(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

1. Problem we want to solveThe 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

1. Problem we want to solve

It is called the simultaneous localization and mapping (SLAM) problem.

1. Problem we want to solve

We face the similar problems in other applications, such as image alignment in computer graphics.

1. Problem we want to solveIn MVG, we already have well-known algorithms.But if we restrict our algorithm/robot only in the man-made 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.

1. Problem we want to solveGoal

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).

1. Problem we want to solve

This is our most wanted pattern to solve.

2. Introduction (2.1 brainstorm section)

Ames Room Escher Waterfall

2. Introduction (2.2 Data-driven vs. Task-driven)

At lower level image processing, we need robust pattern extraction algorithm to detect possible local symmetric structures.We should utilize the high-levelconcepts of the consistency of the symmetry as strong feedback control of our recognition process.

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 task-driven approach relies on the correctness of our assumed hypotheses.

2. Introduction (2.4 A “2.5-D” representation )

We seek a hierarchical representationof different regions of a 2-D image in terms of their 3-D geometric relations.The algorithm provides us both the orientation of the pattern and the location of the camera. (therefore, we break the chicken-egg circle in single view geometry)

2. Introduction (2.4 The big picture)

3. Hierarchical symmetry recognition(Overview)

The lowest level is image-based 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.

3. Hierarchical symmetry recognition

In this way, the symmetry cells will be clustered into different groups, each group with consistent 3-D geometry interpretation is called a symmetry complex.Finally, we may pass this hierarchy to all sorts of higher level applications.

3. Hierarchical symmetry recognition

3.1 Review of the geometryDefinition A set of 3-D features (points of lines) S ⊂ ℜ3

is called a symmetric structure if there exists a non-trivial subgroup G of the Euclidean group E(3) that for any element g∈ G, g defines a one-to-one mapping from S to itself.

3.2 Symmetry cell extraction: Overview

The symmetry cell extraction is really a bottleneck in this research:edge detection, active contour, segmentation

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.

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

3.2 Symmetry cell extraction:local symmetry testing

For each cell, apply reflective symmetry on both axes.Only those with consistent 3-D configuration and orientation will pass this local symmetry test.

3.3 Symmetry complexConnectivity

first step: separate local cells with similar or different orientations.we group cells by topological relations.

3.3 Symmetry complexClustering

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, K-means, ISODATA, Polynomial Segmentation.

3.3 Symmetry complexCoplanar 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 3-D structure.

3.3 Symmetry complexCoplanar assumption

Here the perspective projection has the advantage over orthographic projection.We apply translatory symmetry test.

3.3 Symmetry complexFinal result

3.3 Symmetry complexFinal result

3.3 Symmetry complexApplication to Robotic Mapping

4. Future work and discussionFirst, other possible solutions to the cell extraction and polygon fitting.Color image segmentation may be a possible solution.

drawback: color patchesActive contour:

Slow speed & Init. problem

4. Future work and discussion

4. Future work and discussion

4. Future work and discussion

4. Future work and discussion

4. Future work and discussionSeveral 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.

4. Future work and discussion2. 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 complexwhich itself also gives consistent symmetry properties.

5. ConclusionWe demonstrates that it is computationally feasible to represent an image of man-made environment based on accurate 3-D geometric information.The algorithm we propose is an effective closed-form solution to robotic mapping problem.Future work: robust geometric primitive extraction and maximal symmetry group.