CN100468446C - Dynamic image identification method and system of the same - Google Patents
Dynamic image identification method and system of the same Download PDFInfo
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- CN100468446C CN100468446C CNB2006100035129A CN200610003512A CN100468446C CN 100468446 C CN100468446 C CN 100468446C CN B2006100035129 A CNB2006100035129 A CN B2006100035129A CN 200610003512 A CN200610003512 A CN 200610003512A CN 100468446 C CN100468446 C CN 100468446C
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Abstract
It's a dynamic image identification method on basis of features of different objects, with the image sensor and buffer to do real-time object recognition. Image sensor with multiple pixel methods include the following steps: (a) set the threshold value of gray-scale of images; (B) capture pixel value of images per column ; (C) judge background of the region using the gray-scale threshold and identify image segment of the object; (D) decide which object the image segments belong to by using space-related resolution of adjacent segments in the image; (E ) pool the information of image segments for their respective object; (F) distinct the object attributes based on judgment rule; (G) identify the object of the image as a solid, hollow, long - and short of the characteristic properties after capturing all the pixel values of Images.
Description
Technical field
The invention relates to a kind of image identification method, be meant especially and a kind ofly utilize characteristics of objects diversity (Identification by Objects ' characteristics) to carry out the dynamic image identification method of a plurality of objects and use the system of this method.
Background technology
Video game (TV game) or computer game (PC game) have been common amusement and recreation mode at present, with general computer game is example, mostly be that Games Software is installed on computer installation, the screen of the computer installation of arranging in pairs or groups again and for example input interfaces such as keyboard, mouse or joystick Games Software is controlled; Yet the interactive stage property that the Games Software that collocation manufacturer sells is also arranged, for convenience of description for the purpose of, a kind of interactive game that is disclosed for No. 2004006348 with U.S. Patent Publication No. is changed to example its member and action principle is described.
As shown in Figure 1, interactive entertainment device 700 has the indication stage property 71 and 72 of two dumbbell shapeds, the platform 720 of marking time, screen apparatus 730, video cameras 750, game cartridge 760 and host apparatus 770.Wherein, host apparatus 770 is equipped with Games Software; Indication stage property 71,72 is gripped by player 705 right-hand man respectively, and has luminous object (Lightsource) 711,712 and 721,722 respectively in its end on the indication stage property 71,72; Screen apparatus 730 can show the image that dancer for example virtual in the Games Software 731 is dancing; Host apparatus 770 can be computer installation or table of game player; Screen apparatus 730 is to be connected on the host apparatus 770 with game cartridge 760.
When using above-mentioned interactive entertainment device 700 to carry out dancing and game, player 705 needs to open (Turnon) indication stage property 71,72 power supply is so that luminous object 711,712 and 721,722 be able to luminous, allow video cameras 750 can detect luminous object 711,712 and 721,722 image, and then by game cartridge 760 these luminous objects 711 of calculating, 712 and 721,722 parameters such as position, be entered into host apparatus 770 at last and finish player's 705 hand-held indication stage properties 71,72 luminous object 711,712 and 721, the tracking of 722 positions, and be shown on the picture of screen apparatus 730.
Yet, suppose that player 705 was brandishing existing stage property arbitrarily at 71,72 o'clock, because the feature identical (for example all being circles of homalographic) of luminous object 711,712 and 721,722, therefore wantonly two luminous objects 711,712 and 721,722 images in 760 interpretations of game cartridge are all the pie chart case, then if the overlapping back time of releasing of any two pie chart case tracks is arranged, when game cartridge 760 carries out Flame Image Process, be difficult for telling the difference of the two and the erroneous judgement that causes shift position or motion track after video cameras 750 reading images.
Summary of the invention
Therefore, purpose of the present invention, promptly utilize the characteristics of objects diversity to carry out the dynamic image identification method of a plurality of objects and use the system of this method providing a kind of, since be with each object be solid, hollow, microscler and brachmorphy wherein any characteristic attribute distinguish, therefore can not cause erroneous judgement because of being difficult for telling the difference of the two.
