CN102737361A - Method for transforming full distance of three-dimensional binary image - Google Patents

Abstract

The embodiment of the invention provides a method for transforming a full distance of a three-dimensional binary image. The method comprises the following steps of: dividing the three-dimensional binary image into a corresponding number of two-dimensional binary images along with one axis of the three-dimensional binary image; calculating the two-dimensional full distance transformation of each pixel in each divided two-dimensional binary image; determining the first nearest background pixel range of a first pixel; determining the two-dimensional full distance transformation value of a projection pixel of the first pixel in each two-dimensional binary image in the first nearest background pixel range; and according to the determined two-dimensional full distance transformation value of the projection pixel of the first pixel in each two-dimensional binary image in a first background pixel, determining another first background pixel nearest to the first background pixel in the three-dimensional binary image, and calculating a first full distance between the first background pixel and the first pixel. By the method provided by the embodiment of the invention, calculation speeds can be increased, and calculation accuracy can be improved.

Description

The method of the complete range conversion of a kind of three-dimensional bianry image

Technical field

The present invention relates to image processing field, in particular, relate to the method for the complete range conversion of a kind of three-dimensional bianry image.

Background technology

Range conversion is that the digital picture after range conversion has good rotation, translation and constant rate property to one of digital picture important pretreatment operation, thereby it all plays an important role in the image processing techniques every field.

Bianry image is carried out range conversion to be meant and to be transformed into the process from the distance of its nearest background pixel and this pixel to the pixel value of each pixel in the bianry image.Pixel in the bianry image can be divided into two types of background pixel (pixel value is 0) and object pixels (pixel value is 1), and the range conversion value of background pixel is zero.

Can utilize approximate distance transform method and complete range conversion method that bianry image is carried out range conversion; The basic thought of approximate distance transform method is: utilize an approximate template computing of arriving commonly used in the Flame Image Process; Calculating moves to the bee-line of certain point in the figure outside figure; In the template distance value of sign normally Euclidean distance round approximate value; Simultaneously template also can not be all the time moves along the normal orientation of boundary profile, so these class methods must be that error is arranged, like city block distance, chessboard distance, chamfering distance etc.

Range conversion is an accurate Euclidean distance of asking for its nearest background pixel of each pixel distance fully.Classic method is calculated the distance of each pixel and all background pixels respectively, causes computing time longer, and the range conversion method comprises fully: flank pass broadcasting method and dimension reduction method.

To sum up, the method for existing range conversion has following shortcoming: the first, and there is error in approximation method and is not suitable for the strict image of accuracy requirement is handled, like medical image; The second, the range conversion method is longer working time fully for tradition.

Summary of the invention

In view of this; The invention provides the method and the device of the complete range conversion of a kind of three-dimensional bianry image, have error and be not suitable for problem the strict image of accuracy requirement is handled and operation time is long to overcome the method for calculating range conversion in the prior art.

For realizing above-mentioned purpose, the present invention provides following technical scheme:

The method of the complete range conversion of a kind of three-dimensional bianry image, said three-dimensional bianry image is of a size of m * n * s, comprising:

With said three-dimensional bianry image along two-dimentional two-value picture that is divided into corresponding number wherein;

The two dimension range conversion fully of each pixel in each two-dimentional two-value picture of computed segmentation respectively;

Based on second object pixel and the complete distance that needs first pixel of the complete range conversion of Calculation of Three Dimensional; Reach the three-dimensional fully range conversion value of said second object pixel in said three-dimensional bianry image, confirm the first nearest background pixel scope of said first pixel;

Confirm the complete range conversion value of two dimension of the projected pixel in said first pixel each two-dimentional two-value picture in the said first nearest background pixel scope;

According to the two dimension of the projected pixel of said definite first pixel each two-dimentional bianry image in said first nearest background pixel scope range conversion value fully; Determine the first nearest background pixel of said first pixel of said three-dimensional bianry image middle distance; Calculate the first complete distance of said first background pixel and said first pixel, and with the three-dimensional fully range conversion value of the said first complete distance as said first pixel.

Preferably, the three-dimensional fully range conversion value of said second object pixel in said three-dimensional bianry image is r ₁, said complete distance, and the three-dimensional fully range conversion value of said second object pixel in said three-dimensional bianry image according to second object pixel and first pixel, confirm that the first nearest background pixel scope of said first pixel specifically comprises:

Confirm the complete of said first pixel and said second object pixel apart from r ₂

The said first nearest background pixel scope is for being the centre of sphere with said first pixel, with r ₁+ r ₂Ball O for radius ₁The zone that circumscribed square surrounded; Or the said first nearest background pixel scope is for being the centre of sphere with said second object pixel, with r ₁Ball O for radius ₂In meet square and said ball O ₁The zone that circumscribed square surrounded; Or the said first nearest background pixel scope is for being the centre of sphere with said first pixel, with | r ₁-r ₂| be the ball O of radius ₃In meet square and said ball O ₁The zone that circumscribed square surrounded.

Preferably, said three-dimensional bianry image is divided into s along the z axle and opens two-dimentional two-value picture, and the said first nearest background pixel scope is to be the centre of sphere with said first pixel, with r ₁+ r ₂Ball O for radius ₁The zone that circumscribed square surrounded, the two-dimentional two-value picture at said first pixel place is z ₀, the two dimension of the projected pixel in said definite said first pixel each two-dimentional two-value picture in said first nearest background pixel scope range conversion value fully specifically comprises:

With said two-dimentional two-value picture z ₀For symcenter confirms successively from the inside to surface that along the z direction of principal axis said first pixel is at two-dimentional two-value picture z ₀+ r _xIn the complete square DR of range conversion value of two dimension of projected pixel _x ², and the two dimension confirmed of record fully the range conversion value square, r _x=0, ± 1, ± 2 ..., ± (r ₁+ r ₂);

Judge DR _x ²Whether satisfy

If stop then confirming that first pixel is respectively at two-dimentional two-value picture z ₀± (r _x+ 1) until two-dimentional two-value picture z ₀± (r ₁+ r ₂) in the complete range conversion value of two dimension of projected pixel, if not, continue then to confirm that first pixel is respectively at two-dimentional two-value picture z ₀± (r _x+ 1) the complete range conversion value of the two dimension of projected pixel in is until determining said first pixel at two-dimentional two-value picture z ₀± (r ₁+ r ₂) in the two dimension of projected pixel fully till the range conversion value.

Preferably; The two dimension of said projected pixel according to said first pixel each two-dimentional bianry image in the said first nearest background pixel scope is the range conversion value fully, determines the first nearest background pixel of said first pixel of said three-dimensional bianry image middle distance and specifically comprises:

Utilize formula min{DR _x ²+ | z _x-z ₀| ², z wherein _xThe span of z is determined first background pixel nearest with first pixel distance in the ∈ first nearest background pixel scope;

Utilize formula

to calculate the first complete distance.

Preferably, the two dimension of calculating each two-dimentional two-value picture fully range conversion specifically comprises:

Pre-treatment step; Said pre-treatment step is to confirm first function or confirm second function, and said first function is used for the position of the nearest background pixel of definite capable middle distance the 4th pixel of two-dimentional two-value picture i, and said second function is used for the position of the nearest background pixel of definite said the 4th pixel of two-dimentional two-value picture j row middle distance; Wherein, 1≤i≤m, 1≤j≤n, i and j are integer;

Calculate the two dimension complete distance of said the 4th pixel of distance fully according to the 3rd object pixel and needs; And the complete distance of the two dimension of said the 3rd object pixel in two-dimentional two-value picture; Confirm the second nearest background pixel scope of said the 4th pixel, said the 4th pixel and said the 3rd object pixel all are arranged in same two-dimentional two-value picture;

Utilize the said first function nearest background pixel of said the 4th pixel of detection range in every row of the said second nearest background pixel scope respectively, or utilize the said second function nearest background pixel of said the 4th pixel of detection range in every row of the said second nearest background pixel scope respectively;

From the nearest background pixel of said the 4th pixel of the distance that searches out, determine second background pixel nearest with said the 4th pixel distance; Second two dimension of calculating said second background pixel and said the 4th pixel is distance fully, and will said second two dimension fully distance as the complete range conversion value of the two dimension of said the 4th pixel in the two-dimentional two-value picture at its place.

