基于計(jì)算機(jī)視覺的三維測(cè)量技術(shù)文獻(xiàn)翻譯

1、重 慶 理 工 大 學(xué)文 獻(xiàn) 翻 譯二級(jí)學(xué)院 專 業(yè) 班 級(jí) 學(xué)生姓名 學(xué) 號(hào) 譯文：基于計(jì)算機(jī)視覺的三維測(cè)量技術(shù)摘 要:本文根據(jù)計(jì)算機(jī)視覺原理，提出一種三維非接觸測(cè)量技術(shù)。該技術(shù)根據(jù)人眼感知事物的原理，利用神經(jīng)網(wǎng)絡(luò)擬合圖像坐標(biāo)與空間坐標(biāo)的映射關(guān)系；以光柵投影曲線為特征，采用小波邊緣檢測(cè)和搜索式無監(jiān)督聚類，結(jié)合視覺幾何不變性，實(shí)現(xiàn)亞像素級(jí)的立體精確匹配；并采用小波多尺度多分辨率的特性，拼接圖像，融合數(shù)據(jù)，對(duì)物體進(jìn)行全方位測(cè)量。實(shí)驗(yàn)表明，該技術(shù)設(shè)備簡(jiǎn)單，測(cè)量速度快，測(cè)量精度控制在0.5 mm/m以內(nèi)。關(guān)鍵詞:計(jì)算機(jī)視覺，立體匹配，幾何不變性，神經(jīng)網(wǎng)絡(luò)，小波變換，聚類1 引言目前，三維測(cè)量仍以三維

2、坐標(biāo)測(cè)量機(jī)為主。但是它由于體積大、結(jié)構(gòu)復(fù)雜而不能在線測(cè)量，是接觸測(cè)量而不能測(cè)量柔軟的物體。因此，研究快速無損、非接觸在線測(cè)量在工業(yè)上十分重要。盡管現(xiàn)在有很多方法，如激光掃描法、結(jié)構(gòu)光法、相位測(cè)量法，但是都不能同時(shí)滿足測(cè)量精度、效率、成本、自動(dòng)化和智能化等方面的要求。因此，在本文使用雙攝像機(jī)融合光學(xué)軸抓拍物體。隨著處理圖像，立體匹配圖像和數(shù)據(jù)集成，三維物體的信息就是從這個(gè)立體圖像中獲得。三維測(cè)量技術(shù)已應(yīng)用于測(cè)量系統(tǒng)中的多點(diǎn)壓成型機(jī)的測(cè)量，并取得了良好的效果。2 測(cè)量原理及系統(tǒng)設(shè)計(jì)本文介紹了基于計(jì)算機(jī)視覺的三維非接觸測(cè)量技術(shù)，三維對(duì)象的信息是從一對(duì)立體圖像中獲取。一般來說，有兩個(gè)問題影響的三維物體

3、獲得確切的消息：一種是圖像之間建立特殊點(diǎn)點(diǎn)和準(zhǔn)確的映射關(guān)系，另一種是立體匹配問題。本文神經(jīng)網(wǎng)絡(luò)是用來映射關(guān)系接近的情況下攝像機(jī)標(biāo)定。小波邊緣檢測(cè)，尋找非監(jiān)督聚類和幾何不變性適用于立體匹配。在多尺度，多分辨率的小波屬性應(yīng)用于圖像拼接和數(shù)據(jù)集成。在實(shí)踐中，這項(xiàng)技術(shù)包含了許多方法和技術(shù)，它可以測(cè)量任意大小和形狀的對(duì)象。然而，有一些物體的表面很光滑。匹配功能不明顯，因此用光柵對(duì)象預(yù)測(cè)。而扭曲的條紋上創(chuàng)建的對(duì)象被視為匹配功能。為了提高測(cè)量精度，用兩個(gè)與融合光學(xué)軸相機(jī)，這兩個(gè)相機(jī)和一小型自制的投影機(jī)就構(gòu)成了一種靈活的測(cè)量頭。一個(gè)基于立體視覺的三維測(cè)量的原理草圖如圖1所示。3 建立圖像點(diǎn)和特殊點(diǎn)之間的映射關(guān)

