Distance measuring based on stereoscopic pictures

Transcription

1 9th International Ph Workshop on Systems and Control: Young Generation Viewpoint October 8, Izola, Slovenia istance measuring d on stereoscopic pictures Jernej Mrovlje 1 and amir Vrančić Abstract Stereoscopy is a technique used for recording and representing stereoscopic (3) images. It can create an illusion of depth using two pictures taken at slightly different positions. There are two possible way of taking stereoscopic pictures: by using special two-lens stereo cameras or systems with two single-lens cameras joined together. Stereoscopic pictures allow us to calculate the distance from the camera(s) to the chosen object within the picture. The distance is calculated from differences between the pictures and additional technical data like focal length and distance between the cameras. The certain object is selected on the left picture, while the same object on the right picture is automatically detected by means of optimisation algorithm which searches for minimum difference between both pictures. The calculation of object s position can be calculated by doing some geometrical derivations. The accuracy of the position depends on picture resolution, optical distortions and distance between the cameras. The results showed that the calculated distance to the subject is relatively accurate. I. INTROUCTION Methods for measuring the distance to some objects can be divided into active and passive ones. The active methods are measuring the distance by sending some signals to the object [, 4] (e.g. laser beam, radio signals, ultra-sound, etc.) while passive ones only receive information about object s position (usually by light). Among passive ones, the most popular are those relying on stereoscopic measuring method. The main characteristic of the method is to use two cameras. The object s distance can be calculated from relative difference of object s position on both cameras [6]. The paper shows implementation of such algorithm within program package Matlab and gives results of eperiments d on some stereoscopic pictures taken in various locations in space. II. STEREOSCOPIC MEASUREMENT METHO Stereoscopy is a technique used for recording and representing stereoscopic (3) images. It can create an illusion of depth using two pictures taken at slightly different positions. In 1838, ritish scientist Charles Wheatstone invented stereoscopic pictures and viewing devices [1, 5, 7]. Stereoscopic picture can be taken with a pair of cameras, 1 Jernej Morvlje is with the Faculty of Electrical Engineering, University of Ljubljana, Slovenia; ( jernej.mrovlje@gmail.com). amir Vrančić is was with epartment of Systems and Control, J. Stefan Institute, Jamova 39, 1 Ljubljana, Slovenia ( damir.vrancic@ijs.si). similarly to our own eyes. The most important restrictions in taking a pair of stereoscopic pictures are the following: cameras should be horizontally aligned (see Figure 1), and the pictures should be taken at the same instant [3]. Note that the latest requirement is not so important for static pictures (where no object is moving). horizontal vertical error vertical error Fig. 1. Proper alignment of the cameras (a) and alignments with vertical errors (b) and (c). Stereoscopic pictures allow us to calculate the distance between the camera(s) and the chosen object within the picture. Let the right picture be taken in location S R and the left picture in location S L. represents the distance between the cameras and φ is camera s horizontal angle of view (see Figure ). Object s position (distance ) can be calculated by doing some geometrical derivations. We can epress distance as a sum of distances 1 and : ( a) ( b) ( c) = + ϕ, (1) 1 + = tanϕ1 tan if optical aes of the cameras are parallel, where φ 1 and φ are angles between optical ais of camera lens and the chosen object. istance is as follows: = () tanϕ 1 + tanϕ

2 9th International Ph Workshop on Systems and Control: Young Generation Viewpoint October 8, Izola, Slovenia where φ is camera s horizontal angle of view and picture resolution (in piels). 1 ϕ1 ϕ ϕ 1 ϕ ϕ 1 ϕ S L Fig.. The picture of the object (tree) taken with two cameras. S R S L Using images 3 and 4 and basic trigonometry, we find: 1 tanϕ1 =, (3) ϕ tan Fig. 3. The picture of the object (tree) taken with left camera. istance can be calculated as follows: tanϕ =. (4) ϕ tan ϕ = ϕ tan L ( ) Therefore, if the distance between the cameras (), number of horizontal piels ( ), the viewing angle of the camera (ϕ ) and the horizontal difference between the same object on both pictures ( L - ) are known, then the distance to the object () can be calculated as given in epression (5). The accuracy of the calculated position (distance ) depends on several variables. Location of the object in the right picture can be found within accuracy of one piel (see Fig. 5). Each piel corresponds to the following angle of view ϕ ϕ = (5), (6) Fig. 4. The picture of the object (tree) taken with right camera. Image 5 shows one piel angle of view φ which results in distance error. In image we find: ϕ S R