Preferably, the two dimension of calculating each two-dimentional two-value picture fully range conversion specifically comprises:

Pre-treatment step; Said pre-treatment step is to confirm first function or confirm second function, and said first function is used for the position of the nearest background pixel of definite capable middle distance the 4th pixel of two-dimentional two-value picture i, and said second function is used for the position of the nearest background pixel of definite said the 4th pixel of two-dimentional two-value picture j row middle distance; Wherein, 1≤i≤m, 1≤j≤n, i and j are integer;

Complete distance based on the 3rd object pixel and said the 4th pixel; And the 3rd object pixel and the distance that leaves its nearest background pixel; Confirm the second nearest background pixel scope of the 4th pixel; And the second nearest background pixel scope is divided into first son background pixel range set and second son background pixel range set recently recently according to preset rules; First son background pixel range set recently comprises at least one first son background pixel scope recently; Line number in the nearest background pixel scope of said at least one height is not more than columns, and second son background pixel range set recently comprises at least one second son background pixel scope recently, and the line number in said at least one second sub background pixel scope recently is greater than columns;

Utilize first function nearest background pixel of detection range the 4th pixel in every row of the nearest background pixel range set of first son, utilize second function nearest background pixel of detection range the 4th pixel in every row of the nearest background pixel range set of second son;

From the nearest background pixel of distance the 4th pixel that searches out, determine second background pixel nearest with the 4th pixel distance; Calculate the second complete distance of second background pixel and the 4th pixel, and with the two-dimentional fully range conversion value of this second complete distance as the 4th pixel.

Preferably, the second nearest background pixel scope of said definite said the 4th pixel specifically comprises:

Calculate the two dimension of said the 3rd object pixel in two-dimentional two-value picture fully apart from r ₃

Confirm the complete of said the 4th pixel and said the 3rd object pixel apart from r ₄

The said second nearest background pixel scope is for being the center of circle with said the 4th pixel, with r ₃+ r ₄Round O for radius ₄The zone that circumscribed square surrounded;

Or the said second nearest background pixel scope is for being the center of circle with said the 3rd object pixel, with r ₃Round O for radius ₅In connect the square with said round O ₄The annular region that circumscribed square surrounded;

Or the said second nearest background pixel scope is for being the centre of sphere with said the 4th pixel, with | r ₃-r ₄| be the round O of radius ₆In connect the square with said round O ₄The annular region that circumscribed square surrounded.

Preferably, the x that said the 4th pixel is positioned at two-dimentional two-value picture is capable, the y row; With (x, the y) position of said the 4th pixel of expression in said two-dimentional two-value picture is with (x; Y) be separation,, the y row be divided into the above and below capable left side and the right side of being divided into of x;

Said definite first function specifically comprises:

Confirm to be used to calculate said the 4th pixel (x of said two-dimentional two-value picture x capable left side distance; Y) first subfunction of nearest background pixel place columns; And be used to calculate said the 4th pixel of the capable right side of said two-dimentional two-value picture x distance (x, y) second subfunction of nearest background pixel place columns, wherein; 1≤x≤m, 1≤y≤n;

According to said first subfunction and said second subfunction, confirm said first function;

Said definite second function specifically comprises:

Confirm to be used to calculate the 3rd subfunction of the nearest background pixel place line number of the said two-dimentional two-value picture y side of listing said the 4th pixel of distance, and be used to calculate the 4th subfunction of the nearest background pixel place line number of said the 4th pixel of said two-dimentional two-value picture y row below distance;

According to said the 3rd subfunction and said the 4th subfunction, confirm said second function.

Preferably, said first subfunction is specially L [x, y]:

$L[x,y]=\left\{\begin{array}{cc}y& I(x,y)=0\\ L[x,y-1]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and y=1, so L (x, y)=-Maxlable;

Said second subfunction is specially R [x, y]:

$R[x,y]=\left\{\begin{array}{cc}y& I(x,y)=0\\ R[x,y+1]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and y=n, R [x, y]=Maxlable so;

Then be specially SZ [x, y] according to said first subfunction and definite said first function of said second subfunction:

<math> <mrow> <mi>SZ</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>L</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> </mtd> <mtd> <mi>y</mi> <mo>-</mo> <mi>L</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&lt;;</mo> <mi>R</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>R</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> </mtd> <mtd> <mi>y</mi> <mo>-</mo> <mi>L</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&amp;GreaterEqual;</mo> <mi>R</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow></math>

Said the 3rd subfunction is specially T [x, y]:

$T[x,y]=\left\{\begin{array}{cc}x& I(x,y)=0\\ T[x-1,y]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and x=1, so T [x, y]=-Maxlable;

Said the 4th subfunction is specially D [x, y]:

$D[x,y]=\left\{\begin{array}{cc}x& I(x,y)=0\\ D[x+1,y]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and x=m, D [x, y]=Maxlable so;

Then be specially ZS [x, y] according to said the 3rd subfunction and definite said second function of said the 4th subfunction:

<math> <mrow> <mi>ZS</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>T</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> </mtd> <mtd> <mi>x</mi> <mo>-</mo> <mi>D</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&lt;;</mo> <mi>T</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <mi>D</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> </mtd> <mtd> <mi>x</mi> <mo>-</mo> <mi>D</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&amp;GreaterEqual;</mo> <mi>T</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>x</mi> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow></math>

Wherein, (x y)=1 is expressed as object pixel to I, and (x y)=0 is expressed as background pixel to I, and said Maxlable is preset maximum mark value.

Wherein, said $\mathrm{Maxlable}=(1+\sqrt{2})\mathrm{Max}(m,n).$

Can know via above-mentioned technical scheme; The method of the complete range conversion of quick three-dimensional bianry image that the employing embodiment of the invention provides; At first under the situation of the three-dimensional range conversion fully of known second object pixel, can confirm the first nearest background pixel scope of first pixel based on the three-dimensional range conversion value fully of the second target phase pixel in three-dimensional bianry image; Again during the nearest background pixel of detection range first pixel; Be in the first nearest background pixel scope, to search for, rather than in whole bianry image, search for, thereby improved the speed of searching for nearest background pixel; Secondly; Behind the first nearest background pixel of distance first pixel that searches out, calculate the first complete distance of first background pixel and first pixel again, be not to search out the distance of just calculating this background pixel and first pixel behind the background pixel; Thereby reduced amount of calculation; Improved computational speed, and in whole search procedure and computational process, all do not carried out approximate processing, thus calculate high apart from accuracy.

Description of drawings

In order to be illustrated more clearly in the embodiment of the invention or technical scheme of the prior art; To do to introduce simply to the accompanying drawing of required use in embodiment or the description of the Prior Art below; Obviously, the accompanying drawing in describing below only is embodiments of the invention, for those of ordinary skills; Under the prerequisite of not paying creative work, can also obtain other accompanying drawing according to the accompanying drawing that provides.

Fig. 1 is the process flow diagram of the method for the complete range conversion of the disclosed first kind of three-dimensional bianry image of the embodiment of the invention;

Fig. 2 be first function search for the capable middle distance O of i in the two-dimentional two-value picture (x, y) nearest background pixel is actual is detection range (i, y) the bright procedure chart of nearest background pixel card;

Fig. 3 is first kind of second nearest background pixel scope synoptic diagram;

Fig. 4 is second kind of second nearest background pixel scope synoptic diagram;

Fig. 5 is the third second nearest background pixel scope synoptic diagram;

Fig. 6 is at the actual proof figure for the nearest background pixel of the projected pixel of distance first pixel in this two dimension two-value picture of the nearest background pixel of two-dimentional two-value picture middle distance first pixel;

Fig. 7 is the synoptic diagram of the first nearest background pixel scope;

The two dimension of each pixel schematic flow sheet of range conversion method fully in each two-dimentional two-value picture of a kind of respectively computed segmentation that Fig. 8 provides for the embodiment of the invention;

Shown in Figure 9 is the division synoptic diagram of the second nearest background pixel;

The two dimension of each pixel schematic flow sheet of range conversion method fully in each two-dimentional two-value picture of a kind of respectively computed segmentation that Figure 10 provides for the embodiment of the invention;

Figure 11 is the synoptic diagram of utilization function LR [x, y] with the nearest background pixel of TD [x, y] search;

Figure 12 searches for the synoptic diagram of nearest background pixel for adopting the contour searching method.

