數(shù)字圖像處理外文翻譯--- 數(shù)字圖像處理

1、<p>　　Digital Image Processing</p><p>　　1 Introduction</p><p>　　Many operators have been proposed for presenting a connected component n a digital image by a reduced amount of data or simpl

2、ied shape. In general we have to state that the development, choice and modi_cation of such algorithms in practical applications are domain and task dependent, and there is no \best method". However, it is interesti

3、ng to note that there are several equivalences between published methods and notions, and characterizing such equivalences or di_erences should be useful to cat</p><p>　　1.1 Categories of Methods</p>

4、<p>　　One 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 maximal di

5、sc (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 functi

6、on which is appropriate to digitized pictures. A second class of operat</p><p>　　The third class of operators is characterized by iterative thinning. Historically, Listing [10] used already in 1862 the term

7、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. M

8、any algorithms in image analysis are based on this general concept of thinning. The goal is a calculation of characteristic properties of digital objects </p><p>　　in a unique interpretation besides that it

9、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 _ I of object points is reduce

10、d 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.

11、A digital curve i</p><p>　　1.2 Basics</p><p>　　The 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

12、 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) image is f0; :::Gmaxg with Gmax _ 1. The range of a binary image is f0; 1g. We

13、 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 carri</p><p>　　Two pixel locations p and q in the grid cell model are c

14、alled 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 pixel locations p and q in the grid

15、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 loc

16、atio</p><p>　　2 Non-iterative Algorithms</p><p>　　Non-iterative algorithms deliver subsets of components in specied scan orders without testing connectivity preservation in a number of iteration

17、s. In this section we only use the grid point model.</p><p>　　2.1 \Distance Skeleton" Algorithms</p><p>　　Blum [3] suggested a skeleton representation by a set of symmetric points.In a clos

18、ed subset of the Euclidean plane a point 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.

19、 The set of symmetric points, each labeled with the radius of the associated maximal disc, constitutes the skeleton of the set. This idea of presenting a component of a digital image as a \distance</p><p>　　

20、f1(i; j; I(i; j)) =</p><p><b>　　8><>>:</b></p><p>　　0 if I(i; j) = 0</p><p>　　minfI_(i 􀀀 1; j)+ 1; I_(i; j 􀀀 1) + 1g</p><p>　　

21、if I(i; j) = 1 and i 6= 1 or j 6= 1</p><p>　　m+ n otherwise</p><p>　　f2(i; j; I_(i; j)) = minfI_(i; j); T(i+ 1; j)+ 1; T(i; j + 1) + 1g</p><p>　　The resulting image T is the distanc

22、e 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 value in T equal to T(i; j)+1. For

23、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 t

24、he result of g1 in rever</p><p>　　g1(i; j; T_(i; j)) = maxfT_(i; j); T__(i 􀀀 1; j)􀀀 1; T__(i; j 􀀀 1) 􀀀 1g</p><p>　　g2(i; j; T__(i; j)) = maxfT__(i; j); T___(i

25、 + 1; j)􀀀 1; T___(i; j + 1) 􀀀 1g</p><p>　　The result T___ is equal to the distance transform image T. Both functions g1 and g2 de_ne an operator G, with G(T_) = g2(g1(T_)) = T___, and we ha

26、ve [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 valu

27、es. Informally, the theorem says that the distance transform image is reconstructible from the distance skeleton, and it is the small</p><p>　　2.2 \Critical Points" Algorithms</p><p>　　The

28、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 i

29、mage. We de_ne the 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

30、 case I(i; j) = 1 ^ I(i; j+ 1) = 0 ，in row i, counting from the left, wi</p><p>　　The results are subsets of pixels of the original objects, and these subsets are not necessarily connected. They can form \no

31、isy 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 orientations of object componen

32、ts.</p><p>　　References</p><p>　　[1] C. Arcelli, L. Cordella, S. Levialdi: Parallel thinning of binary pictures. Electron. Lett. 11:148{149, 1975}.</p><p>　　[2] C. Arcelli, G. Sanni