3 9th International Ph Workshop on Systems and Control: Young Generation Viewpoint October 8, Izola, Slovenia tanϕ tan ( ϕ ϕ) + =, (7) Using basic trigonometry identities, the distance error can be epressed as follows: subtracted images are, lower is the mean absolute value of matri I i. Image 6 shows two eamples of subtraction. Images in the first eample do not match, while in the second eample images match almost perfectly. = tan( ϕ). (8) Note that the actual error might be higher due to optical errors (barrel or pincushion distortion, aberration, etc.) [8]. L R ϕ IL ( NN ) I ( MN) Fig. 6. Selected object on the left picture (red colour) and search area in the right picture (green colour). R ϕ STEP 1 I R1 MN NN 1p STEP I R STEP3 p I R3 Fig. 5. istance error caused by 1 piel positioning error. III. OJECT RECOGNITION When the certain object is selected on the left picture, the same object on the right picture has to be automatically located. Let the square matri I L represent selected object on the left picture (see Figure 6). Knowing the properties of stereoscopic pictures (the objects are horizontally shifted), we can define search area within the right picture matri I R. Vertical dimensions of I R and I L should be the same, while horizontal dimension of I R should be higher. Our net step is to find the location within the search area I R, where the picture best fits matri I L. We do that by subtracting matri I L from all possible submatries (in size of matri I L ) within the matri I R. When size of the matri I L is NN and size of the matri I R is MN, where M>N, M-N+1 submatries have to be checked. Image 7 shows the search process. The result of each subtraction is another matri I i which tells us how similar subtracted images are. More similar two STEP M N STEP M N p I RM N I RM N + 1 Fig. 7. Finding appropriate submatri in the right picture.... The matri I k with the lowest mean of its elements, represents the location where matri I L best fits to matri I R. This is also the location of the chosen object within the right image. Knowing the location of the object in the left and right image allow us to calculate the distance between the pictures: L N M = + k 1. (9)

4 9th International Ph Workshop on Systems and Control: Young Generation Viewpoint October 8, Izola, Slovenia Eample 1: I Rj E j = mean( I R j I L ) I j = I Rj I L IL Eample : I Rk Ek = mean( I Rk I L ) Fig. 1. Picture with targets (small white panel boards) located at 1m, m, 3m, 4m, 5m and 6m. I k = I Rk I L IL Fig. 8. The difference between selected object in the left picture and submatri on the right picture. y N / + k 1 CL C L Fig. 11. etailed view of Figure 1 (markers). Fig. 9. Calculation of the horizontal distance of the object between left and right picture. After adjusting the cameras to be parallel, the distances were calculated in program package Matlab. The calculated distances for different locations and different markers (1m, m, 3m, 4m, 5m and 6m) are given in Tables 1 to 6. The calculated difference (9) can be used in calculation of object s distance (5). Table 1. Calculated distance to marker at 1m in various locations M / N / N / M / Marker at 1m IV. EXAMPLES Four eperiments have been conducted in order to test the accuracy of our distance-measuring method. We have used si markers placed at distances 1m, m, 3m, 4m, 5m and 6m. Those markers have been placed at various locations in space (nature) and then photographed by two cameras. One of the pictures (with detail view) is shown in Figs. 1 and 11. [m] location 1 location location 3 location 4, 1,81 1,58 1,1 1,34,3 1,63 1,4 9,77 1,47,4 1,45 1,4 1,1 1,8,5 1,9 1,4 9,81 1,13,6 1,18 1,3 9,9 1,18,7 1,18 9,84 9,96 1,13