4、系實(shí)際上，獲得從兩個(gè)圖像對(duì)三維物體的信息是獲取圖像點(diǎn)之間的映射和特殊點(diǎn)的關(guān)系，但是到現(xiàn)在為止沒有任何方法可以完全描述非線性映射關(guān)系，因?yàn)橛性S多復(fù)雜的非線性影響因素，包括攝像的徑向變形和橫向變形。但是，神經(jīng)網(wǎng)絡(luò)可以模擬人類的視覺，建立了簡(jiǎn)單的非線性映射來處理復(fù)雜的單元，因此本文就從圖像點(diǎn)的過程中當(dāng)作黑箱特殊點(diǎn)。和BP網(wǎng)絡(luò)的6個(gè)神經(jīng)細(xì)胞中間層網(wǎng)絡(luò)來設(shè)置點(diǎn)之間的形象和特殊點(diǎn)的映射關(guān)系。圖片左邊的點(diǎn)A和一個(gè)右邊的點(diǎn)納入BP網(wǎng)絡(luò)，一個(gè)特殊的點(diǎn)被輸出。換言之，這個(gè)BP網(wǎng)絡(luò)的結(jié)構(gòu)是4-6-3。利用神經(jīng)網(wǎng)絡(luò)，樣本的選擇是很重要的。樣本不僅在于衡量的范圍，也顯示測(cè)量系統(tǒng)的測(cè)量范圍。雖然兩個(gè)相機(jī)是用來抓拍對(duì)象，但

5、是這部分對(duì)象只有在焊接處的視野內(nèi)才能被獲取。因此，物體三維信息的立體圖像，鏡頭焦點(diǎn)的測(cè)量精度，測(cè)量范圍和目標(biāo)與攝像機(jī)之間的兩個(gè)基準(zhǔn)距離控制三維測(cè)量系統(tǒng)的測(cè)量范圍。本文的結(jié)構(gòu)和功能和兩個(gè)相機(jī)是用來抓拍對(duì)象構(gòu)成對(duì)稱是相同的，相機(jī)的圖像區(qū)域的是，如圖2所示。該鏡頭的焦點(diǎn)是;兩個(gè)圖像之間的中心垂直線是。共同的部分被視為雙攝像頭的連接視野。而超出的部視為盲區(qū)。假設(shè)視野角度為2，基本的成像關(guān)系公式為： (1)這個(gè)內(nèi)切圓是視野范圍，如果兩個(gè)相機(jī)光軸的夾角是，兩個(gè)圖像中心之間的距離是2，其比例為： (2)這樣，一個(gè)2R×2R的示例模板由8×8的格子組成。這個(gè)示例模板固定在工作臺(tái)上。分別獲取

6、三對(duì)立體圖像，而示例模板沿垂直線方向移動(dòng)到三個(gè)不同高度（0，R，2R）模擬三維測(cè)量范圍。三對(duì)立體圖像被視為訓(xùn)練樣本，把它們輸入網(wǎng)絡(luò)。4 亞像素級(jí)的立體精確匹配對(duì)立體顯示來說立體精確匹配要困難得多，所以申請(qǐng)采用立體顯示在某種程度上受到限制。本文應(yīng)用小波變換檢測(cè)邊緣點(diǎn)，尋找非主管聚類方法，提出以區(qū)分不同的邊緣點(diǎn)群。在同一個(gè)點(diǎn)群的邊緣點(diǎn)的二次曲線擬合，然后在立體精確匹配亞像素級(jí)的水平基礎(chǔ)上取得幾何不變性。41 條紋邊緣擬合中的非聚類搜索一般來說，圖像往往含有隨機(jī)噪聲，小波變換能抑制噪聲和檢測(cè)移動(dòng)，同時(shí)不同結(jié)構(gòu)圖像邊緣的信息傳播在所有決議中。自從轉(zhuǎn)化不變性是最重要的立體匹配的邊緣特征。二次B-spin

7、e被用來處理一個(gè)多尺度的生成元素檢測(cè)條紋邊緣點(diǎn)。實(shí)際上，噪音仍然混合在這些離散邊緣點(diǎn)中，因此，曲線擬合用于轉(zhuǎn)化為連續(xù)曲線離散邊緣點(diǎn)，并減少噪音。然而，在曲線擬合之前，至關(guān)重要的是，所有的離散邊緣點(diǎn)根據(jù)圖像中條紋邊緣的實(shí)際情況分成不同的群。海明距離的聚類中心往往被視為約束條件群，換句話說，假設(shè)一個(gè)點(diǎn)的屬性向量是，一個(gè)聚類中心的屬性向量是，如果，n是聚類總數(shù)，這樣的思想不符合的條紋邊緣點(diǎn)的實(shí)際情況。在曲線擬合之前，不僅給定的群體，而且這組點(diǎn)屬于已知，而群體數(shù)目與條紋邊數(shù)相等。因此，在本文中提出了非主管聚類算法。如果D是一個(gè)集合點(diǎn)，n是D點(diǎn)的數(shù)量，如果D分成組，劃分方法如下所示。1) 如果是屬性向量