Embodiment

To combine the accompanying drawing in the embodiment of the invention below, the technical scheme in the embodiment of the invention is carried out clear, intactly description, obviously, described embodiment only is the present invention's part embodiment, rather than whole embodiment.Based on the embodiment among the present invention, those of ordinary skills are not making the every other embodiment that is obtained under the creative work prerequisite, all belong to the scope of the present invention's protection.

Among all embodiment of the present invention (x, y) with [x, y] in x represent the row in the two-dimentional two-value picture, do not represent horizontal ordinate, (x, y) with [x, y] in y represent the row in the two-value picture, do not represent ordinate.Pixel (x for example ₀, y ₀) represent the x of this pixel in the two-value picture ₀OK, y ₀Row.

Embodiment one

See also accompanying drawing 1, be the process flow diagram of the method for the complete range conversion of the disclosed first kind of three-dimensional bianry image of the embodiment of the invention, this method can comprise:

Step S101: with three-dimensional bianry image along two-dimentional two-value picture that is divided into corresponding number wherein;

Concrete, along the x axle, can become m to open two-dimentional two-value picture three-dimensional binary image segmentation, along the y axle, can become n to open two-dimentional two-value picture three-dimensional binary image segmentation, along the z axle, can become s to open two-dimentional two-value picture three-dimensional binary image segmentation.

Step S101 is that prior art is not given unnecessary details at this.

Step S102: the two dimension range conversion fully of each pixel in each two-dimentional two-value picture of computed segmentation respectively;

Can utilize complete range conversion method of the prior art to calculate the complete range conversion of each pixel in each two-dimentional two-value picture.

The range conversion of preferably, calculating a two-dimentional two-value picture (supposes that two-dimentional two-value picture is of a size of m * n, and m >=1; N >=1), at first calculates the complete range conversion of (1,1) in first row; Calculate the complete range conversion of (1,2) then, be calculated to (1 successively according to from left to right order; N), calculate the complete range conversion of (2,1) in second row again; Be calculated to successively from left to right (2, n), just according to the complete range conversion of each pixel in from top to bottom the order computation two-value picture from left to right.

Step S102 can comprise:

S1021: confirm first function or second function;

Step S1021 is a pre-treatment step, needn't all carry out at every turn.

First function is used for the position of the nearest background pixel of definite capable middle distance the 4th pixel of two-dimentional two-value picture i; Second function is used for the position of the nearest background pixel of definite two-dimentional two-value picture j row middle distance the 4th pixel, wherein, and 1≤i≤m; 1≤j≤n, i and j are integer.

It is capable to suppose that the 4th pixel is positioned at the x of two-dimentional two-value picture, and the y row are with (x, y) expression the 4th pixel is in the position of two-dimentional two-value picture, so that (x y) be separation, with capable left side and the right side of being divided into of x, y is listed as is divided into the above and below.

The method of confirming first function specifically comprises:

Confirm to be used to calculate the capable left side of said two-dimentional two-value picture x distance the 4th pixel (x; Y) first subfunction of nearest background pixel place columns; And be used to calculate the capable right side of said two-dimentional two-value picture x apart from the 4th pixel (x, y) second subfunction of nearest background pixel place columns.Wherein, 1≤x≤m, 1≤y≤n.

According to first subfunction and second subfunction, confirm first function.

Confirm that second function specifically comprises: confirm to be used to calculate the said two-dimentional two-value picture y side of listing distance the 4th pixel (x; Y) the 3rd subfunction of nearest background pixel place line number; And be used for calculating said two-dimentional two-value picture y row below apart from the 4th pixel (x, y) the 4th subfunction of nearest background pixel place line number.

According to the 3rd subfunction and the 4th subfunction, confirm second function.

Concrete, confirm that the first method of first function and second function is specially:

Said first subfunction is specially L [x, y]:

$L[x,y]=\left\{\begin{array}{cc}y& I(x,y)=0\\ L[x,y-1]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and y=1, so L (x, y)=-Maxlable;

Said second subfunction is specially R [x, y]:

$R[x,y]=\left\{\begin{array}{cc}y& I(x,y)=0\\ R[x,y+1]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and y=n, R [x, y]=Maxlable so;

Then be specially SZ [x, y] according to said first subfunction and definite said first function of said second subfunction:

<math> <mrow> <mi>SZ</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>L</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> </mtd> <mtd> <mi>y</mi> <mo>-</mo> <mi>L</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&lt;;</mo> <mi>R</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>R</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> </mtd> <mtd> <mi>y</mi> <mo>-</mo> <mi>L</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&amp;GreaterEqual;</mo> <mi>R</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow></math>

Said the 3rd subfunction is specially T [x, y]:

$T[x,y]=\left\{\begin{array}{cc}x& I(x,y)=0\\ T[x-1,y]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and x=1, so T [x, y]=-Maxlable;

Said the 4th subfunction is specially D [x, y]:

$D[x,y]=\left\{\begin{array}{cc}x& I(x,y)=0\\ D[x+1,y]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and x=m, D [x, y]=Maxlable so;

Then be specially ZS [x, y] according to said the 3rd subfunction and definite said second function of said the 4th subfunction:

<math> <mrow> <mi>ZS</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>T</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> </mtd> <mtd> <mi>x</mi> <mo>-</mo> <mi>D</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&lt;;</mo> <mi>T</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <mi>D</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> </mtd> <mtd> <mi>x</mi> <mo>-</mo> <mi>D</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&amp;GreaterEqual;</mo> <mi>T</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>x</mi> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow></math>

The second method of confirming first function and second function is specially:

Said first subfunction is specially L [x, y]:

$L[x,y]=\left\{\begin{array}{cc}y& I(x,y)=0\\ L[x,y-1]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and y=1, so L (x, y)=-Maxlable;

Said second subfunction is specially R [x, y]:

$R[x,y]=\left\{\begin{array}{cc}y& I(x,y)=0\\ R[x,y+1]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and y=n, R [x, y]=Maxlable so;

Then be specially LR [x, y] according to said first subfunction and definite said first function of said second subfunction:

<math> <mrow> <mi>LR</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>-</mo> <mi>L</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mtd> <mtd> <mi>y</mi> <mo>-</mo> <mi>L</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&lt;;</mo> <mi>R</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <msup> <mrow> <mo>(</mo> <mi>R</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>y</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mtd> <mtd> <mi>y</mi> <mo>-</mo> <mi>L</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&amp;GreaterEqual;</mo> <mi>R</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow></math>

Said the 3rd subfunction is specially T [x, y]:

$T[x,y]=\left\{\begin{array}{cc}x& I(x,y)=0\\ T[x-1,y]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and x=1, so T [x, y]=-Maxlable;

Said the 4th subfunction is specially D [x, y]:

$D[x,y]=\left\{\begin{array}{cc}x& I(x,y)=0\\ D[x+1,y]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and x=m, D [x, y]=Maxlable so;

Then be specially TD [x, y] according to said the 3rd subfunction and definite said second function of said the 4th subfunction:

<math> <mrow> <mi>TD</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <mi>T</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mtd> <mtd> <mi>x</mi> <mo>-</mo> <mi>T</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&lt;;</mo> <mi>D</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <msup> <mrow> <mo>(</mo> <mi>D</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>x</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mtd> <mtd> <mi>x</mi> <mo>-</mo> <mi>T</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&amp;GreaterEqual;</mo> <mi>D</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>x</mi> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow></math>

Wherein, I (x y)=1 is expressed as object pixel, I (x y)=0 is expressed as background pixel, and Maxlable is preset maximum mark value, wherein, $\mathrm{Maxlable}=(1+\sqrt{2})\mathrm{Max}(m,n).$

S1022: according to the complete distance of the 3rd object pixel and the 4th pixel, reach the 3rd object pixel and the complete distance of the two dimension that leaves its nearest background pixel, confirm the second nearest background pixel scope of the 4th pixel.