So, the present invention utilizes the characteristics of objects diversity to carry out the dynamic image identification method of a plurality of objects, this method cooperates the use of imageing sensor and buffer, in order to carry out identification in real time at least one object that has among the image, imageing sensor has a plurality of determinant inducing pixels, and described imageing sensor forms a plurality of image section with the described object of described inducing pixel sensing, each described object is made up of the image section of at least one row and each image section is made up of the inducing pixel of delegation at least, and the method for described image identification comprises following step: the GTG threshold value of (A) setting described image; (B) capture the pixel value of every row in the described image in regular turn; (C) utilize described GTG threshold decision background area and identify the image section that described object has; (D) in the described image of acquisition in the pixel value of every row, utilize the spatial coherence of image section in adjacent two row to differentiate the affiliated object of the image section of unknown object; (E) object of the information that image section added up of compiling described unknown object under it; (F) according to judging that the rule district office states the characteristic attribute of object; And (G) captured once all pixel values of described image after, promptly pick out the characteristic attribute of the described object in the described image.
Image distinguishing system of the present invention utilizes object images feature diversity to carry out identification in real time at least one object that has among the image, described image distinguishing system comprises imageing sensor, analog-digital converter, graphics processing unit and buffer, this imageing sensor has a plurality of determinant inducing pixels, and this imageing sensor forms a plurality of image section with the described object of described inducing pixel sensing, and wherein each described object is made up of the image section of at least one row and each image section is made up of the inducing pixel of delegation at least; This analog-digital converter connects described imageing sensor, is digital signal in order to the simulating signal of the described image of transformation induction; This graphics processing unit connects described analog-digital converter, and this graphics processing unit reads described inducing pixel by row, and is set with the GTG threshold value of described image and in order to the judgement rule of the characteristic attribute of distinguishing described object; This buffer connects described graphics processing unit, in order to the image information of temporary described graphics processing unit described object totally.
Like this, described graphics processing unit can utilize described GTG threshold decision background area and identify the image section that described object has, and in the described image of acquisition in the pixel value of every row, utilize the spatial coherence of image section in adjacent two row to differentiate the affiliated object of the image section of unknown object, the object of the information that image section added up of compiling described unknown object again under it, and the described judgement rule of foundation district office states the characteristic attribute of object, and after having captured once all pixel values of described image, described graphics processing unit promptly picks out the characteristic attribute of the described object in the described image.
Description of drawings
Fig. 1 is the synoptic diagram of a kind of known interactive entertainment device of explanation;
Fig. 2 is the image distinguishing system that dynamic image identification method of the present invention is used in explanation, in order to the characteristic attribute relevant information after the identification is exported to the circuit block diagram of the transmission interface that existing personal computer main frame has;
Fig. 3 is that explanation the present invention utilizes the characteristics of objects diversity to carry out first preferred embodiment of the dynamic image identification method of a plurality of objects, can pick out in the image two to as if belong to the synoptic diagram of solid or hollow object;
Fig. 4 is that explanation uses the present invention to utilize the characteristics of objects diversity to carry out two embodiment of the dynamic image identification method of a plurality of objects, how utilizes the identification of each image section to judge the process flow diagram of object under it in the starting stage of identification;
Fig. 5 be this first preferred embodiment of explanation how to pick out in the image two to as if belong to the process flow diagram of solid or hollow object;
Fig. 6 is that the present invention utilizes the characteristics of objects diversity to carry out second preferred embodiment of the dynamic image identification method of a plurality of objects, how to pick out in the image two to as if belong to process flow diagram microscler or the brachmorphy object; And
Fig. 7 be this second preferred embodiment of explanation can pick out in the image two to as if belong to synoptic diagram microscler or the brachmorphy object.
The primary clustering symbol description
1,2 images, 32 analog-digital converters
11,12,21,22 object images, 33 graphics processing units
111,121 image section, 34 buffers
Starting point 35 interface modules of 111 ', 121 ' image section
111 ", 121 " terminal point 4 personal computers of image section
101～107,110～114,120～125 step 41 main frames
3 image processing systems, 411 transmission interfaces
31 imageing sensors, 42 displays
311 pixels
Embodiment
About aforementioned and other technology contents, characteristics and effect of the present invention, with reference in two graphic DETAILED DESCRIPTION OF THE PREFERRED, can clearly present in following cooperation.