33、ti di Baja: Skeletons of planar patterns. in: Topolog- ical Algorithms for Digital Image Processing (T. Y. Kong, A. Rosenfeld, eds.), North-Holland, 99{143, 1996.}</p><p>　　[3] H. Blum: A transformation for

34、extracting new descriptors of shape. in: Models for the Perception of Speech and Visual Form (W. Wathen- Dunn, ed.), MIT Press, Cambridge, Mass., 362{380, 1967.19}</p><p><b>　　數(shù)字圖像處理</b></p>

35、;<p><b>　　1引言</b></p><p>　　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減少的數(shù)據(jù)量或簡化的形狀。一般我們不得不陳訴在實際應(yīng)用中的運算法則的發(fā)展，選擇和更改，它是依賴于鄰域和任務(wù)的，除此之外沒有更好的辦法了。不過，有趣的是，請注意， 有幾個等價之間出版的方法和觀念，和表征這種等價應(yīng)該是有用的分類的廣泛和多樣性，討論等價是這份報告一個主要的意

36、圖，。 1.1分類方法 一類形狀減少算子是基于距離變換的。一個距離骨架是一個子集點，某一特定的組成部分，例如，每點子，這代表了該中心的一個最大光盤（標記半徑這片光碟）載于特定的組成部分。作為一個例子，在這類算子，本報告討論了一個計算方法距離骨架使用的D4距離函數(shù)，這是適當?shù)臄?shù)字化圖片。 第二類算子產(chǎn)生的中位數(shù)或中心線數(shù)字對象在一個非迭代的方式。通常這樣的算子找到臨界點，并計算出特殊路徑通過對象連接這些點。 第三類

37、是算子的特點是迭代細化。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)變形的前一個連接子一歐氏空間沒有改變的連通原來的設(shè)置，直到只有一套線和點仍然存在。許多算法在圖像分析是在此基礎(chǔ)上的一般概念的細化。目標是計算特性的數(shù)字對象，其中</p><p><b>　　1.2基礎(chǔ)</b></p><p>　　所用符號如下[ 17 ] 。數(shù)字圖像I是一個功能離散集C ，即

38、所謂的載體的形象。要素的C 是網(wǎng)格點或網(wǎng)格細胞和分子性（ P ;I（ p ）） 一個圖像像素（ 2維）或體素（三維案件）。范圍的形象是f0 ; gmaxg 與gmax _ 1 。范圍二進制的形象是f0 ，我們只使用在此報告的二進制圖像。讓它成為一套所有像素的位置與價值1 。 形象載體是對一正交網(wǎng)格在二維或三維空間。 有兩種選擇：使用網(wǎng)格細胞模型的二維像素位置， P是一個封閉的廣場（ 2細胞）在歐氏平面和三維像素的位置是封閉立方體（ 3細

39、胞） ，在歐氏空間，那里邊的長度為1和平行于坐標軸，中心有整數(shù)坐標。作為一個第二個選項，使用網(wǎng)格點模型一二維或三維像素的位置是一個網(wǎng)格點。 兩個像素的位置P和Q在網(wǎng)格中的細胞模型是所謂的0 -毗鄰i_ p 6 = Q和他們分享至少有一個頂點（這是一個零細胞） 。 兩個三維像素的位置P和Q在網(wǎng)格中的細胞模型是所謂的毗鄰i_ p 6 = Q和他們分享至少有一個優(yōu)勢（這是一細胞） 。注意：如果格點模型是用這鄰接在二維或鄰接在三維。最后，兩個像

40、素的三維位置P和Q在網(wǎng)格中的細胞模型被稱為2 -毗鄰i_ </p><p>　　M 是多少行和列正在3維中使用整數(shù)坐標（i; j ; k ）段。 基于鄰域的關(guān)系，我們連通如常： 2 點p; q 2 C是有關(guān)n_ i_有一個序列點，p = p0; p1; p2; pn = q 近鄰，在此序列無論是在M或全部在補M的一個子集M_ C的形象承運人是所謂的_連接i_M，是不是空洞和所有點，在M都成對設(shè)置M 組成的一個子

