Active 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.