The present invention be described in detail before, be noted that in the following description content similarly assembly is represented with identical numbering.In addition; mandatory declaration be; because first preferred embodiment is in order to distinguish solid, hollow characteristic attribute; and second preferred embodiment is a characteristic attribute microscler in order to distinguish, brachmorphy; but in other embodiments; maybe above-mentioned characteristic attribute solid, hollow, microscler and brachmorphy can be mixed and use and discern,, all should be belonged to the category of notion desire protection of the present invention as long as therefore the application of above-mentioned characteristic attribute is arranged.
Shown in Figure 2, the present invention utilizes the characteristics of objects diversity to carry out in two preferred embodiments of dynamic image identification method of a plurality of objects, its employed system is an image processing system 3, and this image processing system 3 has imageing sensor (Image sensor) 31, analog-digital converter (A/D Converter) 32, graphics processing unit (Image processor) 33, buffer (Register) 34 and interface module 35.
Wherein, imageing sensor 31 is that CCD or cmos component are made, have a plurality of determinant inducing pixels, the light of taking thing (figure does not show) reflection in order to induction forms image, and this imageing sensor 31 forms a plurality of image section (effect repeats after holding) with these these objects of inducing pixel sensing, and is converted to simulating signal; Then, the analog-digital converter 32 that exports connection layout image-position sensor 31 to is converted to digital signal, is responsible for the computing of most of signal by graphics processing unit 33; Graphics processing unit 33 connects analog-digital converters 32, reads the signal of these inducing pixels inductions and in addition computing by row ground, and is set with the GTG threshold value of image and in order to the judgement rule of the characteristic attribute of differentiation object; Buffer 34 connects graphics processing units 33, in order to the image information of temporary graphics processing unit 33 these objects totally.
Like this, graphics processing unit 33 can utilize GTG threshold decision background area and identify the image section of object, utilize the image section of the spatial coherence resolution unknown object of image section in adjacent two row to belong to what object, the object of the information of compiling these image section again and being added up under it, and according to the characteristic attribute of judging rule differentiation object, and after having captured all pixel values of this image, graphics processing unit 33 promptly picks out the characteristic attribute of the object in the image.
The interface module 35 of image processing system 3 connects this graphics processing unit 33, in order to the characteristic attribute relevant information after the identification is output as the peripheral protocol data form that meets computing machine, after for example being converted to the signal that meets the USB form, export the transmission interface 411 that the main frame 41 of personal computer 4 has to, receive and in addition after the computing, can on the display 42 of personal computer 4, demonstrate this object images by the main frame 41 of personal computer 4.
Mandatory declaration be that image processing system 3 can be used for shooting with video-corder the discriminating function that picture waits image-taking device, or carries out discriminating function in the mode of the recognition software that is installed in computing machine; In addition, because the aufbauprinciple of imageing sensor 31, analog-digital converter 32, graphics processing unit 33 and other associated component is a known technology, and main concept of the present invention is the discriminating function that cooperates buffer 34 carries out image with graphics processing unit 33, therefore following will only being described with regard to the part that is relevant to the principle of the invention.
Cooperate shown in Fig. 2,3, illustrate that the present invention utilizes the characteristics of objects diversity to carry out first preferred embodiment of the dynamic image identification method of a plurality of objects.Mandatory declaration be, in this preferred embodiment, because imageing sensor 31 has a plurality of determinant inducing pixels (Pixel) 311, and these pixels 311 are to respond to each object 11,12 by the mode of row, therefore, object resulting parts of images in each row that imageing sensor 31 is sensed is called image section (Image Segment), and the method for identification of each image section is for writing down the starting point of each image section in each row and being stored to buffer 34 by row; Then the starting point pointwise from this image section adds up the information of this image section and is stored to this buffer 34; And judge the terminal point of each image section in each row and be stored to buffer 34.
For example: image processing system 3 can be earlier captures every row pixel 311 is sensed in the image 1 pixel value in regular turn by imageing sensor 31 and is converted to digital signal through analog-digital converter 32 and inputs to graphics processing unit 33, the mode that reads is from the first row beginning, from left to right read each pixel value in these row, whenever run through one and be listed as each pixel value that from top to bottom reads every row again, and judge whether the appearance of the image information of object, detect the pixel value that whether has greater than the systemic presupposition threshold value and occur.