Wherein, the 4th pixel and the 3rd object pixel all are arranged in same two-dimentional two-value picture;

In order to improve computing velocity, before confirming the second background pixel scope, can also comprise:

Calculate LR [x, y]; Be not more than at LR [x, y] under 1 the situation, said first fully distance be LR [x, y], LR [x, y] greater than 1 situation under, carry out definite second nearest background pixel scope step.

Perhaps, calculate TD [x, y]; Be not more than at TD [x, y] under 1 the situation, second fully distance be TD [x, y], TD [x, y] greater than 1 situation under, carry out definite second nearest background pixel scope step.

If (x, y)=0 perhaps TD [x, y]=(x y) is background pixel to 0 explanation the 4th pixel to LR.(x, y)=1 (there is background pixel in x in level 2 neighborhoods y) to explanation the 4th pixel, and promptly second fully apart from being 1, if TD [x, y]=(there is background pixel in x in vertical 2 neighborhoods y) to 1 explanation the 4th pixel, and promptly the second complete distance is 1 as if LR.

Before confirming the second background pixel scope, can also comprise:

Calculate (y-SZ [x, y]) ²At (y-SZ [x, y]) ²Be not more than under 1 the situation, second fully distance be (y-SZ [x, y]) ², at (y-SZ [x, y]) ²Under 1 situation, carry out and confirm the second nearest background pixel scope step.

Or, calculate (x-ZS [x, y]) ²At (x-ZS [x, y]) ²Be not more than under 1 the situation, second fully distance be (x-ZS [x, y]) ², at (x-ZS [x, y]) ²Under 1 situation, carry out and confirm the second nearest background pixel scope step.

Utilize the first function nearest background pixel of detection range the 4th pixel in every row of the second nearest background pixel scope respectively, or utilize the second function nearest background pixel of detection range the 4th pixel in every row of the second nearest background pixel scope respectively;

From the nearest background pixel of distance the 4th pixel that searches out, determine second background pixel nearest with the 4th pixel distance; Calculate the second complete distance of second background pixel and the 4th pixel, and with second fully distance as the two dimension of the 4th pixel in the two-dimentional two-value picture at its place range conversion value fully.

The 4th pixel can be the arbitrary pixel that is arranged in two-dimentional two-value picture, just just claim that in order to narrate conveniently arbitrary pixel is the 4th pixel.

When the 4th pixel was background pixel, the nearest background pixel of distance the 4th pixel was exactly itself.

Suppose that the position of above-mentioned the 4th pixel in two-dimentional two-value picture is (x; Y); Because first subfunction is to be used to calculate the arbitrary pixel of the capable left side distance of two-dimentional two-value picture x (second subfunction is used to calculate the arbitrary pixel of two-dimentional two-value picture x capable right side distance (x for x, the y) columns at nearest background pixel place; Y) columns at nearest background pixel place; So the SZ [x, y] that obtains according to first subfunction and second subfunction also be used for confirming x capable on the arbitrary pixel of distance (x, y) columns at nearest background pixel place.

(x, y) above-mentioned the 4th pixel of expression utilize first function to search for i capable (the middle distance O of i ≠ x) (x, y) nearest background pixel with O; Be exactly in fact utilize first function search for the capable middle distance of i (i, so y) nearest background pixel is when execution in step S102; Being actually the function S Z [i, y] that the middle x of the first function S Z [x, y] is replaced to i searches for; Function S Z [i, y] is actually search at the capable middle distance of i (i, y) nearest background pixel; Since the capable middle distance of i (i, y) nearest background pixel is exactly apart from O (x, y) nearest background pixel; So function S Z [i, y] still is used to search for each row middle distance O (x, y) nearest background pixel in essence.

As shown in Figure 2, proof procedure is following: suppose L ₁, L ₂, R ₁, R ₂Be four background pixels of i on capable, and they and O (x, distance y) is respectively | OL ₁|, | OL ₂|, | OR ₁|, | OR ₂|, can know that by geometric knowledge (x, y) nearest background pixel obviously is exactly that ((x, y) position of nearest background pixel is (i, SZ [i, y]) to the capable middle distance O of i to distance for i, y) nearest background pixel apart from O.

In like manner, utilize second function search for j row (among the j ≠ y) apart from O (x, y) nearest background pixel is exactly to utilize second function to search for j row middle distance (x in fact; J) nearest background pixel is so when execution in step S102, be actually the second function ZS [x; Y] in the y function ZS [x, j] that replaces to j search for j row middle distance O (x; Y) position of nearest background pixel be (ZS [x, j], j).Wherein, 1≤i≤m, 1≤j≤n, i and j are positive integer.

Confirm that the second nearest background pixel scope specifically comprises:

At first, calculate the 3rd object pixel O ₃With from its nearest background pixel B ₀Two dimension fully apart from r ₃

Secondly, confirm the 4th pixel O ₄With the 3rd object pixel O ₃Complete in r ₄

Calculate fully apart from r ₃Can calculate through method of the prior art.Distance the 3rd object pixel O ₃Nearest background pixel has a plurality of, only gets one of them background pixel B according to actual conditions ₀Get final product.

Preferably, the 4th pixel O ₄Be positioned at the 3rd object pixel O ₃The neighbours territory in, such the 4th pixel O ₄With the 3rd object pixel O ₃Complete in r ₄=1.Certainly, the 4th pixel O ₄The position be not restricted to the 3rd object pixel O ₃Four fields in, the 4th pixel O ₄Particular location do not influence the realization of the embodiment of the invention, so not to the 4th pixel O ₄Particular location do concrete qualification.

At last, according to complete apart from r ₃And fully apart from r ₄Confirm the 4th pixel O ₄The second nearest background pixel scope.

Referring to Fig. 3, be first kind of second nearest background pixel scope synoptic diagram, the round O among the figure ₄For being the center of circle, with r with the 4th pixel ₃+ r ₄Round O for radius ₄, because digital picture has discreteness, determining accurate is that the border circular areas on border is very consuming time with the circular arc, so the second nearest background pixel scope is to justify O ₄The zone that circumscribed square surrounded.

Referring to Fig. 4, be second kind of second nearest background pixel scope synoptic diagram, the second nearest background pixel scope is with said the 3rd object pixel O ₃Be the center of circle, with r ₃Round O for radius ₅In connect the square with the circle O ₄The zone that circumscribed square surrounded;

Referring to Fig. 5, be the third second nearest background pixel scope synoptic diagram, the second nearest background pixel scope is circle O ₆Circumscribed square with the circle O ₄In connect the annular region that surrounded of square.

Circle O ₆Be to be the center of circle with said the 4th pixel, with | r ₃-r ₄| be the circle of radius.

If the 4th pixel is positioned at the marginal position of two-dimentional two-value picture; When confirming the second nearest background pixel scope; The initial second nearest background pixel scope of confirming may some exceed two-dimentional two-value picture, and the common factor that can get initial second definite nearest background pixel scope and two-dimentional two-value picture this moment is as the second nearest background pixel scope.

Step S103: according to the complete distance of second object pixel and first pixel, reach the three-dimensional fully range conversion value of said second object pixel in three-dimensional bianry image, confirm the first nearest background pixel scope of first pixel;

Second object pixel is arbitrary object pixel in the three-dimensional bianry image.

Confirm that the first nearest background pixel scope can comprise:

Confirm that the three-dimensional fully range conversion value of second object pixel in three-dimensional bianry image is r ₁

Confirm the first pixel O ₁With the second object pixel O ₂Complete in r ₂

The first nearest background pixel scope is with the first pixel O ₁Be the centre of sphere, with r ₁+ r ₂Ball O for radius ₁The zone that circumscribed square surrounded;

Or the first nearest background pixel scope is with the second object pixel O ₂Be the centre of sphere, with r ₁Ball O for radius ₂In meet square and ball O ₁The zone that circumscribed square surrounded;

Or the first nearest background pixel scope is with the said first pixel O ₁Be the centre of sphere, with | r ₁-r ₂| be the ball O of radius ₃In meet square and said ball O ₁The zone that circumscribed square surrounded.

If first pixel is positioned at the marginal position of three-dimensional bianry image; When confirming the first nearest background pixel scope; The initial first nearest background pixel scope of confirming may some exceed three-dimensional bianry image, and the common factor that can get initial first definite nearest background pixel scope and three-dimensional bianry image this moment is as the first nearest background pixel scope.