41、集S的C是一個極大值,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)格的細胞模型，一個組成部分，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細胞是聯(lián)接在其4 細胞和5細胞的。3細胞是連接在其6接口。 為實際目的是易于對數(shù)字圖像中使用的臨近操作的（所謂的本地操作）。價值在P 2架C ，在轉(zhuǎn)化的形象是基于像素值在I在P 2 C和其立即鄰域在N_(p

42、)。 2非迭代算法 非迭代算法提供子組件在特殊掃描命令測試連接保存在一個迭代次數(shù)。 在本節(jié)中，我們只用網(wǎng)格點模型。 2.1 距離算法 Blum[ 3 ]提出了骨骼的代表是一組對稱點。 在一個封閉的子歐氏</p><p>　　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指標。由于二進制數(shù)字形象。我們這個圖像變換到一個新的代表在每屆點P 2 hii D4類-距離

43、像素具有的價值為零。轉(zhuǎn)型包括兩個步驟。我們申請的職能，以F1的形象，我在標準掃描秩序，產(chǎn)生i_ （i; j ）的F1 = （i; j ;i（i; j ）） ，和F2在反向標準掃描秩序，產(chǎn)生（i; j ）= F2的（i; j ; i_ （i; j ）） ，詳情如下： F1的（i; j ;i（i; j ）） = 8 > < > > ：if I（i; j ）= 0 ,minfi_ （i􀀀 1 ; j

44、）+ 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是一個集F至[ （ i ; j ）;T（i; j ）] ： 1 _ i _ n ^1_ j _

45、，讓t</p><p>　　詳情如下： g1(i; j; T_(i; j)) = maxfT_(i; j); T__(i 􀀀 1; j)􀀀 1; T__(i; j 􀀀 1) 􀀀 1g</p><p>　　g2(i; j; T__(i; j)) = maxfT__(i; j); T___(i + 1; j)И

46、576; 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（延長至一個形象有值為0 ，在所有剩余的持倉量）等認為，G（ t0 ） =T， 然后t0 （i; j ）= t_ （i; j ）在各個崗位上的t_與非零值。 非正式的，定理指

47、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。用過的距離， D4從歐幾里德度量。舉例來說，這個D4的遠程骨架，是不是不變根據(jù)輪換。為一近似歐氏距離，一些作者建議使用 的權(quán)數(shù)，格點街道[ 4 ] 。 [ 11 ]介紹了準歐氏距離。 在一般， D4的遠程骨架是一個子像素（p;T（ p ）項）的轉(zhuǎn)變形象，這是不一定的連接。 2.2 臨界點算法 最簡單的一類，這些算法決定的中點子連接組件在標準掃

48、描，以便每一行。讓升被1指數(shù)為若干組件</p><p>　　in row i, counting from the left, with I(i;􀀀1) = 0</p><p>　　oi(l) = _ j if this is the lth case I(i; j) = 1 ^ I(i; j+ 1) = 0</p><p>　　in row i,

49、 counting from the left, with I(i;m+ 1) = 0</p><p>　　mi(l) = int((oi(l) 􀀀 ei(l)=2)+ oi(l)</p><p>　　所連接的元件在連續(xù)中點所有行構(gòu)成了一個臨界點骨架的形象，這種方法的計算是精確的。 結(jié)果子像素的原始物體，而這些子像素不一定是連接的。他們可以形成噪音分枝，當對象組

50、件接近平行的形象行，他們可能的特殊應(yīng)用是有用的，而掃描方向大約是垂直方向的主要對象組件.</p><p>　　參考文獻[ 1 ] C. Arcelli, L. Cordella, S. Levialdi ：并行細化二元圖片 （ 149 ,1975） 。 [ 2 ] C. Arcelli, G. Sanniti di Baja： topolog - iCal的算法為數(shù)字圖像處理</p>&l