Central to many problems in scene understanding based on using a network of tens, hundreds or even thousands of randomly distributed cameras with on-board processing and wireless communication capability is the “efficient” reconstruction of the 3D geometry structure in the scene. What is meant by “efficient” reconstruction? In this paper we investigate this from different aspects in the context of visual sensor networks and offer a distributed reconstruction algorithm roughly meeting the following goals: 1. Close to achievable 3D reconstruction accuracy and robustness; 2. Minimization of the processing time by adaptive computing-job distribution among all the cameras in the network and asynchronous parallel processing; 3. Communication Optimization and minimization of the (battery-stored) energy, by reducing and localizing the communications between cameras. A volumetric representation of the scene is reconstructed with a shape from apparent contour algorithm, which is suitable for distributed processing because it is essentially a local operation in terms of the involved cameras, and apparent contours are robust to ourdoor illumination conditions. Each camera processes its own image and performs the computation for a small subset of voxels, and updates the voxels through collaborating with its neighbor cameras. By exploring the structure of the reconstruction algorithm, we design the minimum-spanning-tree (MST) message passing protocol in order to minimize the communication. Of interest is that the resulting system is an example of “swarm behavior”. 3D reconstruction is illustrated using two real image sets, running on a single computer. The iterative computations used in the single processor experiment are exactly the same as are those used in the network computations. Distributed concepts and algorithms for network control and communication performance are theoretical designs and estimates.

In this paper, the duality in differential form is developed between a 3D primal surface and its dual manifold formed by the surface's tangent planes, i.e., each tangent plane of the primal surface is represented as a four-dimensional vector which constitutes a point on the dual manifold. The iterated dual theorem shows that each tangent plane of the dual manifold corresponds to a point on the original 3D surface, i.e., the dual of the dual goes back to the primal. This theorem can be directly used to reconstruct 3D surface from image edges by estimating the dual manifold from these edges. In this paper we further develop the work in our original conference papers resulting in the robust differential dual operator. We argue that the operator makes good use of the information available in the image data, by using both points of intensity discontinuity and their edge directions; we provide a simple physical interpretation of what the abstract algorithm is actually estimating and why it makes sense in terms of estimation accuracy; our algorithm operates on all edges in the images, including silhouette edges, self occlusion edges, and texture edges, without distinguishing their types (thus resulting in improved accuracy and handling locally concave surface estimation if texture edges are present); the algorithm automatically handles various degeneracies; and the algorithm incorporates new methodologies for implementing the required operations such as appropriately relating edges in pairs of images, evaluating and using the algorithm's sensitivity to noise to determine the accuracy of an estimated 3D point. Experiments with both synthetic and real images demonstrate that the operator is accurate, robust to degeneracies and noise, and general for reconstructing free-form objects from occluding edges and texture edges detected in calibrated images or video sequences.