3D POINT CLOUD CONSTRUCTION FROM STEREO IMAGES

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1 3D POINT CLOUD CONSTRUCTION FROM STEREO IMAGES Brian Peasley * I propose an algorithm to construct a 3D point cloud from a sequence of stereo image pairs that show a full 360 degree view of an object. The sequence of images will be generated using CGI to test the accuracy of the algorithm and to avoid image rectification and any noise that is inherent in cameras. The point cloud will be constructed from depth maps of each pair of stereo images which are obtained by tracking features, using Lucas-Kanade Feature Tracking algorithm, from the image generated by the left camera, to the image generated by the right camera. This depth maps are then rotated about the same axis that the cameras were rotated around to generate the images. The accuracy of the algorithm will be measured by determining the dissimilarity of the point cloud from the object when viewing the point cloud and object from the front, side, and top. INTRODUCTION To scan a three dimensional (3D) object, one would more than likely use a laser scanner to create a point cloud of the object. Although these systems are very accurate and are capable of reproducing the object in great detail, they have their limitations. The first is that they can only scan objects that can fit inside them, restricting the number of objects that can be scanned, such as buildings and trees. Also, they are not cheap so only places like companies and universities would be able to afford one. This project will attempt to overcome these drawbacks by employing a pair of stereo cameras to construct a point cloud of an object which is a low cost, and hopefully more robust alternative than a 3D laser scanner. * Student, Dept. of Electrical and Computer Engineering, Clemson University. 1

2 METHOD Image Fabrication Images were generated using the free open source 3D content creation suite Blender. An object was placed in the 3D scene with two cameras viewing the object. The cameras were placed approximately two times the height of the object away from the object and were offset +/- 3% the distance from the object away from center to create the pair of stereo images. Figure 1. Blender Scene Setup Depth Map Construction To construct the depth map a disparity map was first needed, which was found by using Lucas-Kanade Feature Tracking algorithm. First at most 200 features were found in the image generated by the left camera, and then these features were tracked to the image generated by the right camera, producing a disparity for each feature tracked. Figure 2. Features Tracked From Left Image to Right Image After the disparities for each feature are found a depth map for the feature is found by linearly interpolating its value with a manually constructed disparity array. disparities[] = {96, 57, 41, 31, 26, 22, 21,18,17, 14} (x, in pixels) distance[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (y, distance from camera) The disparity array was created by placing another object in the 3D Blender Scene and locating it a known distance away from the two cameras and viewing the number of pixels the object shifted from the left image to the right image. This was done for distance one through ten away from the camera. Values are ignored if the go beyond a distance of 10 away from the camera or less than 1 distance away from the camera because due to the positioning of the cameras, these values are never possible. Figure 3. Depth Map for Front Pair of Stereo 2

3 Rotating the Points After a depth map has been for a particular view an- gle, all those points need to be rotated to properly mesh into the rest of the point cloud. These points need to rotate around the same axis that the cameras rotated around to generate the images. The points are rotated θ degrees using the standard rotational matrices seen in Fig. 4. θ = (360/num_frames)*current_frame Figure 4. Rotation Matrices Bounding Box It can be seen in Fig. 5 in the experimental results that the initial results from the point cloud aren t too bad when viewing the point cloud and object from the side and front. However, when viewing them from the top, the point cloud looks nothing like the object; this is due to the lack of a camera viewing the top of the object providing information about the topology of the top of the object. So, to remove the noise which is present when viewing from the top, a bounding box was created to restrict the point cloud, and allow points inside the bounding box to be considered valid, while the rest of the points are ignored. The bounding box was constructed by using a Silhouette Intersection algorithm. Using a double thresholding algorithm to obtain the silhouettes of the front, side, and top of the image, the intersection of all three could be found by extending them into their respective third dimension, and where all three intersect is the bounding box. Results from the restricting of the point cloud can be seen in Fig. 6 in the experimental results. Skinning the Point Cloud After a point cloud of reasonable accuracy was created, the obvious extension to the project was to attempt and skin the point cloud. To skin the point cloud Delaunay triangulation was used to connect all the points together. However, in order to speed up the algorithm and avoid putting faces to points on the inside of the point cloud, the interior points were first removed. This was achieved by creating a binary image from each relative z-layer into its own binary image. So points that were 0-1, 1-2, 2-3, etc, units distance away from the camera were put into a binary image. This resulted in a binary image with a lot of 0 s, and only 1 s where the feature points were, the binary image then ran through 15 iterations of dilation and erosion to group create a blob that contained all the points. A simple Prewitt kernel was then convolved with the binary image in order to find the edges. Once the edges were found, points along the edges separated by n-pixels were extended back to the third dimension by having their z-value set to the nearest original point, the points that were initially in the binary image. Delaunay Triangulation Delaunay Triangulation is an algorithm that connects points in a graph together in a way such that no point resides in the circumcircle of a triangle of other points. There are several ways to implement this algorithm; I chose to use the incremental algorithm because it could be extended into n-dimensions and, if implemented properly, has a runtime of O(nlog[n]). The incremental approach adds one vertex at a time to the Delaunay graph and splits into six the tetrahedron that contains that point, the the Flip algorithm would be applied. The Flip algorithm determines if each of the newly formed tetrahedrons created in the incremental algorithm are Delaunay if the determinant in Fig. 9 is less than 0. If not than two edges are randomly swapped and the check is performed again. 3

4 EXPERIMENTAL RESULTS To determine the accuracy of the results the point clouds dissimilarity with the original object will be measured when looking at the point cloud and object from the side, top, and front. It will be measured by creating a binary blob of the point cloud when looking at it from the respective views and subtracting it from a silhouette of original object. It can be seen from the experimental results that some clouds do not benefit that much from being restricted, however there are some that do, and the percent of similarity to the original object always went up. Figure 5. Unrestricted Point Cloud Figure 6. Restricted Point Cloud 72.65% Similar to Object 93.00% Similar to Object Figure 7. Unrestricted Point Cloud Figure 8. Restricted Point Cloud 88.34% Similar to Object 92.04% Similar to Object 4

5 Figure 9. Skinned Point Cloud CONCLUSION In this project I proposed an algorithm to construct a point cloud based on series of stereo images. The stereo images are processed to construct a depth map for a certain view angle and then each point is rotated to properly fit into the point cloud. Initial results show that this method alone can create a point cloud that is close to 90% similar to the original object. This number can be improved upon by restricting the point cloud using a Silhouette Intersection algorithm that bounds the point cloud to the intersection of the front, side, and top silhouettes. Although this method isn t as accurate as using a conventional 3D Laser Scanner and the skinning algorithm didn t yield as good of results as I would have liked, it did closely approximate the shape of an object, and with further testing could be shown that this algorithm works well with pictures taken of real objects with actual cameras. REFERENCES [1] D. Camarillo, D. Loewke, C. Carlson, and J. Salisbury, Vision Based 3-D Shape Sensing of Flexible Manipulators, Robotics and Automation, May 19, [2] Lambert, Delaunay Triangulation Algorithms, Sept 22, [3] M. Jones and J. Oakley, Efficient representation of object shape for silhouette intersection, Image Signal Process, December

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