Using Reeb Graphs Jacopo Aleotti aleotti@ce.unipr.it Stefano - - PowerPoint PPT Presentation

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Jacopo Aleotti aleotti@ce.unipr.it Stefano Caselli caselli@ce.unipr.it

UNIVERSITY OF PARMA, ITALY Dipartimento di Ingegneria dell’Informazione Robotics and Intelligent Machines Laboratory

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Outline

Introduction and motivations Related work Overview of the approach Object decomposition Part-based planning of robot grasps Experiments Discussion

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Robot Grasping

Advanced (service) robots require human like grasping capabilities grasping should be task-oriented

• single hand
• multifingered
• point contacts with friction

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Part-based robot grasping

• objects are usually grasped according to their affordances
• affordances are the ways to grasp an object to perform a task
• objects are composed of different parts
• perception of (grasping) affordances is mediated by object parts

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Part-based robot grasping

• affordances are shared among similar objects

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

• D. D. Hoffman

Parts of Recognition. Cognition, 18(1-3):65–96, 1984 shapes are perceived as an arrangement of simple components (naturally segmented into parts at negative curvature minima).

Related work (psychology)

Psychological findings have shown that human perception of objects is based on part decomposition.

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

• I. Biederman

Recognition-by-Components: A Theory of Human Image Understanding. Psychological Review, 94:115–147, 1987. Recognition-By-Components theory (RBC) Recognition is a bottom-up process where the visual system recognizes objects by separating them into interrelated geons (such as cubes, spheres, cylinders).

• E. Rivlin et al.
• E. Rivlin, S. J. Dickinson, and A. Rosenfeld. Recognition by Functional Parts.

Computer Vision and Image Understanding, 62(2):164–176, Sept. 1995.

Related work (psychology)

explored the issue of functionality by combining functional primitives with shape primitives

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Part-based object decomposition for efficient grasp planning (no semantic) [Kyota et al., 2005] learning grasping positions

(cylinder-likeness, NN)

[K. Hsiao et al., 2006]

learning whole body grasps from imitation by object morphing. Limited nuber of elementary primitives.

[C. Goldfeder et al., 2007]

Grasp Planning via Decomposition Trees (superquadrics)

[K. Huebner et al., 2008]

Minimum Volume Bounding Box Decomposition

Related work (robotics)

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Part-based object decomposition, towards semantic grasping [G. Biegelbauer et al., 2007]

3D Object Detection by Fitting Superquadrics to Range Image Data

[A. Sahbani et al., 2007-2009]

Learning the Natural Grasping Component

• f an Unknown Object based on superquadrics.

[L. Montesano et al., 2009]

Learning affordance visual descriptors for grasping through self-experimentation.

Related work (robotics)

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Focus of this work

Motivation: automatic object recognition and robot grasping should be guided by 3D shape segmentation. Method: an approach for planning robot grasps across similar objects by part correspondence. Novelty: topological decomposition enabling semantic grasp planning. Topological decomposition of a shape provides meaningful information about grasp affordances.

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

3D Object decomposition

The approach is based on the Reeb graph theory

• A Reeb graph is a data structure describing the evolution of a scalar function over a mesh.
• Tracks topological changes of connected components and encodes them in the

nodes of the graph. given a surface S and a real, continuous function f: S → R the Reeb graph is the quotient space of f in S×R by the equivalence relation (X1, f(X1))~(X2, f(X2)) which holds if and only if f(X1) = f(X2) and if the two points X1 and X2 are in the same connected component of f -1(f(X1))

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

3D Object decomposition

the Reeb graph depends on

• 1. the scalar function f
• 2. the number of quantization levels of f
• f is the height function computed along one axis

(computationally efficient few milliseconds, Intel Core 2 quad @2.66Ghz)

• height functions are not invariant under rotation
• a scalar function f that ensures invariance to rotation

is the integral geodesic distance (computationally expensive, O(n2logn))

• the annotated Reeb graph is used as input for

the part-based grasp planner

height function integral geodesic distance

Human model (~25000 triangles)

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

3D Object decomposition

Shape Segmentation with Reeb Graphs: ADVANTAGES

• Provides a topological representation of the shape (skeleton)
• Attempts to extract a semantic segmentation from a 3D shape
• Enables grasp planning among similar objects
• Provides a one-to-one mapping from the mesh vertices to the object parts
• Can be augmented to include geometrical information
• T. Tung and F. Schmitt. Augmented Reeb Graphs for Content-Based

Retrieval of 3D Mesh Models, 2004.

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Part-based grasp planning

A method for grasp planning grounded on part decomposition

• it computes the centroid of the part and plans around the principal axis
• it naturally speeds up the planning process (plans in the neighborhood of a chosen part)

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Part-based grasp planning

• Experiments have been performed with a simulated Barrett Hand
• Principal axes of inertia of each part are computed by PCA
• Random generation of both precision and power grasps
• V-Clip is the adopted for collision detection
• External obstacles may be included

in the simulated environment.

• The planner is scheduled for executing hundreds
• f trials.
• It returns the force closure grasp with the

highest quality value

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Experiments

• The dataset consists of 15 object classes
• Each class contains 20 similar models
• large meshes ranging from 4K to

115K triangles with uniform density

• dataset taken from the 2007 shape

retrieval contest (SHREC).

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Experiments

• force closure grasps with

the highest quality

• three similar objects per

class

• corresponding parts have

the same color

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Experiments

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Experiments

• The best quality grasps are selected from three hundred trials
• All the grasps have a good quality score which ranges from Q = 0.21 to Q = 0.49 (0<Q<1)
• The simplest class of objects is the “cup” category, whose Reeb graph contains 4 nodes
• The most complex class is the octopus category, whose Reeb graph contains 10 nodes
• Segmentation is correct even with “strange” postures (e.g. sitting human model)
• Objects of the same category may have a slightly different topology
• All the 3D models are “watertight”
• Automatic part annotation requires an “ontological” model, provided by the user

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

STANDARD QUALITY METRIC:

• Q: radius of the largest sphere centered at the origin contained in the GWS

(if Q<0 the grasp isn’t force closed) Complexity:

• bject segmentation

̴ 20s/1min grasp synthesis, evaluation and animation ̴ 3s

Grasp quality measure

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Experiments

• additional assessment of the grasp planner
• frequency histogram of the grasp quality Q (300 grasps, chair shape)
• most of the planned grasps have a good quality
• the proposed planning strategy allows an

effective exploration of the configuration space in proximity of the object’s part being grasped

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

Discussion

pure graph-based approaches do not discriminate between classes

• f objects that have the same topological structure

invariance under rotation for complex shapes is computationally expensive suitable for single handed grasps that encompass single parts requires an annotated object database requires watertight 3D models (while real sensor data are sparse)

IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs

An approach for planning robot grasps across similar objects has been proposed The method is based on shape decomposition and part correspondence Motivated by well-established psychological findings Application of Reeb graphs for object segmentation and grasping Topological decomposition is a general and flexible approach The approach is suitable for for generalizing grasps to previously unseen objects (HRI and programming by demonstration)

Conclusions