5 9th International Ph Workshop on Systems and Control: Young Generation Viewpoint October 8, Izola, Slovenia Table. Calculated distance to marker at m in various locations Table 6. Calculated distance to marker at 6m in various locations Marker at m Marker at 6m [m] location 1 location location 3 location 4, 1,3 1,57 1,57,56,3,86 1,87 1,87,68,4,81,49,49,33,5,4,6,6,6,6,19,59,59,14,7,44,41,41 19,86 Table 3. Calculated distance to marker at 3m in various locations Marker at 3m [m] location 1 location location 3 location 4, 3,8 3,47 33, 9,57,3 31,81 31,56 7,97 31,13,4 3,5 3,93 3,1 3,65,5 3,5 31,55 9, 9,77,6 3,88 31,58 3,6 3,8,7 3,74 3,33 31,5 3,71 [m] location 1 location location 3 location 4, 63,36 67,69 7,67 53,6,3 63,56 64,63 59,9 64,99,4 64,97 6,6 6, 6,95,5 61,95 63,97 6,1 59,4,6 6,7 63,75 6,13 61,1,7 61,57 61,4 61,75 6,55 Figures 1 to 17 show the results graphically. It can be seen that the distance to the subjects is calculated quite well taking into account the camera s resolution, barrel distortion [8] and chosen. As epected, better accuracy is obtained with wider between the cameras Location Table 4. Calculated distance to marker at 4m in various locations Marker at 4m [m] location 1 location location 3 location 4 1, 4,49 45,8 4,9 37,98,3 41,67 4,7 4,76 39,78,4 4,4 4,86 38,61 4,93,5 4,17 41,4 4,5 38,4,6 4,69 41,34 41,8 4,4,7 41,1 4,84 39,73 4, Fig. 1. Calculated distances to marker set at 1m at 4 different locations..5 Location Table 5. Calculated distance to marker at 5m in various locations Marker at 5m [m] location 1 location location 3 location 4, 5,7 57,53 47,38 46,8,3 54,4 5,74 45,9 5,,4 53,1 51,16 57,5 5,15,5 51, 5,5 49,1 48,1,6 51,41 5,34 51,48 5,3,7 5,3 5,5 53,85 5, Fig. 13. Calculated distances to marker set at m at 4 different locations.

6 th International Ph Workshop on Systems and Control: Young Generation Viewpoint October 8, Izola, Slovenia Location 75 Location Fig. 14. Calculated distances to marker set at 3m at 4 different locations. Fig Calculated distances to marker set at 6m at 4 different locations Location Fig. 15. Calculated distances to marker set at 5m at 4 different locations. V. CONCLUSION The proposed method for non-invasive distance measurement is d upon the pictures taken from two horizontally displaced cameras. The user should select the object on left camera and the algorithm finds similar object on the right camera. From displacement of the same object on both pictures, the distance to the object can be calculated. Although the method is d on relatively simple algorithm, the calculated distance is still quite accurate. etter results are obtained with wider (distance between the cameras). This is all according to theoretical derivations. In future research, the proposed method will be tested on some other target objects. The influence of lens barrel distortion on measurement accuracy will be studied as well Location Fig Calculated distances to marker set at 5m at 4 different locations. REFERENCES [1] M. Vidmar, AC sodobne stereofotografije z maloslikovnimi kamerami, Cetera, [] H. Walcher, Position sensing Angle and distance measurement for engineers, Second edition, utterworth- Heinemann Ltd., [3]. Vrančić and S. L. Smith, Permanent synchronization of camcorders via LANC protocol, Stereoscopic displays and virtual reality systems XIII : January, 6, San Jose, California, USA, (SPIE, vol. 655). [4] Navigation, Radio Navigation, Revised edition, Oford Aviation Training, 4. [5] P. Gedei, Ena in ena je tri, Monitor, july 6, (1.1.7). [6] J. Carnicelli, Stereo vision: measuring object distance using piel offset, (9.11.7). [7] A. Klein, Questions and answers about stereoscopy, (8.1.7). [8] A. Woods, Image distortions and stereoscopic video systems, (7.1.7).