8、，被稱為初始群體，這里是，的組數(shù)等于n；2）假如=，結(jié)束；3）在覆蓋下的基礎(chǔ)上，兩個(gè)群體之間的距離也就可以計(jì)算所有群體。假如，且（T代表轉(zhuǎn)置矩陣）， = min，最近的兩組被選擇；4）和是合并到，于是，所以群體總數(shù)減少；5）重復(fù)步驟（2）。42 基于幾何不變性的相應(yīng)點(diǎn)搜索幾何不變性的定義是幾何圖案和矢量保持精確不變。對(duì)于一個(gè)特殊的多邊形，兩種不同的成行將得到兩種透視變換圖像位面。以同樣的方式，對(duì)于一個(gè)三維曲線，兩種不同的二維曲線得到兩個(gè)圖像位面。因此，幾何不變性應(yīng)用于匹配直線和曲線。對(duì)于直線匹配，幾何不變性由5個(gè)點(diǎn)在同一條直線或5條直線在同一平面所代表。我們假設(shè)是特殊平面上的任意5條直線，直線

9、方程為： (3)我們?nèi)我膺x擇3直線，和在5條直線上(k1,k2,k3=1,2,3,4,5,k1k2,k1,k3,k2k3)。這三條直線方程給出為： (4)這些直線均按直線的角度轉(zhuǎn)變成圖像。直線的特征也轉(zhuǎn)換相應(yīng)的直線方程的參數(shù)。參數(shù)顯示在上標(biāo)處（例如）。它證明，盡管這連續(xù)的五條直線的形狀可以有更多的變化，它們也服從幾何不變性，如果M屬于A，它們是： , (5)類似地，有一個(gè)組的二次曲線的一些幾何不變量。如果這個(gè)特殊平面上的一條二次曲線，它的方程可以表現(xiàn)為如下的二次曲線： (6)如果是二次曲線的參數(shù)矩陣，它也表現(xiàn)為如下矩陣： (7)如果有兩條二次曲線和，它們的參數(shù)矩陣分別為和。運(yùn)用幾何投影將它們轉(zhuǎn)

10、化為和，其參數(shù)矩陣為和。它證明，如果是矩陣的軌道，有兩個(gè)幾何不變量不管幾何投影模式是否變化。 (8) (9)這樣，直線和曲線就有效匹配了。本文光柵投影在垂直方向和水平方向被分別提出來，而兩相機(jī)抓拍圖像。隨著小波邊緣檢測(cè)，搜索式無監(jiān)督聚類，邊緣點(diǎn)到二次曲線擬合。幾何不變性，二次曲線匹配，垂直曲線和橫向曲線交叉點(diǎn)的計(jì)算。因此，亞像素級(jí)的立體精確匹配得以實(shí)現(xiàn)。5 基于小波的圖像拼接當(dāng)大規(guī)模的測(cè)量表面時(shí)，許多對(duì)立體圖象在不同的觀點(diǎn)或者移動(dòng)和旋轉(zhuǎn)中被抓拍到。兩個(gè)相鄰圖像需要鑲嵌。圖像鑲嵌的重要問題是圖像配準(zhǔn)，也就是說，兩個(gè)相鄰圖像之間的重疊部分，以便付諸表決，并且兩個(gè)相鄰圖像之間的相應(yīng)匹配也是圖像鑲嵌的