When reading, can judge in each row the image section starting point of these objects 11,12 and terminal point in the lump wherein, what object is the image section that so just can then utilize the spatial coherence (repeating after the appearance) of image section in adjacent two row to differentiate unknown object belong to.For example: the initial image information that object is arranged of the 4th row in image 1, and these image informations belong to two objects 11,12, therefore right from a left side, the starting point 111 ' of the image section 111 that record occurs earlier also is stored to buffer 34, pointwise adds up the information of image section 111 and is stored to buffer 34 again, then judge the terminal point 111 that has this image section 111 in these row " and be stored to buffer 34 after; write down the starting point 121 ' and terminal point 121 of object 12 again in the image section 121 of these row " and the information of pointwise accumulative total behind buffer 34, carry out the judgement of next column again, the rest may be inferred.
And differentiate the mode that these image section belong to what object 11,12 respectively, promptly utilize the image section of the spatial coherence resolution unknown object of image section in adjacent two row to belong to what object, judge that then decidable unknown object image section belongs to this object i as meeting following formula 1:
Seg-L ≦ Preline-Obji-R; And
Seg-R ≧ Preline-Obji-L; Formula 1
Wherein, formula 1 is when for example representing the Y column data in reading to image; Seg-L represents to read the left starting point X coordinate figure that Y lists this existing unknown object image section; Seg-R represents to read the right-hand terminal point X coordinate figure that Y lists this existing unknown object image section; And Preline-Obji-R represents the previous column of Y row, that is Y-1 lists the right-hand terminal point X coordinate figure of the image section of existing respectively this object i; Preline-Obji-L represents that Y-1 lists the left starting point X coordinate figure of the image section of existing respectively this object i, if meet the judgement formula of Seg-L ≦ Preline-Obji-R and Seg-R ≧ Preline-Obji-L, represent that promptly the image section that this unknown object image section and Y-1 list existing this object i belongs to same target i.
As shown in Figure 4, illustrate how two preferred embodiments that the present invention utilizes the characteristics of objects diversity to carry out the dynamic image identification method of a plurality of objects judge what object is image section belong to, and details are as follows for step that it has and action principle when initial:
At first need set the GTG threshold value (step 101) of this image; Then capture the pixel value (step 102) of every row in this image in regular turn; Utilize this GTG threshold decision background area (step 103); Identify the image section (step 104) of this object, its substep comprises the starting point of the image section of this unknown object in these row of record and is stored to buffer (104a); Then the starting point pointwise from this image section adds up the information of this image section and is stored to buffer (104b); And judge the image section terminal point of this unknown object in these row and be stored to buffer (104c); What object (step 105) is the image section of utilizing the spatial coherence of image section in adjacent two row to differentiate this unknown object belong to; Compile information that this image section the adds up object (step 106) under it; In like manner, carry out the judgement (step 107) that this is listed as next image section.
Cooperating shown in Fig. 4,5, illustrate that the present invention utilizes the characteristics of objects diversity to carry out in first preferred embodiment of dynamic image identification method of a plurality of objects, is how to pick out solid or hollow object, and details are as follows for step that this method has and action principle:
At first use step 101～107 to judge what object is each image section belong to, then need to distinguish the solid of these objects or hollow features attribute according to the judgement rule, the judgement rule of present embodiment is divided into two parts, the one, judge that respectively this image section that is surrounded by the background area belongs to same target? (step 110) if, this background area is judged as the hollow area that belongs to this object, and carry out step 111, if not, then carry out step 112; Is another step 111 to add up the value of (the hollow area area/entire area of this object) greater than a threshold value? if be not more than this threshold value, then carry out step 112, if greater than this threshold value, then carry out step 113; Mandatory declaration be that the entire area system image section that this object of this hollow area and this hollow area periphery is all is all listed calculating in, and is about between 0.05～0.08 through obtaining preferred this threshold value after the experiment; Step 113 is that the characteristic attribute of this object of classification is hollow object; And step 112 is that the characteristic attribute of sorting out this object is a solid object, so just finished solid, the hollow characteristic attribute discriminating function (step 114) of object.
Again as shown in Figure 3, use the present invention to utilize the characteristics of objects diversity to carry out first preferred embodiment of the dynamic image identification method of a plurality of objects, can pick out two objects the 11, the 12nd in the image 1, belong to solid or hollow object, for example the object among the figure 11 i.e. judgement after identification belongs to solid object, and the i.e. judgement after identification of the object 12 among the figure belongs to hollow object.
