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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

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

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

where p = [ 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
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
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
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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