數(shù)字圖像處理 外文翻譯 外文文獻(xiàn) 英文文獻(xiàn) 數(shù)字圖像處理

1、 digital image processing1 introductionmany operators have been proposed for presenting a connected component n a digital image by a reduced amount of data or simplied shape. in general we have to state that the development, choice and modi_cation of such algorithms in practical applications are dom

2、ain and task dependent, and there is no best method". however, it is interesting to note that there are several equivalences between published methods and notions, and characterizing such equivalences or di_erences should be useful to categorize the broad diversity of published methods for skel

3、etonization. discussing equivalences is a main intention of this report.1.1 categories of methodsone class of shape reduction operators is based on distance transforms. a distance skeleton is a subset of points of a given component such that every point of this subset represents the center of a maxi

4、mal disc (labeled with the radius of this disc) contained in the given component. as an example in this _rst class of operators, this report discusses one method for calculating a distance skeleton using the d4 distance function which is appropriate to digitized pictures. a second class of operators

5、 produces median or center lines of the digital object in a non-iterative way. normally such operators locate critical points _rst, and calculate a speci_ed path through the object by connecting these points.the third class of operators is characterized by iterative thinning. historically, listing 1

6、0 used already in 1862 the term linear skeleton for the result of a continuous deformation of the frontier of a connected subset of a euclidean space without changing the connectivity of the original set, until only a set of lines and points remains. many algorithms in image analysis are based on th

7、is general concept of thinning. the goal is a calculation of characteristic properties of digital objects which are not related to size or quantity. methods should be independent from the position of a set in the plane or space, grid resolution (for digitizing this set) or the shape complexity of th

8、e given set. in the literature the term thinning" is not usedin a unique interpretation besides that it always denotes a connectivity preserving reduction operation applied to digital images, involving iterations of transformations of speci_ed contour points into background points. a subset q _

9、 i of object points is reduced by a de_ned set d in one iteration, and the result q0 = q n d becomes q for the next iteration. topology-preserving skeletonization is a special case of thinning resulting in a connected set of digital arcs or curves. a digital curve is a path p =p0; p1; p2; :; pn = q

10、such that pi is a neighbor of pi􀀀1, 1 _ i _ n, and p = q. a digital curve is called simple if each point pi has exactly two neighbors in this curve. a digital arc is a subset of a digital curve such that p 6= q. a point of a digital arc which has exactly one neighbor is called an end point

11、of this arc. within this third class of operators (thinning algorithms) we may classify with respect to algorithmic strategies: individual pixels are either removed in a sequential order or in parallel. for example, the often cited algorithm by hilditch 5 is an iterative process of testing and delet

12、ing contour pixels sequentially in standard raster scan order. another sequential algorithm by pavlidis 12 uses the de_nition of multiple points and proceeds by contour following. examples of parallel algorithms in this third class are reduction operators which transform contour points into backgrou

13、nd points. di_erences between these parallel algorithms are typically de_ned by tests implemented to ensure connectedness in a local neighborhood. the notion of a simple point is of basic importance for thinning and it will be shown in this report that di_erent de_nitions of simple points are actual

14、ly equivalent. several publications characterize properties of a set d of points (to be turned from object points to background points) to ensure that connectivity of object and background remain unchanged. the report discusses some of these properties in order to justify parallel thinning algorithm

15、s.1.2 basicsthe used notation follows 17. a digital image i is a function de_ned on a discrete set c , which is called the carrier of the image. the elements of c are grid points or grid cells, and the elements (p; i(p) of an image are pixels (2d case) or voxels (3d case). the range of a (scalar) im

16、age is f0; :gmaxg with gmax _ 1. the range of a binary image is f0; 1g. we only use binary images i in this report. let hii be the set of all pixel locations with value 1, i.e. hii = i􀀀1(1). the image carrier is de_ned on an orthogonal grid in 2d or 3d space. there are two options: using th

17、e grid cell model a 2d pixel location p is a closed square (2-cell) in the euclidean plane and a 3d pixel location is a closed cube (3-cell) in the euclidean space, where edges are of length 1 and parallel to the coordinate axes, and centers have integer coordinates. as a second option, using the gr

18、id point model a 2d or 3d pixel location is a grid point.two pixel locations p and q in the grid cell model are called 0-adjacent i_ p 6= q and they share at least one vertex (which is a 0-cell). note that this speci_es 8-adjacency in 2d or 26-adjacency in 3d if the grid point model is used. two pix

