Figure 6:Experiment 1-The plane/ball/corner scene: Figure 7:Experiment 2-The cup/plane/ball scene:The Two views of the mesh generated from the cloud of points ob scanned objects were a cup,the plane and the ball.The ini- tained after triangulation.The original sequence was 270 frames tial image of the scene is shown on the left,and the final re- long,the images being 320 x 240 pixels each.At 60 Hz acquisi- constructed mesh on the right.We found agreement between tion frequency,the entire scanning take 5 seconds.The camera the estimated height of the cup from the 3D reconstruction, was positioned at distance d=16.7 cm from the desk plane, 11.040.09 cm,and the measured height (obtained using a tilted down by 0 =41.3 degrees.The light source was at height ruler),10.95+0.05 cm.Once again the right portion on the hs 37.7 cm,on the left of the camera at angles =157.1 reconstructed scene is noisier than the left portion.This was degrees and=64.8 degrees.From the right-hand figure we expected since the light source was,once again,standing to the notice that the right-hand side of the reconstructed scene is left of the camera.Geometrical parameters:d=22.6 cm, more noisy than the left-hand side.This was expected since the 0=38.2 degrees,hs 43.2 cm,155.9 degrees,and =69 lamp was standing on the left of the camera (refer to section 3 degrees. for details). Figures 7 and 8 report the reconstruction results Geometry of the corner:We fit 2 planes to the achieved on two other scenes. corner structure,one corresponding to the top surface (the horizontal plane)and the other one to the frontal 5 Conclusion and future work surface (vertical plane).We estimated the surface We have presented a simple,low cost system for noise of the top surface to 0.125 mm,and that of the extracting surface shape of objects.The method re frontal face to 0.8 mm (almost 7 times larger).This quires very little processing and image storage so that noise difference between the two planes can be ob- it can be implemented in real time.The accuracies we served on figure 6.Once again,after fitting quadratic obtained on the final reconstructions are reasonable patches to the two planar portions,we did not no- (at most 1%or 0.5:mm noise error)considering the tice any significant global geometric distortion in the little hardware requirement.The user can adjust the scene (from planar to quadratic warping,the residual speed of scanning to obtain the desired accuracy.In noise decreased by only 5%in standard deviation) addition,the final outcome is a dense coverage of the From the reconstruction,we estimated the height H surface (one point in space for each pixel in the image) and width D of the right angle structure,as well as allowing for direct texture mapping the angle t between the two reconstructed planes,and An error analysis was presented together with the compared them to their true values: description of a simple technique for merging multi- ple 3D scans together in order to (a)obtain a better coverage of the scene,and (b)reduce the estimation Parameters Estimates True Relative values errors noise.The overall calibration procedure,even in the H(cm】 2.57±0.02T2.65±0.02 3% case of multiple scans,is very intuitive,simple,and D(cm】 3.06±0.02 3.02±0.02 1.3% sufficiently accurate. (degrees) 86.21 90 1% Another advantage of our approach is that it easily scales to larger scenarios indoors-using more power- The overall reconstructed structure does not have ful lamps like photo-floods -and outdoors where the any major noticeable global deformation(it seems that sun may be used as a calibrated light source (given the calibration process gives good enough estimates). latitude,longitude,and time of day).These are ex The most noticeable source of errors is the surface periments that we wish to carry out in the future. noise due to local image processing.A figure of merit Other extensions of this work relate to multiple to keep in mind is a surface noise between 0.1 mm (for view integration.We wish to extend the alignment planes roughly parallel to the desk)and 0.8 mm (for technique to a method allowing the user to move freely frontal plane in the right corner).In most portions the object in front of the camera and the lamp between of the scene,the errors are of the order of 0.3 mm scans in order to achieve a full coverage.That is nec- i.e.less than 1%.Notice that these figures may very essary to construct complete 3D models. well vary from experiment to experiment,especially It is also part of future work to incorporate a geo- depending on how fast the scanning is performed.In metrical model of extended light source to the shadow all the presented experiments,we kept the speed of edge detection process,in addition to developing an the shadow approximately uniform uncalibrated (or projective)version of the method 49Figure 6: Experiment 1 - The plane/ball/corner scene: Two views