international conference on computer vision and graphics, iccvg ‘2002 algorithm for fusion of 3d...
Post on 30-Dec-2015
218 Views
Preview:
TRANSCRIPT
International Conference on Computer Vision and Graphics, ICCVG ‘2002
Algorithm for Fusion of 3D SceneAlgorithm for Fusion of 3D Sceneby Subgraph Isomorphism by Subgraph Isomorphism with Procrustes Analysiswith Procrustes Analysis
Krzysztof Skabek, Przemysław KowalskiKrzysztof Skabek, Przemysław Kowalski
Instytut Informatyki Teoretycznej i Stosowanej PAN,Instytut Informatyki Teoretycznej i Stosowanej PAN,ul. Bałtycka 5, 44-100 Gliwiceul. Bałtycka 5, 44-100 Gliwicee-mail: e-mail: krzysiek@iitis.gliwice.plkrzysiek@iitis.gliwice.pl
ContentsContents
1. Active vision
2. Stages of 3D fusion
3. Graph representation and algorithms
5. Matching structure graphs
4. Algorithm for 3D Fusion
5. Experiments
Active Vision PlatformActive Vision Platform
Platform movementsThe observed 3D scene
Purpose:Purpose:
Obtaining a complete 3D representation of the scene and relations between components of the scene
basing on a set of 3D frames from multiple viewpoints.
Assumptions:Assumptions:No a-priori information about objects of the scene.
Unknown location of the viewpoint.
We focus on polyhedral objects.
Architecture of Active VisionArchitecture of Active Vision
Act Act
SensingSensing
PlanningPlanning
camera camera
Mision planning
Navigator
Pilot
Controller
Engines
Image preprocessing
Model integration
Location: x,y,z,
3D modelMethods of 3D fusion
3D Fusion of Multipoint Views3D Fusion of Multipoint Views
3D Fusion3D Fusion – integration process of objects in 3D scene on the basis of visual information
from several viewpoints.
Stages of 3D FusionStages of 3D Fusion
Current view
Viewpoint loc.
3D model
Corection
Vision device
Prediction
Navigation to a new viewpoint
Knowledge of the scene
Comparing the view and the model
Exact viewpoint loc.
Updating the model
Hypothesis aboutthe scene objects
Checking the completeness
Preprocessing of Visual InformationPreprocessing of Visual Information
Improvement of image quality, noise reduction Image segmentation, extraction of lines,
segments,vertices: Susan, Hough Methods Stereo matching, depth map: active contours,
hardware support (ranging lasers, depth sensors)
Algorithms prepared for Khoros platform
Viewpoint parametersViewpoint parameters T – vector of translation (3×1),
R – rotation matrix (3×3, orthogonal)
s – scale (scalar)
Relation between coordinates of point P:
Pw – global coordinates,
Pk – coordinate system of the camera
Pk = R(Pw –T)s
Graph representation of 3D sceneGraph representation of 3D scene
0 . 03 3
0 . 0
0 . 0 0 . 0
4 4
4
ContourContourgraphgraph
Face graphFace graph
1
2
3
4
1
2
3
4
5
6
7
Graph IsomorphismGraph IsomorphismGraph IsomorphismGraph Isomorphism
23
32
23
32
Subgraph IsomorphismSubgraph Isomorphism
23
32
23
3
3
3
2
Weak Subgraph IsomorphismWeak Subgraph Isomorphism
23
32
23
3
3
3
2
4
4
Detection of Graph IsomorphismsDetection of Graph Isomorphisms Permutation method Clique detection method Ullman method A* method (error correction) Decision tree method
Algorthm with analysis of 3D structure deformation(decision tree, consistency checking, branch pruning, geometric similarity)
Similarity of Shape – Procrustes analysisSimilarity of Shape – Procrustes analysis
--- - object A
--- - object B
--- - A to B matching
D2(A, B) = || B – S·R·A – T ||2
Translation (T)
Scale (S)
Rotation (R)
Implementation of 3D FusionImplementation of 3D Fusion(matching contour graphs)(matching contour graphs)
Stage I:Stage I:
Generation of groups of vertices Generation of groups of vertices (quadruplets) fulfilling conditions:(quadruplets) fulfilling conditions: Procrustes distance < Procrustes distance < Preserving edge topologyPreserving edge topology
Stage II:Stage II: (for eqch group of vertices from stage I)(for eqch group of vertices from stage I)
Calculation of local transformation Calculation of local transformation ((TTLL R RLL S SLL))
Matching the remaining vertices:Matching the remaining vertices: Local Procrustes distance < Local Procrustes distance < Preserving edge topologyPreserving edge topology
Calculation of exact transformation Calculation of exact transformation ((T R ST R S))
0
2
3
4
1
0
2
3
4
1
5
6
n
ISOMORPHISMS
V
Implementation of 3D FusionImplementation of 3D Fusion(model updating)(model updating)
A
B
C
D
E
5
1
4
3
6
2F
GMi-1 GIi
A
B
C
D
E
F
5
GMi
Implementation of 3D FusionImplementation of 3D Fusion(hypothesis of the scene objects)(hypothesis of the scene objects)
Introducing Introducing unconfirmed unconfirmed elements.elements.
Hypothesis of scene objects:Hypothesis of scene objects: Connecting edgesConnecting edges Closing facesClosing faces Connecting partial facesConnecting partial faces Ground plane detectionGround plane detection Completing vertical facesCompleting vertical faces
Conditions of experimentsConditions of experimentsTotal transformation error consists of:Total transformation error consists of:
rotation, translation, scalerotation, translation, scale
Tolerance of rotation (Tolerance of rotation (RR – matrix of rotation error): – matrix of rotation error):
R = RR = RRR
Estimation of rotation error:Estimation of rotation error:
= ½ [1 – cos(= ½ [1 – cos() ]) ]½½
Assumed value of rotation error:Assumed value of rotation error:
= 0.1 for = 0.1 for 16 16°°
ExperimentsExperiments
Thank you for your attentionThank you for your attention
Graph representation of 3D scene IIGraph representation of 3D scene IIContour graphContour graph: :
Face graphFace graph::
CCCCC EVG ,,,
FFFFF EVG ,,,
CV
CCC VVE
CC VVCC LLV ,:
CECC LV :
- a set of vertices in the scenea set of vertices in the scene- a set of edges between verticesa set of edges between vertices- coordinates coordinates (x,y,z)(x,y,z) of vertices of vertices
- a set of faces in the scenea set of faces in the scene- a set of connections between facesa set of connections between faces- parameters of facesparameters of faces- parameters of connections between parameters of connections between facesfaces
FV
FFF VVE
FF VVFF LLV ,:
FF EEFF LLV ,:
Implementation of 3D FusionImplementation of 3D FusionInput data:Input data:
GIGIii – contour graphs for views (– contour graphs for views (i=1..ni=1..n))
TTii R Rii S Sii – estimated transformation – estimated transformation (from navigation unit)(from navigation unit)
ii – transformation tolerance – transformation tolerance (for navigation unit)(for navigation unit)
ii – observation tolerance – observation tolerance (for optical unit)(for optical unit)
Output data:Output data:
GMGMn n – Contour graphs of model– Contour graphs of model
TTii R Rii S Sii – computed transformation – computed transformation
First step of fusion:First step of fusion:
GMGM11 GI GI11
Experiment IExperiment I
top related