Step S104: confirm first pixel two dimension range conversion value fully of the projected pixel in each the two-dimentional two-value picture in the first nearest background pixel scope respectively;

See also Fig. 6, suppose that (x, y z) are a object pixel on the two-dimentional two-value picture z, pixel O to pixel O ₀(x, y, z ₀) be that (x, y is z) at two-dimentional two-value picture z for O ₀On projected pixel, be located at two-dimentional two-value picture z ₀Go up apart from pixel O ₀(x, y, z ₀) nearest background pixel B ₀With pixel O ₀(x, y, z ₀) two dimension fully the range conversion value square do | O ₀B ₀| ², so two-dimentional two-value picture z ₀Upward (z) nearest background pixel obviously also is B for x, y apart from pixel O ₀, and $\left|{\mathrm{<figure-callout\; id="0"\; label="OB"\; filenames="HDA00001791446100052.png"\; state="\{\{state\}\}">OB</figure-callout>}}_0\right|=\sqrt{{\left|O_0{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="HDA00001791446100052.png"\; state="\{\{state\}\}">B</figure-callout>}}_0\right|}^2+{\left|\mathrm{<figure-callout\; id="0"\; label="O\; O"\; filenames="HDA00001791446100052.png"\; state="\{\{state\}\}">O</figure-callout>}{O}_{}{}_0\right|}^2}.$

Suppose that three-dimensional bianry image is divided into s along the z axle and opens two-dimentional two-value picture, the first nearest background pixel scope is with the first pixel O ₁Be the centre of sphere, with r ₁+ r ₂Ball O for radius ₁The zone that circumscribed square surrounded, see also Fig. 7, be the synoptic diagram of the first nearest background pixel scope, the r=r among Fig. 7 ₁+ r ₂, B is ball O ₁On a pixel, represent O with O among the figure ₁, can find out that by Fig. 7 the first nearest background pixel scope can regard as by 2 (r ₁+ r ₂)+1 pictures is formed by stacking along the z axle, supposes the first pixel O ₁The two-dimentional two-value picture at place is z ₀, preferred, at first confirm two-dimentional two-value picture z ₀In first pixel two dimension fully the range conversion value (this moment, first pixel was at two-dimentional two-value picture z ₀On projected pixel be exactly itself), secondly confirm that first pixel is respectively at two-dimentional two-value picture z ₀The complete range conversion value of the two dimension of projected pixel in ± 1 confirms that again first pixel is respectively at two-dimentional two-value picture z ₀The complete range conversion value of the two dimension of projected pixel in ± 2 is until two-dimentional two-value picture z ₀± (r ₁+ r ₂).Promptly with two-dimentional two-value picture z ₀The two dimension of confirming the projected pixel of first pixel in each two-dimentional two-value picture from the inside to surface successively respectively along the z direction of principal axis for symcenter is the range conversion value fully, supposes at two-dimentional two-value picture z ₀+ r _xOn determine first pixel at two-dimentional two-value picture z ₀+ r _xIn projected pixel two dimension fully the variable in distance value square be DR _x ², r _x∈ [(r ₁+ r ₂), r ₁+ r ₂], because at two-dimentional two-value picture z ₀± (r _x+ 1) minimum value of the square distance of the nearest background pixel of middle distance first pixel and first pixel is (r _x+ 1) ²So, work as DR _x ²+ r _x ²≤(r _x+ 1) ²The time, stop to confirm that first pixel is respectively at two-dimentional two-value picture z ₀± (r _x+ 2) until two-dimentional two-value picture z ₀± (r ₁+ r ₂) in the complete range conversion value of two dimension of projected pixel, if DR _x ²+ r _x ²>(r _x+ 1) ², continue then to confirm that first pixel is respectively at two-value picture z ₀± (r _xThe two dimension of the projected pixel+2) is the range conversion value fully, until arriving two-dimentional two-value picture z ₀± (r ₁+ r ₂).

The first nearest background pixel scope can be regarded as by 2 (r ₁+ r ₂)+1 pictures is formed by stacking along the z axle; And probably the nearest background pixel of the projected pixel of certain Zhang Erwei two-value picture middle distance first pixel not in the first nearest background pixel scope; But this does not influence the realization of the embodiment of the invention, so do not distinguish at this.

Step S105: according to first pixel of the confirming two dimension of the projected pixel of each two-dimentional bianry image range conversion value fully in first background pixel respectively; Determine at the first nearest background pixel of three-dimensional bianry image middle distance first pixel; Calculate the first complete distance of first background pixel and first pixel, and with the three-dimensional fully range conversion value of this first complete distance as first pixel.

Suppose that the position of first pixel in three-dimensional bianry image is for (x, y z), because the complete distance of the two dimension of each pixel in each two-dimentional two-value picture has all calculated, suppose DR _xExpression is from two-dimentional bianry image z _xMiddle distance first pixel is at two-dimentional bianry image z _xIn the square value of the nearest background pixel of projected pixel, wherein footmark x represent first pixel projected pixel at two-dimentional bianry image z _xOn, step S105 specifically comprises so:

Utilize formula min{DR _x ²+ | z _x-z| ², z wherein _xThe span of z axle is determined first background pixel nearest with first pixel distance in the ∈ first nearest background pixel scope, utilizes formula again

Obtain the first complete distance.

Preferably; When calculating the three-dimensional range conversion fully of each pixel in each two-dimentional two-value picture; Suppose that three-dimensional bianry image is divided into s along the z axle and opens two-dimentional two-value picture, it is [1, s] that this s opens the scope of two-dimentional two-value picture in the z axle; Then at first calculate the three-dimensional range conversion fully of each pixel each two-dimentional two-value picture from two-dimentional two-value picture z=1; Secondly, calculate the three-dimensional range conversion fully of each pixel among the two-dimentional two-value picture z=2, calculate the three-dimensional range conversion fully of each pixel among the two-dimentional two-value picture z=3 again; And the like the three-dimensional range conversion fully of each pixel in having calculated two-dimentional two-value picture z=s, promptly be calculated to the maximal value of z by the minimum value of z in the two-dimentional two-value picture.

The method of the complete range conversion of quick three-dimensional bianry image that the employing embodiment of the invention provides; At first under the situation of the three-dimensional range conversion fully of known second object pixel; Can be according to the three-dimensional fully range conversion value of the second target phase pixel in three-dimensional bianry image; Confirming the first nearest background pixel scope of first pixel, during the nearest background pixel of detection range first pixel, is in the first nearest background pixel scope, to search for again; Rather than in whole bianry image, search for, thereby improved the speed of searching for nearest background pixel; Secondly; Behind the first nearest background pixel of the distance that searches out first pixel, calculate the first complete distance of first background pixel and first pixel again, be not to search out the distance of just calculating this background pixel and first pixel behind the background pixel; Thereby reduced calculated amount; Improved computing velocity, and in whole search procedure and computation process, all do not carried out approximate processing, thus calculate high apart from accuracy.

Embodiment two

See also Fig. 8, the two dimension of each pixel schematic flow sheet of range conversion method fully in each two-dimentional two-value picture of a kind of respectively computed segmentation that provides for the embodiment of the invention, i.e. the implementation method of step S102 among the embodiment one, this method can comprise:

Step S801: based on the complete distance of the 3rd object pixel and the 4th pixel; And the 3rd object pixel and the distance that leaves its nearest background pixel; Confirm the second nearest background pixel scope of the 4th pixel; And the second nearest background pixel scope is divided into first son background pixel range set and second son background pixel range set recently recently according to preset rules; First son background pixel range set recently comprises at least one first son background pixel scope recently; Line number in the nearest background pixel scope of said at least one height is not more than columns, and second son background pixel range set recently comprises at least one second son background pixel scope recently, and the line number in said at least one second sub background pixel scope recently is greater than columns;

Before step S801, also comprise: calculate LR [x, y] and TD [x, y]; At LR [x, y] or TD [x, y]

Be not more than under 1 the situation, said second fully distance be min{LR [x, y], TD [x, y] }, at LR [x, y]

And TD [x, y] gets into step S802 all greater than under 1 the situation.

