(Robust?) 3D symmetry extraction with applications to robot navigation


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1 (Robust?) 3D symmetry extraction with applications to robot navigation Allen Y. Yang, Shankar Rao, Jie Lai and Professor Yi Ma Perception and Decision Lab, part of Coordinated Science Lab, UIUC Dec. 12, 2002
2 1. Problem we want to solve The main problem in vision based robot navigation is Robotic mapping. The mapping problem is regarded to be a chicken and egg problem. robot pose environment
3 1. Problem we want to solve It is called the simultaneous localization and mapping (SLAM) problem.
4 1. Problem we want to solve We face the similar problems in other applications, such as image alignment in computer graphics.
5 1. Problem we want to solve In MVG, we already have wellknown algorithms. But if we restrict our algorithm/robot only in the manmade environment, we may observe ubiquitous symmetric objects. A series of research done recently have given us effective algorithms to compute the 3D pose of symmetric patterns.
6 1. Problem we want to solve Goal A computational framework for recognition of 3D symmetric structures. A fast implementation system of such framework in robotic application. Robustness analysis and the ability to extend to other applications (future).
7 1. Problem we want to solve This is our most wanted pattern to solve.
8 2. Introduction (2.1 brainstorm section) Ames Room Escher Waterfall
9 2. Introduction (2.2 Datadriven vs. Taskdriven) At lower level image processing, we need robust pattern extraction algorithm to detect possible local symmetric structures. We should utilize the highlevel concepts of the consistency of the symmetry as strong feedback control of our recognition process.
10 2. Introduction (2.3 Geometry vs. Statistics) Local symmetry: The effective homography decomposition will give us precise 3D structure of planar patterns under symmetry assumption. Global symmetry: The success of the taskdriven approach relies on the correctness of our assumed hypotheses.
11 2. Introduction (2.4 A 2.5D representation ) We seek a hierarchical representation of different regions of a 2D image in terms of their 3D geometric relations. The algorithm provides us both the orientation of the pattern and the location of the camera. (therefore, we break the chickenegg circle in single view geometry)
12 2. Introduction (2.4 The big picture)
13 3. Hierarchical symmetry recognition(overview) The lowest level is imagebased local symmetry extraction. We call planar patterns which satisfy local symmetry constraints symmetry cells. Next we pass these local symmetry cells into a higher level of hypothesis testing to verify certain global geometric consistency among them.
14 3. Hierarchical symmetry recognition In this way, the symmetry cells will be clustered into different groups, each group with consistent 3D geometry interpretation is called a symmetry complex. Finally, we may pass this hierarchy to all sorts of higher level applications.
15 3. Hierarchical symmetry recognition
16 3.1 Review of the geometry Definition A set of 3D features (points of lines) S R 3 is called a symmetric structure if there exists a nontrivial subgroup G of the Euclidean group E(3) that for any element g G, g defines a onetoone mapping from S to itself.
17 3.2 Symmetry cell extraction: Overview The symmetry cell extraction is really a bottleneck in this research: edge detection, active contour, segmentation
18 3.2 Symmetry cell extraction: Polygon fitting using constant curvature The idea of constant curvature criterion is to decompose the contour in its curvature map.
19 3.2 Symmetry cell extraction: constant curvature vs. Hough transform Sym. Cell: rectangles with high SNR. the limitation of Hough transform: window size and continuity
20 3.2 Symmetry cell extraction: local symmetry testing For each cell, apply reflective symmetry on both axes. Only those with consistent 3D configuration and orientation will pass this local symmetry test.
21 3.3 Symmetry complex Connectivity first step: separate local cells with similar or different orientations. we group cells by topological relations.
22 3.3 Symmetry complex Clustering second step: a clustering algorithm will be used on the normal vectors of each symmetry cell. We then obtain the distribution map of all the normal vectors in each group. Use your favorite clustering algorithm: EM, Kmeans, ISODATA, Polynomial Segmentation.
23 3.3 Symmetry complex Coplanar assumption From the last step, two adjacent cells which do not have similar normal vectors will be considered not coplanar. But how if their normal vectors are similar? Coplanar assumption is a higher level description of the 3D structure.
24 3.3 Symmetry complex Coplanar assumption Here the perspective projection has the advantage over orthographic projection. We apply translatory symmetry test.
25 3.3 Symmetry complex Final result
26 3.3 Symmetry complex Final result
27 3.3 Symmetry complex Application to Robotic Mapping
28 4. Future work and discussion First, other possible solutions to the cell extraction and polygon fitting. Color image segmentation may be a possible solution. drawback: color patches Active contour: Slow speed & Init. problem
29 4. Future work and discussion
30 4. Future work and discussion
31 4. Future work and discussion
32 4. Future work and discussion
33 4. Future work and discussion Several criteria we set up: 1. In low level geometric primitive extraction, we request the algorithm to fully automatically extract the boundaries of candidate primitives from (noisy) real images.
34 4. Future work and discussion 2. The algorithm should have parameters to adjust the minimal size of region of interest (ROI). 3. In global symmetry test, we expect an algorithm which may use the hierarchy to find the maximal symmetry complex which itself also gives consistent symmetry properties.
35 5. Conclusion We demonstrates that it is computationally feasible to represent an image of manmade environment based on accurate 3D geometric information. The algorithm we propose is an effective closedform solution to robotic mapping problem. Future work: robust geometric primitive extraction and maximal symmetry group.
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