11、復(fù)雜工作。通訊匹配在相應(yīng)的立體視覺匹配之后。在這之前，從相同的角度或者不同的角度沿著基本路線轉(zhuǎn)換來抓住兩個(gè)圖像，并在這之后，這兩張圖片的角度不僅要是轉(zhuǎn)換，而且要旋轉(zhuǎn)。本文，一些隨機(jī)黑點(diǎn)能容易的鑲嵌，這些黑點(diǎn)被認(rèn)為是重要的拼接點(diǎn)。同時(shí)，我們用線性和對(duì)稱雙正交分解兩個(gè)圖像來鑲嵌，使粗糙的圖像可以得到很好的匹配和拼接，最終得到一個(gè)大的圖像。事實(shí)上，小波變換是一種帶通濾波，小波向量的顯示用不同尺度的頻帶寬度來衡量，所以每個(gè)小波的頻率帶寬是不相等的。兩個(gè)圖像用Mallat算法分解成不同頻率波段的小波向量，然后不同規(guī)模選擇不同的鑲嵌寬度來滿足和拼接，于是一個(gè)大的鑲嵌圖便順利且很好的完成了。6 實(shí)驗(yàn)及結(jié)果分

12、析在本次設(shè)計(jì)中，這項(xiàng)技術(shù)在MPF機(jī)的測(cè)量系統(tǒng)中得到了應(yīng)用。在應(yīng)用了該技術(shù)后，測(cè)量結(jié)果返回到CAD / CAE系統(tǒng)中顯示閉環(huán)控制得到了實(shí)現(xiàn)。表面形狀后測(cè)量，測(cè)量結(jié)果返回到CAD / CAE系統(tǒng)和閉環(huán)控制的實(shí)現(xiàn)。據(jù)測(cè)量條件、測(cè)量精度一旦成熟，我們選擇兩個(gè)攝像頭（MTV1881CB），兩個(gè)鏡頭和一個(gè)圖像記錄裝置（METEOR）。這兩個(gè)攝像頭之間的距離為300毫米；物體表面和兩部相機(jī)之間的距離為500毫米。A 150×150 mm的曲面是該工藝的標(biāo)準(zhǔn)測(cè)量范圍，測(cè)量結(jié)果在標(biāo)簽 1上顯示，測(cè)量步驟如下：1） 建立與圖像點(diǎn)和特殊點(diǎn)之間的映射關(guān)系；2）三維表面在工作臺(tái)上進(jìn)行，首先，二個(gè)攝像機(jī)在沒有干

13、擾和光線的情況下同時(shí)抓拍一對(duì)立體圖像。其次，在抓住兩對(duì)立體圖像對(duì)，一對(duì)在光柵的垂直方向上抓拍，另一對(duì)在光柵的橫向上抓拍；3）進(jìn)程映像，消除背景，減少噪音，如圖3a，3b所示；4）功能檢測(cè)，如圖3c；5）搜索對(duì)應(yīng)點(diǎn)，并鑲嵌圖像；6）計(jì)算三維坐標(biāo)，重建三維表面，如圖3d。實(shí)驗(yàn)表明，測(cè)量誤差小于0.5mm，測(cè)量時(shí)間約2秒，包括圖像抓拍、圖像處理、建立圖像點(diǎn)和特殊點(diǎn)的映射關(guān)系、搜索相應(yīng)的坐標(biāo)點(diǎn)和調(diào)整計(jì)算。 圖、3 圖像處理7 結(jié)束語在本文中，提出了一種新的基于計(jì)算機(jī)視覺的三維測(cè)量技術(shù)，該技術(shù)設(shè)備簡(jiǎn)單、測(cè)量速度快、成本低?？梢詼y(cè)量大型對(duì)象，測(cè)量精度低于0.5 mm/m。它還提供了一個(gè)適用于工業(yè)計(jì)算機(jī)視覺

14、的新思路。實(shí)驗(yàn)結(jié)果表明，三維測(cè)量技術(shù)是非常完美的。原文：3D Measurement Technology Basedon Computer Vision Abstract: On the basis of computer vision, a noncontact 3D measurement technology was proposed in this paper. Using neural network, the mapping relation between image point and special point was established. The projection

15、 of grating on object is regarded as matching features, with wavelet edge detection, searching non-supervisor clustering and geometric invariance. Stereo precision matching is achieved at subpixel level. Furthermore, the multi-scale and multi-resolution attributes of wavelet are applied to image mos

16、aic and data integration, so a large scale object can be measured. Experiments show that the technology has many advantages, such as simple equipment, fast speed and low cost, and that the measuring error is less than 0.5 mm/m. Key words: Computer vision; stereo matching; geometric invariance; neura

17、l network; wavelet transform; clustering1 IntroductionAt present, three-dimensional(3D) measuring machine is still a main role in 3D measurement. But it cannot measure on line because of its bulk and its complex construction, and it obtains data from point contact so that it cannot measure soft obje