If (x, y)=0 perhaps TD [x, y]=(x y) is background pixel to 0 explanation the 4th pixel to LR.(x, y)=1 (there is background pixel in x in level 2 neighborhoods y) to explanation the 4th pixel, and promptly second fully apart from being 1, if TD [x, y]=(there is background pixel in x in vertical 2 neighborhoods y) to 1 explanation the 4th pixel, and promptly the second complete distance is 1 as if LR.

The second nearest background pixel scope such as Fig. 4 or the second nearest background pixel scope shown in Figure 5; Extend to the border of circumscribed square the interior line segment that connects a foursquare opposite side crossing; Here be that example is divided with second kind of second nearest background pixel scope; As shown in Figure 9, be the division synoptic diagram of the second nearest background pixel, dot-and-dash line is circle O ₃In connect the extended line of a square opposite side; This opposite side is divided into four nearest background pixel scopes of son up and down with the second nearest background pixel scope; Be referred to as upper area, lower zone, left zone and right-hand zone; Obviously up in zone and the lower zone line number less than columns, in left zone and right-hand regional midrange less than line number.Certainly, also can use round O ₃In connect the square another opposite side extended line, nearest background pixel scope is divided into four zones up and down.

Preset rules is meant circle O ₃In connect a foursquare opposite side line segment extend to the border of circumscribed square and intersect, this opposite side is divided into four nearest background pixel scopes of son up and down with the second nearest background pixel scope.

First son background pixel range set recently comprises: upper area and lower zone; Second son background pixel range set recently comprises: left zone and right-hand zone.

Step S802: utilize first function nearest background pixel of detection range the 4th pixel in every row of the nearest background pixel range set of first son, utilize second function nearest background pixel of detection range the 4th pixel in every row of the nearest background pixel range set of second son;

When the line number of the nearest background pixel range set of first son is not more than columns; Utilize first function to search for, used search time is few, at second son when recently the line number of background pixel range set is greater than columns; Utilize second function to search for, used search time is few.

Step S803: from the nearest background pixel of distance the 4th pixel that searches out, determine second background pixel nearest with the 4th pixel distance; Calculate the second complete distance of second background pixel and the 4th pixel, and with the two-dimentional fully range conversion value of this second complete distance as the 4th pixel.

Adopt the embodiment of the invention; Because the second nearest background pixel scope is divided according to pre-defined rule; Because first son line number of background pixel range set recently is not more than columns; Utilize first function nearest background pixel of detection range the 4th pixel in every row of the nearest background pixel range set of first son, because the line number of the nearest background pixel range set of second son, is utilized second function nearest background pixel of detection range the 4th pixel in every row of the nearest background pixel range set of second son greater than columns; More accelerate search speed, thereby improved computing velocity.

Embodiment three

See also Figure 10, the two dimension of each pixel schematic flow sheet of range conversion method fully in each two-dimentional two-value picture of a kind of respectively computed segmentation that provides for the embodiment of the invention, i.e. step S102 implementation method among the embodiment one, this method can comprise:

Step S1001: according to the complete distance of the 3rd object pixel and the 4th pixel, reach the 3rd object pixel and the complete distance of the two dimension that leaves its nearest background pixel, confirm the second nearest background pixel scope of the 4th pixel;

Step S1002: utilize first function and the second function nearest background pixel of detection range the 4th pixel in every layer of the second nearest background pixel scope respectively;

The foursquare border that it is the center that every layer of the second nearest background pixel scope is meant with said the 4th pixel or said the 3rd object pixel.

Concrete, utilize first function and second function from r _xLayer begins search until at r _x+ k layer searches the nearest background pixel of distance the 4th pixel, r _xLayer is nearest one deck of distance the 4th pixel in the nearest background pixel scope, k=0,1,2 ... Q-1, a total q layer in the second nearest background pixel scope;

From at r _xIn the nearest background pixel of distance the 4th pixel that+k layer searches out, determine r _xThe background pixel that+k layer middle distance the 4th pixel is nearest, and write down r _xThe background pixel that the 4th pixel of distance described in the+k layer is nearest and the complete square distance value of the 4th pixel

Relatively

With (r _x+ k+1) ²+ (r _x+ k) ², when The time, stop search, when

The time, continue search one deck down, until the search r that finishes _x+ q-1 layer finishes.

The second nearest background pixel scope with as shown in Figure 5 is an example, and S1002 describes to step, and each layer of the second nearest background pixel all is with O<sub >4</sub>Be the foursquare border at center, half of this square length of side is exactly the number of plies of this layer, the method that the thought that adopts the contour search is searched in background pixel scope recently for from<img file="BDA00001791446000185.GIF" he="94" img-content="drawing" img-format="GIF" inline="yes" orientation="portrait" wi="231" />Layer (half of the inscribed square length of side) beginning successively scans up to r<sub >1</sub>+ r<sub >2</sub>Layer (half of the circle circumscribed square length of side) finishes, and supposes scanning r<sub >x</sub>Layer, wherein<img file="BDA00001791446000186.GIF" he="96" img-content="drawing" img-format="GIF" inline="yes" orientation="portrait" wi="497" />Referring to Figure 11, for the synoptic diagram of utilization function LR [x, y], for r with the nearest background pixel of TD [x, y] search<sub >x</sub>Pixel on the layer is divided into R along x, y direction with it respectively<sub >1</sub>(with dashed lines area surrounded in the drawings), R<sub >2</sub>(using the dot-and-dash line area surrounded in the drawings), R<sub >3</sub>(area surrounded is realized in the left side in the drawings) and R<sub >4</sub>(right side realization area surrounded in the drawings) four groups, the element in being prone to know these four groups is respectively (x-r<sub >x</sub>) OK, (x+r<sub >x</sub>) OK, (y-r<sub >x</sub>) row, (y+r<sub >x</sub>) list the part of pixel.At (x-r<sub >x</sub>) row mid-range objectives pixel O nearest background pixel (is designated as B<sub >X1</sub>) coordinate do<img file="BDA00001791446000187.GIF" he="71" img-content="drawing" img-format="GIF" inline="yes" orientation="portrait" wi="509" />Or<img file="BDA00001791446000188.GIF" he="71" img-content="drawing" img-format="GIF" inline="yes" orientation="portrait" wi="535" />If<img file="BDA00001791446000189.GIF" he="55" img-content="drawing" img-format="GIF" inline="yes" orientation="portrait" wi="356" />Then show B<sub >X1</sub>∈ R<sub >1</sub>, i.e. R<sub >1</sub>In have background pixel, in like manner if LR [x+r<sub >x</sub>, y]<r<sub >x</sub><sup >2</sup>, TD [x, y-r<sub >x</sub>]<r<sub >x</sub><sup >2</sup>TD [x<sub >x</sub>, y+r]<r<sub >x</sub><sup >2</sup>, then show R respectively<sub >2</sub>, R<sub >3</sub>, R<sub >4</sub>In have background pixel, establish tD=min{LR [x-r<sub >x</sub>, y], LR [x+r<sub >x</sub>, y], TD [x, y-r<sub >x</sub>], TD [x<sub >x</sub>, y+r] }, note r<sub >x</sub>The distance of nearest background pixel of distance the 4th pixel and the 4th pixel square is DT on the layer<sub >x</sub><sup >2</sup>=tD+r<sub >x</sub><sup >2</sup>, because at r<sub >x</sub>The minimum value of tD is (r in+1 layer<sub >x</sub>+ 1)<sup >2</sup>So, as tD≤(r<sub >x</sub>+ 1)<sup >2</sup>The time, stop search, perhaps judge<img file="BDA000017914460001810.GIF" he="71" img-content="drawing" img-format="GIF" inline="yes" orientation="portrait" wi="426" />When<img file="BDA000017914460001811.GIF" he="71" img-content="drawing" img-format="GIF" inline="yes" orientation="portrait" wi="384" />In time, stop search.