Cooperating shown in Fig. 4,6, illustrate that the present invention utilizes the characteristics of objects diversity to carry out in second preferred embodiment of dynamic image identification method of a plurality of objects, is how to pick out microscler or the brachmorphy object, and details are as follows for step that this method has and action principle:
At first also use step 101～107 to judge what object is each image section belong to, then need to judge that according to another rule distinguish the characteristic attribute of the microscler or brachmorphy of these objects that the judgement rule of present embodiment is judged earlier and captured the four end points coordinates (step 120) that this object is suitable for; Then calculate long limit, the minor face vector (step 121) of this object; Calculate (area of the long edge lengths of this object square/this object) again greater than a threshold value? (step 122) then carry out step 123 if greater than this threshold value, if be not more than this threshold value, then carry out step 124; Step 123 is to judge that the characteristic attribute of this object is microscler object; And step 124 is to judge that the characteristic attribute of this object is the brachmorphy object, has so just finished the characteristic attribute discriminating function (step 125) of microscler, the brachmorphy of object; Preferably, the value of (area of the long edge lengths of this object square/this object) through experiment after, this threshold value that obtains is about between 2～3.
As shown in Figure 7, use the present invention to utilize the characteristics of objects diversity to carry out the dynamic image identification method of a plurality of objects, two objects the 21, the 22nd in the image 2 be can pick out, elongated or brachmorphy object belonged to, for example the circular object among the figure 21 i.e. judgement after identification belongs to the brachmorphy object, and the i.e. judgement after identification of the rectangular object 22 among the figure belongs to microscler object.
Conclude above-mentioned, since at present for the image of desiring interpretation if the overlapping back time of releasing of any two graphics tracks is arranged, when then carrying out Flame Image Process, the erroneous judgement of telling the difference of the two with being difficult for and causing shift position or motion track, therefore, the present invention utilizes the characteristics of objects diversity to carry out the dynamic image identification method of a plurality of objects and uses the system of this method, owing to be to utilize GTG threshold decision background area and identify the object images section, and utilize the image section of the spatial coherence resolution unknown object of image section in adjacent two row to belong to what object, and judge that with specific judgement rule each object is solid, hollow, microscler and brachmorphy is any characteristic attribute wherein, therefore except that carrying out in real time the discriminating function, can not cause erroneous judgement because of being difficult for telling the difference of the two yet.
The above person only is the preferred embodiments of the present invention, and when not limiting scope of the invention process with this, promptly the simple equivalent of being done according to claim of the present invention and invention description content generally changes and modifies, and all belongs in the scope that patent of the present invention contains.
Claims (8)
1. method of utilizing the characteristics of objects diversity to carry out the dynamic image identification of a plurality of objects, this method cooperates the use of imageing sensor and buffer, in order to carry out identification in real time at least one object that has among the image, described imageing sensor has a plurality of determinant inducing pixels, and described imageing sensor forms a plurality of image section with the described object of described inducing pixel sensing, each described object is made up of the image section of at least one row and each image section is made up of the inducing pixel of delegation at least, and the method for described image identification comprises following step:
(A) the GTG threshold value of the described image of setting;
(B) capture the pixel value of every row in the described image in regular turn;
(C) utilize described GTG threshold decision background area and identify the image section of described object;
(D) in the described image of acquisition in the pixel value of every row, utilize the spatial coherence of image section in adjacent two row to differentiate the affiliated object of the image section of unknown object;
(E) object of the information that image section added up of compiling described unknown object under it;
(F) according to judging that the rule district office states the characteristic attribute of object; And
(G) captured once all pixel values of described image after, promptly pick out the characteristic attribute of the described object in the described image.
2. the method for utilizing the characteristics of objects diversity to carry out the dynamic image identification of a plurality of objects according to claim 1, wherein, this judgement rule of step (F) has following step:
(H-1) do you judge that respectively this image section that is surrounded by the background area belongs to same target? if, then carry out step (H-2), if not, then carry out step (H-5);
(H-2) this background area is judged as the hollow area that belongs to this object;
(H-3) is the value of the hollow area area/entire area of this object of accumulative total greater than a threshold value? if greater than this threshold value, then carry out step (H-4), if be not more than this threshold value, then carry out step (H-5);
(H-4) characteristic attribute of judging this object is hollow object; And
(H-5) characteristic attribute of judging this object is a solid object.