19、el locations p and q in the grid cell model are called 1- adjacent i_ p 6= q and they share at least one edge (which is a 1-cell). note that this speci_es 4-adjacency in 2d or 18-adjacency in 3d if the grid point model is used. finally, two 3d pixel locations p and q in the grid cell model are calle

20、d 2-adjacent i_ p 6= q and they share at least one face (which is a 2-cell). note that this speci_es 6-adjacency if the grid point model is used. any of these adjacency relations a_, _ 2 f0; 1; 2; 4; 6; 18; 26g, is irreexive and symmetric on an image carrier c. the _-neighborhood n_(p) of a pixel lo

21、cation p includes p and its _-adjacent pixel locations. coordinates of 2d grid points are denoted by (i; j), with 1 _ i _ n and 1 _ j _ m; i; j are integers and n;m are the numbers of rows and columns of c. in 3dwe use integer coordinates (i; j; k). based on neighborhood relations we de_ne connected

22、ness as usual: two points p; q 2 c are _-connected with respect to m _ c and neighborhood relation n_ i_ there is a sequence of points p = p0; p1; p2; :; pn = q such that pi is an _-neighbor of pi􀀀1, for 1 _ i _ n, and all points on this sequence are either in m or all in the complement of

23、m. a subset m _ c of an image carrier is called _-connected i_ m is not empty and all points in m are pairwise _-connected with respect to set m. an _-component of a subset s of c is a maximal _-connected subset of s. the study of connectivity in digital images has been introduced in 15. it follows

24、that any set hii consists of a number of _-components. in case of the grid cell model, a component is the union of closed squares (2d case) or closed cubes (3d case). the boundary of a 2-cell is the union of its four edges and the boundary of a 3-cell is the union of its six faces. for practical pur

25、poses it is easy to use neighborhood operations (called local operations) on a digital image i which de_ne a value at p 2 c in the transformed image based on pixel values in i at p 2 c and its immediate neighbors in n_(p).2 non-iterative algorithmsnon-iterative algorithms deliver subsets of componen

26、ts in specied scan orders without testing connectivity preservation in a number of iterations. in this section we only use the grid point model.2.1 distance skeleton" algorithmsblum 3 suggested a skeleton representation by a set of symmetric points.in a closed subset of the euclidean plane a po

27、int p is called symmetric i_ at least 2 points exist on the boundary with equal distances to p. for every symmetric point, the associated maximal disc is the largest disc in this set. the set of symmetric points, each labeled with the radius of the associated maximal disc, constitutes the skeleton o

28、f the set. this idea of presenting a component of a digital image as a distance skeleton" is based on the calculation of a speci_ed distance from each point in a connected subset m _ c to the complement of the subset. the local maxima of the subset represent a distance skeleton". in 15 the

29、 d4-distance is specied as follows. de_nition 1 the distance d4(p; q) from point p to point q, p 6= q, is the smallest positive integer n such that there exists a sequence of distinct grid points p = p0,p1; p2; :; pn = q with pi is a 4-neighbor of pi􀀀1, 1 _ i _ n. if p = q the distance betw

30、een them is de_ned to be zero. the distance d4(p; q) has all properties of a metric. given a binary digital image. we transform this image into a new one which represents at each point p 2 hii the d4-distance to pixels having value zero. the transformation includes two steps. we apply functions f1 t

31、o the image i in standard scan order, producing i_(i; j) = f1(i; j; i(i; j), and f2 in reverse standard scan order, producing t(i; j) = f2(i; j; i_(i; j), as follows:f1(i; j; i(i; j) =8><>>:0 if i(i; j) = 0minfi_(i 􀀀 1; j)+ 1; i_(i; j 􀀀 1) + 1gif i(i; j) = 1 and i 6= 1

32、or j 6= 1m+ n otherwisef2(i; j; i_(i; j) = minfi_(i; j); t(i+ 1; j)+ 1; t(i; j + 1) + 1gthe resulting image t is the distance transform image of i. note that t is a set f(i; j); t(i; j) : 1 _ i _ n 1 _ j _ mg, and let t_ _ t such that (i; j); t(i; j) 2 t_ i_ none of the four points in a4(i; j) has a