Referring to Figure 12; Search for the synoptic diagram of nearest background pixel for adopting the contour searching method; Suppose that needing the 4th pixel of computed range conversion is object pixel A, on behalf of ground floor, numeral 2, numeral 1 represent the 2nd layer, digital 3 to represent the 3rd layer and digital 4 to represent the 4th layer, only draw four layers among the figure among the figure; But in practical application, might not be four layers, suppose at r _x, search a background pixel B at=2 o'clock ₄, obvious background pixel B ₄With the distance of object pixel A do

But

Square value 18 greater than (3+1) ²So, need to continue the 3rd layer of search, at r _x, search two background pixel B at=3 o'clock ₁With B ₃, because background pixel B ₁With the distance of object pixel A do

Obvious 13 less than (4+1) ²So, stopping the search of one deck down, the nearest background pixel of distance first pixel that utilizes this moment first function and second function in nearest background pixel scope, to search has B ₁, B ₃And B ₄

Above-mentioned is to be example with nearest background pixel scope shown in Figure 4, and to the explanation that step S1002 carries out, if the second nearest background pixel is with shown in Figure 2, every layer of the second nearest background pixel scope is meant with O ₄Be the foursquare border at center, the method that the thought that adopts contour to search for is so searched in nearest background pixel scope is: since the 1st layer (promptly 8 fields from the center of circle begin), successively scan up to r ₁+ r ₂Layer (half of the circle circumscribed square length of side) finishes; If the second nearest background pixel is with shown in Figure 3, every layer of the second nearest background pixel scope is meant with O ₃Form for the square at center, the method that the thought that adopts the contour search is so searched in background pixel scope recently is: since the 1st layer of 8 fields of the center of circle (promptly from) beginning, when being scanned up to r ₁(r during layer ₁Layer is circle O ₃The circumscribed square length of side half the), the left side of the second nearest background pixel scope has been searched for and has been finished, every layer of this second nearest background pixel scope is by with O ₃For the border of the dot-dash wire frame as shown in Figure 3 at center, from r ₁Search for up to r for+1 layer ₁+ r ₂Layer.

Step S1003: from the nearest background pixel of distance the 4th pixel that searches out, determine second background pixel nearest with the 4th pixel distance; Calculate the second complete distance of second background pixel and the 4th pixel, and with the two-dimentional fully range conversion value of this second complete distance as the 4th pixel.

Fully distance is meant the bee-line of this second background pixel and the 4th pixel, i.e. air line distance, range conversion value are meant and the nearest background pixel of object pixel and the distance value of this object pixel.

Concrete; Step S1003 comprises: based on the nearest background pixel of said the 4th pixel of distance of record and the complete square distance value of said the 4th pixel, determine and nearest second background pixel of the 4th pixel distance and the second complete square distance value of the 4th pixel; The said second complete square distance value evolution is obtained the said second complete distance.

Note r _xThe distance of nearest background pixel of distance the 4th pixel and the 4th pixel square does on+the k layer Only suppose to have found the nearest background pixel of distance the 4th pixel at the 3rd layer, the 4th layer and layer 5, then step S1003 specifically comprises:

Utilize formula

to determine second background pixel nearest with the 4th pixel distance, utilize formula again:

calculates the second complete distance.

The method that the embodiment of the invention provides not only has the beneficial effect of embodiment one, and owing to be to utilize first function and second function in every layer of background pixel recently, to search for, so more accelerated search speed.

Further understand the advantage of the embodiment of the invention for those skilled in the art; The inventor uses the complete range conversion of each pixel in the said method Calculation of Three Dimensional bianry image; And use prior art that the three-dimensional bianry image of same pair is carried out complete range conversion, and the two operation result is compared.

Prior art is meant Euclidean distance transform of digital images in arbitrary dimensions.PCM 2006, LNCS, 2006, the method for putting down in writing among the 4261:72-79.

As shown in table 1, be (the unit: working time of the complete range conversion of prior art Calculation of Three Dimensional second) with the time contrast form that utilizes the complete range conversion of this method Calculation of Three Dimensional.

Table 1

From table 1, can find out; Image to different size carries out range conversion; The time of the method operation that the time that prior art is carried out three-dimensional range conversion fully all provides than the embodiment of the invention is long; In order to express more intuitively high this theory of method efficient of the three-dimensional range conversion fully of carrying out that the embodiment of the invention provides, give the ratio of the time of " method that prior art/embodiment of the invention provides " operation in the table 1.

Each embodiment adopts the mode of going forward one by one to describe in this instructions, and what each embodiment stressed all is and the difference of other embodiment that identical similar part is mutually referring to getting final product between each embodiment.For the disclosed device of embodiment, because it is corresponding with the embodiment disclosed method, so description is fairly simple, relevant part is partly explained referring to method and is got final product.

The method of describing in conjunction with embodiment disclosed herein or the step of algorithm can be directly with the software modules of hardware, processor execution, and perhaps the combination of the two is implemented.Software module can place the storage medium of any other form known in random access memory (RAM), internal memory, ROM (read-only memory) (ROM), electrically programmable ROM, electrically erasable ROM, register, hard disk, moveable magnetic disc, CD-ROM or the technical field.

To the above-mentioned explanation of the disclosed embodiments, make this area professional and technical personnel can realize or use the present invention.Multiple modification to these embodiment will be conspicuous concerning those skilled in the art, and defined General Principle can realize under the situation that does not break away from the spirit or scope of the present invention in other embodiments among this paper.Therefore, the present invention will can not be restricted to these embodiment shown in this paper, but will meet and principle disclosed herein and features of novelty the wideest corresponding to scope.

Claims (10)

1. the method for the complete range conversion of a three-dimensional bianry image, said three-dimensional bianry image is of a size of m * n * s, it is characterized in that, comprising:

With said three-dimensional bianry image along two-dimentional two-value picture that is divided into corresponding number wherein;

The two dimension range conversion fully of each pixel in each two-dimentional two-value picture of computed segmentation respectively;

Based on second object pixel and the complete distance that needs first pixel of the complete range conversion of Calculation of Three Dimensional; Reach the three-dimensional fully range conversion value of said second object pixel in said three-dimensional bianry image, confirm the first nearest background pixel scope of said first pixel;

Confirm the complete range conversion value of two dimension of the projected pixel in said first pixel each two-dimentional two-value picture in the said first nearest background pixel scope;

According to the two dimension of the projected pixel of said definite first pixel each two-dimentional bianry image in said first nearest background pixel scope range conversion value fully; Determine the first nearest background pixel of said first pixel of said three-dimensional bianry image middle distance; Calculate the first complete distance of said first background pixel and said first pixel, and with the three-dimensional fully range conversion value of the said first complete distance as said first pixel.

2. according to the said method of claim 1, it is characterized in that the three-dimensional fully range conversion value of said second object pixel in said three-dimensional bianry image is r ₁, said complete distance, and the three-dimensional fully range conversion value of said second object pixel in said three-dimensional bianry image according to second object pixel and first pixel, confirm that the first nearest background pixel scope of said first pixel specifically comprises:

Confirm the complete of said first pixel and said second object pixel apart from r ₂

The said first nearest background pixel scope is for being the centre of sphere with said first pixel, with r ₁+ r ₂Ball O for radius ₁The zone that circumscribed square surrounded; Or the said first nearest background pixel scope is for being the centre of sphere with said second object pixel, with r ₁Ball O for radius ₂In meet square and said ball O ₁The zone that circumscribed square surrounded; Or the said first nearest background pixel scope is for being the centre of sphere with said first pixel, with | r ₁-r ₂| be the ball O of radius ₃In meet square and said ball O ₁The zone that circumscribed square surrounded.

3. according to the said method of claim 2, it is characterized in that said three-dimensional bianry image is divided into s along the z axle and opens two-dimentional two-value picture, the said first nearest background pixel scope is to be the centre of sphere with said first pixel, with r ₁+ r ₂Ball O for radius ₁The zone that circumscribed square surrounded, the two-dimentional two-value picture at said first pixel place is z ₀, the two dimension of the projected pixel in said definite said first pixel each two-dimentional two-value picture in said first nearest background pixel scope range conversion value fully specifically comprises:

With said two-dimentional two-value picture z ₀For symcenter confirms successively from the inside to surface that along the z direction of principal axis said first pixel is at two-dimentional two-value picture z ₀+ r _xIn the complete square DR of range conversion value of two dimension of projected pixel _x ², and the two dimension confirmed of record fully the range conversion value square, r _x=0, ± 1, ± 2 ..., ± (r ₁+ r ₂);

Judge DR _x ²Whether satisfy

If stop then confirming that first pixel is respectively at two-dimentional two-value picture z ₀± (r _x+ 1) until two-dimentional two-value picture z ₀± (r ₁+ r ₂) in the complete range conversion value of two dimension of projected pixel, if not, continue then to confirm that first pixel is respectively at two-dimentional two-value picture z ₀± (r _x+ 1) the complete range conversion value of the two dimension of projected pixel in is until determining said first pixel at two-dimentional two-value picture z ₀± (r ₁+ r ₂) in the two dimension of projected pixel fully till the range conversion value.