3. the method for utilizing the characteristics of objects diversity to carry out the dynamic image identification of a plurality of objects according to claim 1, wherein, this judgement rule of step (F) has following step:
(I-1) judge and capture the four end points coordinates that this object is suitable for;
(I-2) calculate long limit, the minor face vector of this object;
(I-3) calculate the area of long edge lengths square/this object of this object greater than a threshold value? if greater than this threshold value, then carry out step (I-4), if be not more than this threshold value, then carry out step (I-5);
(I-4) characteristic attribute of judging this object is microscler object; And
(I-5) characteristic attribute of judging this object is the brachmorphy object.
4. the method for utilizing the characteristics of objects diversity to carry out the dynamic image identification of a plurality of objects according to claim 1, wherein, identification respectively this image section comprises the steps:
(C-1) write down this image section starting point and be stored to this buffer in these row;
(C-2) the starting point pointwise of this image section adds up the information of this image section and is stored to this buffer certainly;
(C-3) judge this image section terminal point and be stored to this buffer in these row; And
(C-4) when there is other object in these row, carry out the judgement of the image section of next object in these row.
5. the method for utilizing the characteristics of objects diversity to carry out the dynamic image identification of a plurality of objects according to claim 1, wherein, in the step (D), the mode of affiliated object of differentiating the image section of described unknown object is, when judgement meets following formula, then the image section of the described unknown object of decidable belongs to object i:
Seg-L ≦ Preline-Obj
i-R; And
Seg-R≧Preline-Obj
i-L；
Wherein, this formula is when being illustrated in the Y column data that reads in the image, and Seg-L represents to read the left starting point X coordinate figure that Y lists the image section of existing described unknown object; Seg-R represents to read the right-hand terminal point X coordinate figure that Y lists the image section of existing described unknown object; Preline-Obj
i-R represents that Y-1 lists the right-hand terminal point X coordinate figure of the image section of existing respectively this object i; Preline-Obj
i-L represents that Y-1 lists the left starting point X coordinate figure of the image section of existing respectively this object i.
6. an image distinguishing system utilizes object images feature diversity to carry out identification in real time at least one object that has among the image, and described image distinguishing system comprises:
Imageing sensor, have a plurality of determinant inducing pixels, in order to respond to described image, and described imageing sensor forms a plurality of image section with the described object of described inducing pixel sensing, and wherein each described object is made up of the image section of at least one row and each image section is made up of the inducing pixel of delegation at least;
Analog-digital converter connects described imageing sensor, is digital signal in order to the simulating signal of the described image of transformation induction;
Graphics processing unit connects described analog-digital converter, and described graphics processing unit reads described inducing pixel by row, and is set with the GTG threshold value of described image and in order to the judgement rule of the characteristic attribute of distinguishing described object; And
Buffer connects described graphics processing unit, in order to the image information of temporary described graphics processing unit described object totally;
Like this, described graphics processing unit can utilize described GTG threshold decision background area and identify the image section of described object, and in the described image of acquisition in the pixel value of every row, utilize the spatial coherence of image section in adjacent two row to differentiate the affiliated object of the image section of unknown object, the object of the information that image section added up of compiling described unknown object again under it, and the described judgement rule of foundation district office states the characteristic attribute of object, and after having captured once all pixel values of described image, described graphics processing unit promptly picks out the characteristic attribute of the described object in the described image.
7. image distinguishing system according to claim 6, wherein, the judgement rule that this graphics processing unit is set is judged and is comprised solid, hollow, microscler and brachmorphy any characteristic attribute wherein.
8. image distinguishing system according to claim 6, wherein, also comprise interface module, this interface module connects this graphics processing unit, in order to the picture signal after the identification is output as the peripheral protocol data form that meets computing machine transmission interface with the main frame that exports this computing machine to, receive and in addition after the computing, can on the display of this computing machine, demonstrate this object images by the main frame of this computing machine.
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| 图像处理、分析与机器视觉(第二版). Milan Sonka、Vaclav Hlavax、Roger Boyle等著，第159页第6.1部分、第173页至178页的第6.3部分基于区域的形状表示与描述，人民邮电出版社. 2003 |
| 图像处理、分析与机器视觉(第二版). Milan Sonka、Vaclav Hlavax、Roger Boyle等著，第159页第6.1部分、第173页至178页的第6.3部分基于区域的形状表示与描述，人民邮电出版社. 2003 * |
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