33、 value in t equal to t(i; j)+1. for all remaining points (i; j) let t_(i; j) = 0. this image t_ is called distance skeleton. now we apply functions g1 to the distance skeleton t_ in standard scan order, producing t_(i; j) = g1(i; j; t_(i; j), and g2 to the result of g1 in reverse standard scan order

34、, producing t_(i; j) = g2(i; j; t_(i; j), as follows:g1(i; j; t_(i; j) = maxft_(i; j); t_(i 􀀀 1; j)􀀀 1; t_(i; j 􀀀 1) 􀀀 1gg2(i; j; t_(i; j) = maxft_(i; j); t_(i + 1; j)􀀀 1; t_(i; j + 1) 􀀀 1gthe result t_ is equal to the distance transform image t.

35、 both functions g1 and g2 de_ne an operator g, with g(t_) = g2(g1(t_) = t_, and we have 15: theorem 1 g(t_) = t, and if t0 is any subset of image t (extended to an image by having value 0 in all remaining positions) such that g(t0) = t, then t0(i; j) = t_(i; j) at all positions of t_ with non-zero v

36、alues. informally, the theorem says that the distance transform image is reconstructible from the distance skeleton, and it is the smallest data set needed for such a reconstruction. the used distance d4 di_ers from the euclidean metric. for instance, this d4-distance skeleton is not invariant under

37、 rotation. for an approximation of the euclidean distance, some authors suggested the use of di_erent weights for grid point neighborhoods 4. montanari 11 introduced a quasi-euclidean distance. in general, the d4-distance skeleton is a subset of pixels (p; t(p) of the transformed image, and it is no

38、t necessarily connected.2.2 critical points" algorithmsthe simplest category of these algorithms determines the midpoints of subsets of connected components in standard scan order for each row. let l be an index for the number of connected components in one row of the original image. we de_ne t

39、he following functions for 1 _ i _ n: ei(l) = _ j if this is the lth case i(i; j) = 1 i(i; j 􀀀 1) = 0 in row i, counting from the left, with i(i;􀀀1) = 0 ，oi(l) = _ j if this is the lth case i(i; j) = 1 i(i; j+ 1) = 0 ，in row i, counting from the left, with i(i;m+ 1) = 0 ，mi(l) = in

40、t(oi(l) 􀀀 ei(l)=2)+ oi(l) ，the result of scanning row i is a set of coordinates (i;mi(l) of midpoints ，of the connected components in row i. the set of midpoints of all rows constitutes a critical point skeleton of an image i. this method is computationally eÆcient.the results are subs

41、ets of pixels of the original objects, and these subsets are not necessarily connected. they can form noisy branches" when object components are nearly parallel to image rows. they may be useful for special applications where the scanning direction is approximately perpendicular to main orienta

42、tions of object components.references1 c. arcelli, l. cordella, s. levialdi: parallel thinning of binary pictures. electron. lett. 11:148149, 1975.2 c. arcelli, g. sanniti di baja: skeletons of planar patterns. in: topolog- ical algorithms for digital image processing (t. y. kong, a. rosenfeld, eds.

43、), north-holland, 99143, 1996.3 h. blum: a transformation for extracting new descriptors of shape. in: models for the perception of speech and visual form (w. wathen- dunn, ed.), mit press, cambridge, mass., 362380, 1967.19 數(shù)字圖像處理1引言許多研究者已提議提出了在數(shù)字圖像里的連接組件是由一個(gè)減少的數(shù)據(jù)量或簡(jiǎn)化的形狀。一般我們不得不陳訴在實(shí)際應(yīng)用中的運(yùn)算法則的發(fā)展，選擇和更

44、改，它是依賴(lài)于鄰域和任務(wù)的，除此之外沒(méi)有更好的辦法了。不過(guò)，有趣的是，請(qǐng)注意， 有幾個(gè)等價(jià)之間出版的方法和觀念，和表征這種等價(jià)應(yīng)該是有用的分類(lèi)的廣泛和多樣性，討論等價(jià)是這份報(bào)告一個(gè)主要的意圖，。 1.1分類(lèi)方法 一類(lèi)形狀減少算子是基于距離變換的。一個(gè)距離骨架是一個(gè)子集點(diǎn)，某一特定的組成部分，例如，每點(diǎn)子，這代表了該中心的一個(gè)最大光盤(pán)（標(biāo)記半徑這片光碟）載于特定的組成部分。作為一個(gè)例子，在這類(lèi)算子，本報(bào)告討論了一個(gè)計(jì)算方法距離骨架使用的d4距離函數(shù)，這是適當(dāng)?shù)臄?shù)字化圖片。 第二類(lèi)算子產(chǎn)生的中位數(shù)或中心線數(shù)字對(duì)象在一個(gè)非迭代的方式。通常這樣的算子找到臨界點(diǎn)，并計(jì)算出特殊路徑通過(guò)對(duì)象連接這些點(diǎn)。 第