18、ct. Therefore, it is important for industry to research noncontact fast nondestructive measurement on line. Although there have been many methods, such as laserscanning method, structured light method, phase measuring method, they cannot simultaneously satisfy the demands of measurement precision, m

19、easurement speed, automation and intellectualization, and low cost.Consequently, in this paper, using two-camera with the converging optical-axis to grab image. With processing image, stereo matching image mosaic and data integration, 3D information of object is obtained from a pair of stereo images

20、. The 3D measurement technology has been applied to the measurement system of the Multi-point Press-forming Machine (MPF machine)2, and good results are obtained.2 Measurement Principle and System Design This paper describes the 3D noncontact measurement technology based on computer vision, and 3D i

21、nformation of object is obtained from a pair of stereo images. Generally, there are two problems that influence obtaining 3D exact information of object: the one is establishing the exact mapping relation between image point and special point; the other is stereo matching problem. In this paper, neu

22、ral network is used to approaching the mapping relation without camera calibration. Wavelet edge detection, searching non-supervisor clustering and geometric invariance are applied to stereo matching. The multi-scale and multi-resolution attribute of wavelet is applied to image mosaic and data integ

23、ration. In practice, the technology includes many methods and techniques, it can measure arbitrary size and shape object. However, the surfaces of some objects are smooth. Matching features are inconspicuous, so grating is projected on object. And the distorted stripes are created on object. They ar

24、e regarded as matching features. For improving measurement precision, two-camera with converging optical-axis is chosen. And the two-camera and the small self-made projector constitute a flexible measuring head. A sketch of the 3D measurement principle based on stereo vision is shown in Fig.1. 3 Est

25、ablishment of the Mapping Relation Between Image Point and Special Point Actually, obtaining 3D information of object from a pair of two images is by mapping relation between image point and special point, but until now no approach can completely describe the nonlinear mapping relation since there a

26、re many complex nonlinear influencing factors including radial distortion and lateral distortion of camera. However, neural network can simulate human vision to establish complex mapping by simple nonlinear processing cells, so this paper regards the middle process from image point to special point

27、as a black box. And BP network with a middle layer of six neural cells is used to set up the mapping relation between image point and special point. Point A in left image and a point in right image are input into the BP network, a special point is output. In other words, the structure of BP network

28、is 4-6-3. Using neural network, the choosing of training samples is important The training samples not only lie in the measurable range, but also show measurement range of measurement system.While two-camera is used to grab object, the object and the part of object only in jointing viewing field can

29、 be able to be grabbed. So 3D information of object from a pair of stereo images, lens focus, measurement precision, once measuring area and the distance between object and baseline of two-camera control 3D measurement range of the system are obtained.In this paper, the structure and function of the

30、 two cameras that are posed symmetrically are identical, and the image area is , just as Fig.2. The lens focus is f; the line between two image centers is perpendicular to . The common part is regarded as joining viewing field of two-camera. And the part out of is known as blind area. If 2 is viewin

31、g field angle, on the basic of imaging relation, the formula is (1) An inscribed circle is done in the joining viewing field, if is included angle of two-camera optical axis, 2 is the distance between two image centers, its ratio is (2)In this way, a 2R×2R sample template with 8×8 grids is

32、 made. The sample template is put worktable. Three pairs of stereo images are grabbed respectively, while the sample template is moved to three different heights (0, R, 2R) along the vertical direction to simulate 3D measurement range. The three pairs of stereo images are regarded as training sample

33、s, and they are input network.4 Stereo Precise Matching at Subpixel Level Stereo precise matching is much more difficult in stereo vision, so the applying of stereo vision is restricted in a way. In this paper, wavelet transform is applied to detect edge points, searching non-supervisor clustering a

34、pproach is proposed to distinguish the different edge point groups. The edge points in the same point group are fitted quadratic curve, and then stereo precise matching is achieved at subpixel level based on geometry invariance.4.1 Stripe Edges Fitting Based on Searching Nonsupervisor Clustering Gen

35、erally, image often contains random noise, and wavelet transform can restrain noise and detect edge, while different structure image edges are described by the information spreading in all resolutions. Since translating invariance is the most important in stereo matching based on edge feature. Quadr

36、atic B-spine is selected for a multi-scale generating element to detect edge points of stripe.Actually, noise is still mixed in these discrete edge points, so curve fitting is used to translate the discrete edge points into a continuous curve, and to reduce noise. However, before curves are fitted,

