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SCALE RATIO ICP FOR 3D POINT CLOUDS WITH DIFFERENT SCALES Baowei Lin 1 , Toru Tamaki 1 , Bisser Raytchev 1 , Kazufumi Kaneda 1 and Koji Ichii 1 1 Hiroshima University, Japan INTRODUCTION FEATURES DESCRIPTORS FINDING THE RATIO EXPERIMENTAL RESULTS CONCLUSION Point clouds of same scene generated by structure from motion (SfM) usually have different sizes Different size It is challenge work to do 3D registration of point clouds with different sizes. Related Work to Scale Alignment Iterative closest point (ICP) based alignment [Besl 1991]. -Need simple scenes -Need initial pose and scale -Not robust to clutters and occlusions and missing part spin images [Johnson 1998], NARF [Steder 2010], shape context [Belongie 2002], etc. Feature based alignment -Need appropriate neighborhood size 3D SIFT [Scovanner 2007], 3D SURF [Knopp 2010], etc. -Not robust to clutters and occlusions and missing part Easy data Different data Fixed scale Adaptive scale All non-scale-invariant features can be used.(spin images [Johnson 1998], NARF [steder 2010], etc.) Here, we select spin images. Spin Images Point cloud Spin images: Spin(w) Image width w (only points close to 3D point p are used to make a spin image) p Because spin images are not scale invariant a certain range of local area (neighborhood) should be specified. Hence, to find the appropriate image width, or scale, w becomes very important. Decide which set of spin images have minimum of similarity by using Contribution rate. Similar to each other Different to each other Similar to each other Scale Estimation of a Single Point Cloud [Tamaki 2010] • Define keyscale similarity w Minimum (keyscale) Sometimes, minimum is not unique. Finding them is not stable. We improve this method to estimate the scale ratio directly. similarity w • Limitation Scale Ratio Estimation of Two Point Clouds • Scale Ratio ICP 2 () . d d w w d i y y Et w tw Objective function: ( , ) d w wy ( ,y ) d w w Scale ratio t is estimated by registering two plots of point clouds (plot (a) and (b)). We use the strategy of ICP to estimate t as follows: 1. Initialization An exhaustive search is used to find an initial rough estimate of t. First, overlapping curves are extracted as plot (c) and (d). Then we find the minimum in the range at discrete steps as the initial estimate t init : arg min ( ). init t t Et 2. Find putative correspondences For each point on curves (a), find the closest point on the curves (d) with the current estimate t. 3. Estimate t The estimate of t based on the correspondences can be obtained in a closed-form. By taking the derivative of E(t) with respect to t and setting it to 0. we have: ' 2 . ww t w 4. Iteration Step 2 and 3 are iterated as t is updated until the estimate converges. Simulations Original bunny 5 times larger bunny • Dataset For simulations demonstrating the concept, we generated two synthetic 3D point clouds from stanford bunny. One of them was scaled by the factor of 5. For showing the robustness, we down-sampled or added noise for the two synthetic bunnies. • Results simulations ground truth ours method keyscale [Tamaki 2010] mesh-resolution [Johnson 1998] noise-free, no random sampling 5 5.000 5.000 5.000 noise-free, both random sampling 5 5.052 5.053 5.053 noise-free, random sampling of one dataset 5 4.733 5.818 8.727 noise(0.1), no random sampling 10 10.000 10.000 1.000 noise(0.5), no random sampling 10 10.086 9.898 12.727 noise(1.0), no random sampling 10 10.842 10.909 16.363 Small and Real blocks Our method always have the best performances Small blocks Real blocks Point clouds Fail registration using ICP without our method Good registration using ICP with our method The proposed method works very efficiently for both small and real blocks. We have proposed a method for matching scales of 3D point clouds. Experimental results demonstrated that the proposed method works well for easy and different point cloud datasets. In future works, we will try to reduce the computational cost, which is still not so small due to the repetition of PCA.
