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Segmentation into Planar Patches for Recovery of Unmodeled Objects. Kok-Lim Low COMP 290-075 Computer Vision 4/26/2000. The Big Picture. Work by Marjan Trobina “From planar patches to grasps: a 3-D robot vision system handling unmodeled objects.” Ph.D. thesis, ETHZ, 1995.

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Segmentation into Planar Patches for Recovery of Unmodeled Objects

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Segmentation into planar patches for recovery of unmodeled objects

Segmentation into Planar Patches for Recovery of Unmodeled Objects

Kok-Lim Low

COMP 290-075

Computer Vision

4/26/2000


The big picture

The Big Picture

  • Work by Marjan Trobina

    • “From planar patches to grasps: a 3-D robot vision system handling unmodeled objects.” Ph.D. thesis, ETHZ, 1995.

  • Overview of whole system

acquire range images from 2 or more views

segment into planar patches

generate object hypotheses

compute grasping points

robot arm


Setup

Setup


Segmentation into planar patches

Segmentation into Planar Patches

  • Objectives

    • extract planar patches from range images in a robust way

    • just sufficient info for recovery of unmodeled objects for computing grasping points

  • Can be viewed as data compression

    • transforming range image to just a few parameters


Related work

Related Work

  • 1) Edge-based segmentation

    • detect surface discontinuities

    • find closed edge chains

    • not robust against noisy data

  • 2) Split-and-merge paradigm

    • tessellation of image

    • using quadtrees or Delaunay triangles


Related work1

Related Work

  • 3) Clustering

    • map data to feature space

    • find clusters

    • points in feature space have no image-space connectivity

  • 4) Region growing

    • grow region until approximation error too large

    • order dependent, result usually far from optimal

  • 5) Recover-and-select paradigm


Recover and select paradigm rs

input

model recovery

iterate until remaining models are completely grown

model selection

output

Recover-and-Select Paradigm (RS)

  • Originally proposed by Leonardis

  • Very robust against statistical noise and outliers

  • Consists of 2 intertwined stages:


Overview of rs algorithm

Overview of RS Algorithm

  • Model recovery

    • regularly place seeds

    • grow statistically consistent seeds independently

    • fit a plane (model) to each region

    • stop growth of region if planar fit is lousy

    • stop growth of region if no compatible points can be added

  • Model selection

    • select some recovered (plane) models

    • minimize number of selected models while keeping approximation error low


Planar fitting

Planar Fitting

  • Planar patch parameterized by a1, a2, a3 in

    f(X, Y) = a1X + a2Y + a3 = Z

  • Distance function from range data point r(m) to planar patch

    d2(m) = ( r(m) – f(m) )2


Planar fitting1

Planar Fitting

  • Approximation error for set D of n points is

  • For each set of points D, minimize  by Linear Least Squares method to obtain plane parameters a1, a2, a3.


Model recovery

Model Recovery

  • Place seeds in regular grid of 7x7 windows

  • Define model acceptance thresholdT

  • Grow seed if its  < T (statistically consistent)

  • Define compatibility constraint C

  • Add adjacent point m to patch if d2(m) < C (compatible)

  • Stop when T or no compatible point can be added

  • Output is a set of overlapping planar patch models


Model selection

Model Selection

  • Select smallest number of models while keeping approximation error small

  • Objective function (to be maximized) for model si

    F(si) = K1ni – K2i– K3Ni

    where ni = | D |

    i = approximation error of model si

    Ni = number of parameters in model si


Model selection1

Model Selection

  • Objective function for M models

    wherep = [ p1...pM ] and pi = 0 or 1

    cii = K1ni – K2i– K3Ni

    cij = ( –K1 | DiDj | + K2ij) / 2

  • Use greedy algorithm to find vector p so that F(p) is near to maximum


Example

Example


Result

Result


Result1

Result


Multiresolution recover and select mrs

Multiresolution Recover-and-Select (MRS)

  • In RS, many seeds are grown and then discarded

  • MRS uses hierarchical approach to reduce waste

  • Basic idea

    • build an image pyramid

    • apply standard RS on coarsest image

    • selected patches are projected to the next finer level and used as seeds for the new level

    • start new seeds on the unprojected regions in the next finer level

  • Speedup of 10 to 20 times


Result2

Result


Viewpoint invariant segmentation

Viewpoint Invariant Segmentation

  • Range images from different viewpoints

  • A planar patch extracted from different views should have same parameters and error measure

  • Modifications to model recovery stage:

    • project data points into direct 3-D space prior to the segmentation

    • minimizing the orthogonal distance to the plane


Viewpoint invariant segmentation1

Viewpoint Invariant Segmentation

  • Planar patch now parameterized by a1, a2, a3, a4 in

    f(X, Y, Z) = a1X + a2Y + a3Z + a4 = 0

  • Distance function from 3-D range data point M to planar patch

    d2(M) = f(M)2


Viewpoint invariant segmentation2

Viewpoint Invariant Segmentation

  • Approximation error

     = 1

    where 1is the smallest eigenvalue of the covariance matrix of the n points in the patch

  • The normal (a1, a2, a3) of the planar patch is the eigenvector with eigenvalue 1


Postprocessing

Postprocessing

  • create explicit patch boundary description

  • post-processing to clean edge

  • classify patches as “true planes” or “curved patches”, and fit points on curved planes with quadrics

  • classify adjacency relation as concave or convex

  • e.t.c.


Generating object hypotheses

Generating Object Hypotheses

  • Objects are unmodeled

  • Group planar patches into Single-View Object Hypotheses (SVOHs)

  • Combine SVOHs into Global Object Hypotheses (GOHs)

  • Prefer oversegmentation to undersegmentation — avoid grasping 2 objects at the same time


Generating svohs

Generating SVOHs

  • A SVOH is a set of connected patches, such that for any 2 patches, there exists at least one path that does not contain any concave relation


Establishing gohs

Establishing GOHs

  • A GOH is a set of SVOHs, such that for any SVOHi there is at least one SVOHj (from a different view) such that SVOHi and SVOHj have at least one pair of patches sk (from SVOHi) and sl (from SVOHj) which fulfills the same-surface predicate

  • Rough idea of “same-surface predicate”

    • when 2 patches satisfy the same-surface predicate, they are on the same plane or on the same curved surface and they are intersecting each other


Result3

Result


References

References

  • Marjan Trobina

    • “From Planar Patches to Grasps: A 3-D Robot Vision System Handling Unmodeled Objects.” Ph.D. thesis, ETHZ, 1995

  • A. Leonardis

    • “Image Analysis Using Parametric Models: Model-Recovery and Model-Selection Paradigm.” Ph.D. thesis, University of Ljubljana, 1993

  • A. Leonardis

    • “Recover-and-Select on Multiple Resolutions.” Technical report LRV-95, Computer Vision Lab, University of Ljubljana, 1995


References1

References

  • Frank Ade, Martin Rutishauser and Marjan Trobina

    • “Grasping Unknown Objects.” ETHZ, 1995

  • Martin Rutishauser, Markus Stricker and Marjan Trobina

    • “Merging Range Images of Arbitrarily Shaped Objects.” Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 1994


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