45、三類(lèi)是算子的特點(diǎn)是迭代細(xì)化。從歷史上看， 用已經(jīng)在1862年任期線性骨架為結(jié)果連續(xù)變形的前一個(gè)連接子一歐氏空間沒(méi)有改變的連通原來(lái)的設(shè)置，直到只有一套線和點(diǎn)仍然存在。許多算法在圖像分析是在此基礎(chǔ)上的一般概念的細(xì)化。目標(biāo)是計(jì)算特性的數(shù)字對(duì)象，其中不相關(guān)的大小或數(shù)量。方法應(yīng)是獨(dú)立的立場(chǎng)從一組，在平面或空間，網(wǎng)格的決議（數(shù)字化這套）或形狀復(fù)雜該給定。在文獻(xiàn)中的任期間是沒(méi)有用在一個(gè)獨(dú)特的解釋?zhuān)送?，它始終是指連接維護(hù)減少運(yùn)作，適用于數(shù)字圖像，所涉及的迭代變革的特殊輪廓點(diǎn)到背景點(diǎn)。一個(gè)字集 q_i的對(duì)象點(diǎn)是減少了設(shè)置，在一迭代和q0的結(jié)果= q n d成為q報(bào)表下次迭代。拓?fù)渚S護(hù)骨架是一個(gè)特殊的案件細(xì)化，

46、導(dǎo)致連接的一套數(shù)碼化的圓弧或曲線。數(shù)字曲線的道路是一條在p=p0 ;p1 ; p2的 ;qn= q等,pi是pi 1的近鄰， ， 1 _ i _n和p =q,數(shù)字曲線是所謂的簡(jiǎn)單元素，如果每點(diǎn)pi有準(zhǔn)確的兩個(gè)鄰域在這曲線。數(shù)碼弧是一個(gè)子集數(shù)字曲線，如p6 =q.一點(diǎn)的數(shù)碼弧其中，正是一鄰居是所謂的一歸宿，這電弧。在這第三類(lèi)算子（細(xì)化算法） ，我們可能分類(lèi)方面的算法策略：個(gè)別像素要么拆除在一個(gè)順序或平行進(jìn)行。舉例來(lái)說(shuō)，經(jīng)常提到的算法hilditch 是一個(gè)迭代的過(guò)程中的測(cè)試和刪去的輪廓像素，按順序在標(biāo)準(zhǔn)光柵掃描秩序。另一種序貫算法pavlidis 使用的多點(diǎn)和收益由輪廓下列的的例子，并行算法在這

47、第三類(lèi)是減少算子，其中變換輪廓點(diǎn)到背景點(diǎn)。這些并行算法通常是測(cè)試實(shí)施連通性，以確保在目標(biāo)連接和內(nèi)部數(shù)據(jù)沒(méi)有改變。概念一簡(jiǎn)單點(diǎn)是基本的重要性細(xì)化且它將會(huì)顯示在這報(bào)告說(shuō)，簡(jiǎn)單點(diǎn)，其實(shí)是相等的。 若干出版物的特點(diǎn)性能是一套署點(diǎn)（可從對(duì)象點(diǎn)到背景點(diǎn)轉(zhuǎn)變）去確定目標(biāo)和背景的連貫性仍然沒(méi)變.報(bào)告討論了一些性質(zhì)是為了證明平行細(xì)算法的正確性.1.2基礎(chǔ)所用符號(hào)如下 17 。數(shù)字圖像i是一個(gè)功能離散集c ，即所謂的載體的形象。要素的c 是網(wǎng)格點(diǎn)或網(wǎng)格細(xì)胞和分子性（ p ;i（ p ） 一個(gè)圖像像素（ 2維）或體素（三維案件）。范圍的形象是f0 ; gmaxg 與gmax _ 1 。范圍二進(jìn)制的形象是f0 ，我們

