Active 3-D ReconstructionActive 3-D reconstruction
3-D reconstruction deals with the computation of 3-D geometry of an
object. This geometry is needed in many other applications, e.g. image
based rendering or Augmented Reality. The information about the object
geometry is acquired by camera images. The word "active" in Active 3-D
reconstruction does not mean that active sensors, such as laser sensors
or structured light or similar, are used. Instead, we actively steer
the camera in a purposive way, i.e. we plan views which minimize
the expected error of the reconstruction.Our approach uses an extended Kalman Filter. This enables an easy
update of the estimate of the 3-D information, which is provided by a
new image. The estimate is given by a multidimensional normal distribution.
The expected value is the best linear estimate, in the sense of the least
square error. The covariance matrix measures the
uncertainty of the estimation. Furthermore, the Kalman filter allows us to predict the influence of
integrating an image, taken with certain parameters, on the covariance
matrix. This can be done without actually integrating the information of
a new image. So we are able to search for the next best
configuration of camera parameters on the basis of the current estimate.
The best configuration is that which most reduces the uncertainty of
the estimate. For uncertainty measurement two approaches were tested:
D-criterion: The determinant of a covariance of a normal distribution is (neglecting some constants) equivalent to the entropy. Minimizing the determinant means minimizing the entropy, which again means increasing information. So this criterion is information theoretically motivated.
E-criterion: the covariance has a 3x3 block diagonal structure. Each block represents the uncertainty of a point in the three directions. The eigenvector, which belongs to the largest eigenvalue, defines the direction of largest uncertainty.
The E-criterion is defined as the sum over the largest eigenvalue of all blocks. So this criterion is geometrically motivated. For real time experiments there are two further conditions, which have to be
considered:
We use a robot arm to position the camera. The kinematics of the robot have to be considered, since we should not analyze unreachable positions.
In certain camera configurations, some regions of the object can be occluded by the object itself. These self occlusions may render an image unusable for the 3-D reconstruction. Since the self occlusions are modelled in a probabilistic way, it was integrated in the probabilistic Kalman filter approach.
In real world experiments, we could show that the active 3-D reconstruction is
more accurate than a passive one, i.e. one without view planning, in the sense
of reconstruction accuracy. The geometrical
E-criterion gives better results than the D-criterion. With the usage of
self occlusion modelling, we are now able to reconstruct non planar objects. | Project manager: Prof. em. Dr.-Ing. Dr.-Ing. h.c. Heinrich Niemann
Project participants: Dr.-Ing. Stefan Wenhardt
Keywords: 3-D Reconstruction; active vision, computer vision
Duration: 1.1.2004 - 31.5.2007
| Publications |
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Wenhardt, Stefan ; Denzler, Joachim ; Niemann, Heinrich: On Minimizing Errors in 3-D-Reconstruction for Stereo Camera Systems. In: Geppener, V.V. ; Gurevich, I.B. ; Ivanova, S.E. ; Nemirko, A.P. ; Niemann, Heinrich ; Puzankov, D.V. ; Trusova, Yu.O. ; Zhuravlev, Yu.I. (Ed.) : 7th International Conference on Pattern Recognition and Image Analysis 2004: New Information Technologies (7th International Conference on Pattern Recognition and Image Analysis 2004: New Information Technologies St. Petersburg, Russia). St. Petersburg : SPbETU, 2004, pp 562–565. | Wenhardt, Stefan ; Deutsch, Benjamin ; Hornegger, Joachim ; Niemann, Heinrich ; Denzler, Joachim: An Information Theoretic Approach for Next Best View Planning in 3-D Reconstruction. In: Tang, Y.Y. ; Wang, S.P. ; Lorette, G. ; Yeung, D.S. ; Yan, H. (Ed.) : The 18th International Conference on Pattern Recognition (18th International Conference on Pattern Recognition (ICPR 2006) Hong Kong 20 - 24 August, 2006). Vol. 1. Los Alamitos, California, Washington, Tokyo : IEEE Computer Society, 2006, pp 103-106. (IEEE Computer Society Order Number P2521) - ISBN 0-7695-2521-0 |
Institution: Chair of Computer Science 5 (Pattern Recognition)
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