal number

Calculate the set of optimum piecemeal number

in the corresponding comprehensive contribution factor of each piecemeal number η _i:

${\mathrm{\&eta;}}_i=\mathrm{\&lambda;}\&CenterDot;(1-\frac{t_{(i+N_k)}}{t_{N_k}})+(\mathrm{\&lambda;}-1)\&CenterDot;\frac{{\mathrm{\&alpha;}}_{(i+N_k)}}{\mathrm{XDIM}},i=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,(N_{(k+1)}-N_k),$

Wherein,

with

mean that respectively the piecemeal number is (i+N _k) and N _kthe time reconstruction time, ${\mathrm{\&alpha;}}_{(i+N_k)}=\mathrm{XDIM}\mathrm{mod}(i+N_k);$

Obtain the set of optimum piecemeal number

in comprehensive contribution factor η corresponding to each block count _iafter, the block count of getting this value minimum and piecemeal minimum number is optimum piecemeal number N ₀ ^*.

Images