4. according to the said method of claim 3; It is characterized in that; The two dimension of said projected pixel according to said first pixel each two-dimentional bianry image in the said first nearest background pixel scope is the range conversion value fully, determines the first nearest background pixel of said first pixel of said three-dimensional bianry image middle distance and specifically comprises:

Utilize formula min{DR _x ²+ | z _x-z ₀| ², z wherein _xThe span of z is determined first background pixel nearest with first pixel distance in the ∈ first nearest background pixel scope;

Utilize formula

to calculate the first complete distance.

5. according to the said method of claim 1, it is characterized in that the complete range conversion of two dimension of calculating each two-dimentional two-value picture specifically comprises:

Pre-treatment step; Said pre-treatment step is to confirm first function or confirm second function, and said first function is used for the position of the nearest background pixel of definite capable middle distance the 4th pixel of two-dimentional two-value picture i, and said second function is used for the position of the nearest background pixel of definite said the 4th pixel of two-dimentional two-value picture j row middle distance; Wherein, 1≤i≤m, 1≤j≤n, i and j are integer;

Calculate the two dimension complete distance of said the 4th pixel of distance fully according to the 3rd object pixel and needs; And the complete distance of the two dimension of said the 3rd object pixel in two-dimentional two-value picture; Confirm the second nearest background pixel scope of said the 4th pixel, said the 4th pixel and said the 3rd object pixel all are arranged in same two-dimentional two-value picture;

Utilize the said first function nearest background pixel of said the 4th pixel of detection range in every row of the said second nearest background pixel scope respectively, or utilize the said second function nearest background pixel of said the 4th pixel of detection range in every row of the said second nearest background pixel scope respectively;

From the nearest background pixel of said the 4th pixel of the distance that searches out, determine second background pixel nearest with said the 4th pixel distance; Second two dimension of calculating said second background pixel and said the 4th pixel is distance fully, and will said second two dimension fully distance as the complete range conversion value of the two dimension of said the 4th pixel in the two-dimentional two-value picture at its place.

6. according to the said method of claim 1, it is characterized in that the complete range conversion of two dimension of calculating each two-dimentional two-value picture specifically comprises:

Pre-treatment step; Said pre-treatment step is to confirm first function or confirm second function, and said first function is used for the position of the nearest background pixel of definite capable middle distance the 4th pixel of two-dimentional two-value picture i, and said second function is used for the position of the nearest background pixel of definite said the 4th pixel of two-dimentional two-value picture j row middle distance; Wherein, 1≤i≤m, 1≤j≤n, i and j are integer;

Complete distance based on the 3rd object pixel and said the 4th pixel; And the 3rd object pixel and the distance that leaves its nearest background pixel; Confirm the second nearest background pixel scope of the 4th pixel; And the second nearest background pixel scope is divided into first son background pixel range set and second son background pixel range set recently recently according to preset rules; First son background pixel range set recently comprises at least one first son background pixel scope recently; Line number in the nearest background pixel scope of said at least one height is not more than columns, and second son background pixel range set recently comprises at least one second son background pixel scope recently, and the line number in said at least one second sub background pixel scope recently is greater than columns;

Utilize first function nearest background pixel of detection range the 4th pixel in every row of the nearest background pixel range set of first son, utilize second function nearest background pixel of detection range the 4th pixel in every row of the nearest background pixel range set of second son;

From the nearest background pixel of distance the 4th pixel that searches out, determine second background pixel nearest with the 4th pixel distance; Calculate the second complete distance of second background pixel and the 4th pixel, and with the two-dimentional fully range conversion value of this second complete distance as the 4th pixel.

7. according to claim 5 or 6 arbitrary said methods, it is characterized in that the second nearest background pixel scope of said definite said the 4th pixel specifically comprises:

Calculate the two dimension of said the 3rd object pixel in two-dimentional two-value picture fully apart from r ₃

Confirm the complete of said the 4th pixel and said the 3rd object pixel apart from r ₄

The said second nearest background pixel scope is for being the center of circle with said the 4th pixel, with r ₃+ r ₄Round O for radius ₄The zone that circumscribed square surrounded;

Or the said second nearest background pixel scope is for being the center of circle with said the 3rd object pixel, with r ₃Round O for radius ₅In connect the square with said round O ₄The annular region that circumscribed square surrounded;

Or the said second nearest background pixel scope is for being the centre of sphere with said the 4th pixel, with | r ₃-r ₄| be the round O of radius ₆In connect the square with said round O ₄The annular region that circumscribed square surrounded.

8. according to claim 5 or 6 arbitrary said methods, it is characterized in that the x that said the 4th pixel is positioned at two-dimentional two-value picture is capable; The y row are with (x, y) position of said the 4th pixel of expression in said two-dimentional two-value picture; With (x; Y) be separation,, the y row be divided into the above and below capable left side and the right side of being divided into of x;

Said definite first function specifically comprises:

Confirm to be used to calculate said the 4th pixel (x of said two-dimentional two-value picture x capable left side distance; Y) first subfunction of nearest background pixel place columns; And be used to calculate said the 4th pixel of the capable right side of said two-dimentional two-value picture x distance (x, y) second subfunction of nearest background pixel place columns, wherein; 1≤x≤m, 1≤y≤n;

According to said first subfunction and said second subfunction, confirm said first function;

Said definite second function specifically comprises:

Confirm to be used to calculate the 3rd subfunction of the nearest background pixel place line number of the said two-dimentional two-value picture y side of listing said the 4th pixel of distance, and be used to calculate the 4th subfunction of the nearest background pixel place line number of said the 4th pixel of said two-dimentional two-value picture y row below distance;

According to said the 3rd subfunction and said the 4th subfunction, confirm said second function.

9. said according to Claim 8 method is characterized in that, said first subfunction is specially L [x, y]:

$L[x,y]=\left\{\begin{array}{cc}y& I(x,y)=0\\ L[x,y-1]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and y=1, so L (x, y)=-Maxlable;

Said second subfunction is specially R [x, y]:

$R[x,y]=\left\{\begin{array}{cc}y& I(x,y)=0\\ R[x,y+1]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and y=n, R [x, y]=Maxlable so;

Then be specially SZ [x, y] according to said first subfunction and definite said first function of said second subfunction:

<math> <mrow> <mi>SZ</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>L</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> </mtd> <mtd> <mi>y</mi> <mo>-</mo> <mi>L</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&lt;;</mo> <mi>R</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>R</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> </mtd> <mtd> <mi>y</mi> <mo>-</mo> <mi>L</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&amp;GreaterEqual;</mo> <mi>R</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow></math>

Said the 3rd subfunction is specially T [x, y]:

$T[x,y]=\left\{\begin{array}{cc}x& I(x,y)=0\\ T[x-1,y]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and x=1, so T [x, y]=-Maxlable;

Said the 4th subfunction is specially D [x, y]:

$D[x,y]=\left\{\begin{array}{cc}x& I(x,y)=0\\ D[x+1,y]& I(x,y)=1\end{array}\right.;$

If I (x, y)=1 and x=m, D [x, y]=Maxlable so;

Then be specially ZS [x, y] according to said the 3rd subfunction and definite said second function of said the 4th subfunction:

<math> <mrow> <mi>ZS</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>T</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> </mtd> <mtd> <mi>x</mi> <mo>-</mo> <mi>D</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&lt;;</mo> <mi>T</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <mi>D</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> </mtd> <mtd> <mi>x</mi> <mo>-</mo> <mi>D</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>&amp;GreaterEqual;</mo> <mi>T</mi> <mo>[</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>]</mo> <mo>-</mo> <mi>x</mi> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow></math>

Wherein, (x y)=1 is expressed as object pixel to I, and (x y)=0 is expressed as background pixel to I, and said Maxlable is preset maximum mark value.

10. according to the said method of claim 9; It is characterized in that said

Images