48、只使用在此報(bào)告的二進(jìn)制圖像。讓它成為一套所有像素的位置與價(jià)值1 。 形象載體是對(duì)一正交網(wǎng)格在二維或三維空間。 有兩種選擇：使用網(wǎng)格細(xì)胞模型的二維像素位置， p是一個(gè)封閉的廣場(chǎng)（ 2細(xì)胞）在歐氏平面和三維像素的位置是封閉立方體（ 3細(xì)胞） ，在歐氏空間，那里邊的長(zhǎng)度為1和平行于坐標(biāo)軸，中心有整數(shù)坐標(biāo)。作為一個(gè)第二個(gè)選項(xiàng)，使用網(wǎng)格點(diǎn)模型一二維或三維像素的位置是一個(gè)網(wǎng)格點(diǎn)。 兩個(gè)像素的位置p和q在網(wǎng)格中的細(xì)胞模型是所謂的0 -毗鄰i_ p 6 = q和他們分享至少有一個(gè)頂點(diǎn)（這是一個(gè)零細(xì)胞） 。 兩個(gè)三維像素的位置p和q在網(wǎng)格中的細(xì)胞模型是所謂的毗鄰i_ p 6 = q和他們分享至少有一個(gè)優(yōu)勢(shì)（這是

49、一細(xì)胞） 。注意：如果格點(diǎn)模型是用這鄰接在二維或鄰接在三維。最后，兩個(gè)像素的三維位置p和q在網(wǎng)格中的細(xì)胞模型被稱(chēng)為2 -毗鄰i_ p 6 = q和他們分享至少有一個(gè)面對(duì)的（這是一個(gè)2細(xì)胞） 。請(qǐng)注意，如果格點(diǎn)模型是用這鄰接的。 任何這些鄰接關(guān)系; 1 ; 2 ; 4 ; 6 ; 18; 26是和對(duì)稱(chēng)對(duì)一的形象， n_ （ p ）條像素位置p包括p和其_ -相鄰像素的位置。 坐標(biāo)的二維網(wǎng)格點(diǎn)是指由（i; j ）中，與1_i n和1_j_m; j是整數(shù)和n ;m 是多少行和列正在3維中使用整數(shù)坐標(biāo)（i; j ; k ）段。 基于鄰域的關(guān)系，我們連通如常： 2 點(diǎn)p; q 2 c是有關(guān)n_ i_有一

50、個(gè)序列點(diǎn)，p = p0; p1; p2; pn = q 近鄰，在此序列無(wú)論是在m或全部在補(bǔ)m的一個(gè)子集m_ c的形象承運(yùn)人是所謂的_連接i_m，是不是空洞和所有點(diǎn)，在m都成對(duì)設(shè)置m 組成的一個(gè)子集s的c是一個(gè)極大值,連接子s的研究連通性數(shù)碼影像已在 15 介紹了。 因此，任何一套集合組成了若干組件。在案件該網(wǎng)格的細(xì)胞模型，一個(gè)組成部分，是聯(lián)接的封閉空間（二維情況下） 或關(guān)閉的立方體（三維案件） 。邊界2細(xì)胞是聯(lián)接在其4 細(xì)胞和5細(xì)胞的。3細(xì)胞是連接在其6接口。 為實(shí)際目的是易于對(duì)數(shù)字圖像中使用的臨近操作的（所謂的本地操作）。價(jià)值在p 2架c ，在轉(zhuǎn)化的形象是基于像素值在i在p 2 c和其立即鄰

51、域在n_(p)。 2非迭代算法 非迭代算法提供子組件在特殊掃描命令測(cè)試連接保存在一個(gè)迭代次數(shù)。 在本節(jié)中，我們只用網(wǎng)格點(diǎn)模型。 2.1 距離算法 blum 3 提出了骨骼的代表是一組對(duì)稱(chēng)點(diǎn)。 在一個(gè)封閉的子歐氏平面一點(diǎn)p是被稱(chēng)為對(duì)稱(chēng)i_ 。至少有2點(diǎn)存在于邊界與平等的距離頁(yè)每對(duì)稱(chēng)點(diǎn)，相關(guān)的最大光盤(pán)是在這一套世界上最大的光盤(pán)。 一套對(duì)稱(chēng)點(diǎn)，每一個(gè)標(biāo)記半徑相關(guān)最大的光碟，構(gòu)成了骨架的一套。 這個(gè)想法提交的一個(gè)組成部分，數(shù)字圖像作為一個(gè)距離骨架的基礎(chǔ)上，計(jì)算一個(gè)距離各點(diǎn)在一個(gè)連通子米_ c至補(bǔ)子。本地最高的子代表一距離骨架。在 15 d4類(lèi)-距離是如下特殊的距離， d4（p; q ）的從點(diǎn)p點(diǎn)q ，