of the mesh generated from the cloud of points ob￾tained after triangulation. The original sequence was 270 frames long, the images being 320 x 240 pixels each. At 60 Hz acquisi￾tion frequency, the entire scanning take 5 seconds. The camera was positioned at distance dd = 16.7 cm from the desk plane, tilted down by 0 = 41.3 degrees. The light source was at height hs = 37.7 cm, on the left of the camera at angles < = 157.1 degrees and = 64.8 degrees. From the right-hand figure we notice that the right-hand side of the reconstructed scene is more noisy than the left-hand side. This was expected since the lamp was standing on the left of the camera (refer to section 3 for details). Parameters H (cm) li, (degrees) D (cm) Geometry of the corner: We fit 2 planes to the corner structure, one corresponding to the top surface (the horizontal plane) and the other one to the frontal surface (vertical plane). We estimated the surface noise of the top surface to 0.125 mm, and that of the frontal face to 0.8 mm (almost 7 times larger). This noise difference between the two planes can be ob￾served on figure 6. Once again, after fitting quadratic patches to the two planar portions, we did not no￾tice any significant global geometric distortion in the scene (from planar to quadratic warping, the residual noise decreased by only 5% in standard deviation). From the reconstruction, we estimated the height H and width D of the right angle structure, as well as the angle between the two reconstructed planes, and compared them to their true values: True Relative values errors Estimates 2.57 & 0.02 2.65 & 0.02 3% 3.06 k 0.02 3.02 zk 0.02 1.3% 86.21 90 1% The overall reconstructed structure does not have any major noticeable global deformation (it seems that the calibration process gives good enough estimates). The most noticeable source of errors is the surface noise due to local image processing. A figure of merit to keep in mind is a surface noise between 0.1 mm (for planes roughly parallel to the desk) and 0.8 mm (for frontal plane in the right corner). In most portions of the scene, the errors are of the order of 0.3 mm, i.e. less than 1%. Notice that these figures may very well vary from experiment to experiment, especially depending on how fast the scanning is performed. In all the presented experiments, we kept the speed of the shadow approximately uniform. Figure 7: Experiment 2 - The cup/plane/ball scene: The scanned objects were a cup, the plane and the ball. The ini￾tial image of the scene is shown on the left, and the final re￾constructed mesh on the right. We found agreement between the estimated height of the cup from the 3D reconstruction, 11.04 f 0.09 cm, and the measured height (obtained using a ruler), 10.95 j, 0.05 cm. Once again the right portion on the reconstructed scene is noisier than the left portion. This was expected since the light source was, once again, standing to the left of the camera. Geometrical parameters: dd = 22.6 cm, 0 = 38.2 degrees, hs = 43.2 cm, < = 155.9 degrees, and 4 = 69 degrees. Figures 7 and 8 report the reconstruction results achieved on two other scenes. 5 Conclusion and future work We have presented a simple, low cost system for extracting surface shape of objects. The method re￾quires very little processing and image storage so that it can be implemented in real time. The accuracies we obtained on the final reconstructions are reasonable (at most 1% or 0.5 mm noise error) considering the little hardware requirement. The user can adjust the speed of scanning to obtain the desired aclcuracy. In addition, the final outcome is a dense coverage of the surface (one point in space for each pixel in the image) allowing for direct texture mapping. An error analysis was presented together with the description of a simple techinique for merging multi￾ple 3D scans together in order to (a) obtain a better coverage of the scene, and (b) reduce the estimation noise. The overall calibration procedure, even in the case of multiple scans, is very intuitive, simple, and sufficiently accurate. Another advantage of our approach is that it easily scales to larger scenarios indoors - using more power￾ful lamps like photo-floods - and outdoors where the sun may be used as a calibrated light source (given latitude, longitude, and time of day). These are ex￾periments that we wish to carry out in the Future. Other extensions of this work relate to multiple view integration. We wish to extend the alignment technique to a method allowing the user to rnove freely the object in front of the camera and the lamp between scans in order to achieve a full coverage. That is nec￾essary to construct complete 3D models. It is also part of future work to incorpor&e a geo￾metrical model of extended light source to the shadow edge detection process, in addition to developing an uncalibrated (or projective) version of the method. 49