37、it is crucial that all discrete edge points are distinguished into different groups according to the practical situation of the stripe edges in images. Hamming distance to clustering center is often regarded as constraint condition to cluster, in other words, if the attribute vector of a point is Xl

38、,and the attribute vector of a clustering center is , and if , n is the total number of groups, then Xli, so the idea doesn't accord with the practical situation of stripe edge points. Before curves are fitted, not only is the number of groups given, but also which group a point belongs to is kn

39、own, and the number of groups is equal to the number of stripe edges. Therefore, a searching non-supervisor clustering algorithm is proposed in this paper.If D is an aggregate of points, n is number of points in D, and if D is divided into groups, dividing approach is shown as follows.1) If is attri

40、bute vector, is known as initial group , that is ,the number of groups is equal to n; 2) If =, end;3) On the basis of under hood, the distance between two groups is computed for all groups. If , and (T stands for transpose), that is = min, and two nearest groups are chosen; 4) and are merged into ,

41、that is , so the total of groups decrease 1;5) Return (2).4.2 Searching Corresponding Points Based on Geometric InvarianceGeometric invariance is defined that geometrical figure and vector keep invariance in mathematical manipulation.For a special polygon, two different shape polygons will be obtain

42、ed in two image planes by perspective transform. In the same way, for a 3D curve, two different 2D curves are obtained in two image planes. Therefore geometric invariance is applied to matching straight lines and curves.For straight-line matching, representational geometric invariance is composed of

43、 five points in the same straight line or five straight lines in the same surface.We assume that is arbitrary five straight lines on special plane, straight-line equation is (3)We arbitrarily choose three straight lines ,and in the five straight lines (k1,k2,k3=1,2,3,4,5,k1k2,k1,k3,k2k3). The system

44、 of equations of the three straight lines are given by (4)And these straight lines are translated into image straight lines by perspective transform. The image straight lines have also corresponding straight-line equation parameters. And the parameters are shown with superscript (for example ). It i

45、s testified, though the shapes of five straight lines can more change, there are geometric invariants, if Mis det A, they are , (5)Analogously, there are some geometric invariants for a group of quadratic curves. If is a quadratic curve on the special plane, its equation can be shown as follows (6)A

46、nd if is parameter matrix of quadratic curve, it is also shown by matrix as follows (7)If there are two quadratic curves and ,their parameter matrixes are respectively and . They are translated into and by geometric projection, and their parameter matrixes are and . It is testified, if is track of m

47、atrix, there are two geometric invariants whether mode of geometric projection is changed. (8) (9)In this way, straight lines and curves are matched effectively.In this paper, grating is projected on object in vertical direction and lateral direction respectively, while two cameras grab images. With

48、 wavelet edge detection, searching non-supervisor, edge points are fitted into quadratic curves. With geometric invariance, quadratic curves are matched, and cross points of vertical curves and lateral curves are computed. So stereo precise matching at subpixel level is achieved.5 Image Mosaic Based

49、 on WaveletWhen large-scale surface is measured, many pairs of stereo images are grabbed from different viewpoints or with moving and rotating object. And two adjacent images need mosaic. The important question of image mosaic is image registration, that is to say, overlapped parts between two adjac

50、ent images are put in order, and corresponding matching between two adjacent images is also involved in image mosaic. Corresponding matching in registration is deferred from corresponding matching in stereo vision. In the former, two images are grabbed from the same viewpoint or from the different v

51、iewpoints that are translated along the basic line, and in the latter, the viewpoints of two images are not only translated but also revolved.In this paper, some black points are pasted at random on object in order to mosaic easily, and the black points are regarded as registration feature points. M

52、eanwhile, we use biorthogonal wavelet with linearity and symmetry to decompose two images that are will be mosaic, so the images can be matched and registered from coarse to fine on multi-scale, and lastly a big image is become.In fact, wavelet transform is a band-pass filter, wavelet vector on diff

53、erent scales shows the stated width of frequency band, and so frequency bandwidth of each wavelet vector is unequal. Two images are decomposed into wavelet vectors on different frequency bands based on Mallat algorithm, and then the different mosaic widths are selected on different scales to match and register, so a big mosaic image is smooth and fine.6 Experiments and Results Analysis In this paper, the technology is applied to the measurement system of MPF machine. After the s