52、p6 =q是最小的積極整數(shù)n ，如存在著一種序列具有鮮明的網(wǎng)格點(diǎn)， p值p0 ，p2;pn= q是4 -近鄰，pi 1 ， 1_i_n. 如果p值q之間的距離是趨向于為零，則d4 （p; q ）的距離為所有性能的一個(gè)指標(biāo)。由于二進(jìn)制數(shù)字形象。我們這個(gè)圖像變換到一個(gè)新的代表在每屆點(diǎn)p 2 hii d4類(lèi)-距離像素具有的價(jià)值為零。轉(zhuǎn)型包括兩個(gè)步驟。我們申請(qǐng)的職能，以f1的形象，我在標(biāo)準(zhǔn)掃描秩序，產(chǎn)生i_ （i; j ）的f1 = （i; j ;i（i; j ） ，和f2在反向標(biāo)準(zhǔn)掃描秩序，產(chǎn)生（i; j ）= f2的（i; j ; i_ （i; j ） ，詳情如下： f1的（i; j ;i（i;

53、j ） = 8 > < > > ：if i（i; j ）= 0 ,minfi_ （i􀀀 1 ; j ）+ 1 ; i_ （i; j 􀀀 1 ） + 1,if i（i; j ）= 1 ，i6 = 1或j 6 = 1 m+n 否則,f2的（i; j ; i_ （i; j ） = minf_i_ （i; j ）;（i+ 1 ; j ）+ 1 ;（i; j + 1 ） + 1 由此產(chǎn)生的圖像，是距離變換的形象，一，注意t是一個(gè)集f至 （ i ; j ）;t（i; j ） ： 1 _ i _ n 1_ j _，讓t_ _t, （i; j ）;t

54、（一; j ） 2 t_ i_沒(méi)有四點(diǎn)為a4 （ （i; j ）有一個(gè)價(jià)值在t等于t（i; j ）+1 。對(duì)所有其余各點(diǎn)（i; j ），讓t_ （i; j ）= 0 。這個(gè)形象t_是所謂的距離骨架。 我們現(xiàn)在申請(qǐng)的職能的g1到距離骨架t_在標(biāo)準(zhǔn)掃描秩序，產(chǎn)生t_（i; j ）條的g1 = （i; j ; t_ （i; j ），和g2到的結(jié)果，在g1期逆向掃描的標(biāo)準(zhǔn)秩序，產(chǎn)生t_（i; j ）g2（i; j ; t_ （i; j ） ，詳情如下： g1(i; j; t_(i; j) = maxft_(i; j); t_(i 􀀀 1; j)􀀀 1; t_(i;

55、j 􀀀 1) 􀀀 1gg2(i; j; t_(i; j) = maxft_(i; j); t_(i + 1; j)􀀀 1; t_(i; j + 1) 􀀀 1結(jié)果t_是平等的向距離變換的圖像，兩種職能g1和g2 ，與g（ t_ ） = g2(g1(t_) = t_,我們有 15 ： 定理1g（ t_ ） =t，如果t0是任何子的形象t（延長(zhǎng)至一個(gè)形象有值為0 ，在所有剩余的持倉(cāng)量）等認(rèn)為，g（ t0 ） =t， 然后t0 （i; j ）= t_ （i; j ）在各個(gè)崗位上的t_與非零值。 非正式的，定理指出，距離變換的圖像是可重構(gòu)從距離骨骼，它是迄今發(fā)現(xiàn)的最小的數(shù)據(jù)集需要這樣的重建工作。用過(guò)的距離， d4從歐幾里德度量。舉例來(lái)說(shuō)，這個(gè)d4的遠(yuǎn)程骨架，是不是不變根據(jù)輪換。為一近似歐氏距離，一些