Three-dimensional (3D) image processing and interpretation is very important in many medical and industrial applications. Detection of 3D boundaries is an essential step in most of the 3D image analysis tasks. In this paper a new computational approach to 3D edge detection is proposed. Optimality criteria such as signal-to-noise ratio, localization, and spurious response for zero-crossing-based, rotationally invariant 3D step edge detectors are derived. An optimal 3D step edge detector is obtained by optimizing a penalty function which combines all the three criteria. The closed form solution to the optimization problem yields the optimal detector. The detector is the Laplacian of a rotationally invariant function, which has a finite spatial support. The behavior of the proposed detector is theoretically analyzed and compared to that of the 3D Laplacian of Gaussian detector. Experimental results with some synthetic and real images are presented.
This paper addresses the issue of optimal motion and structure estimation from monocular image sequences of a rigid scene. The new method has the following characteristics: (1) the dimension of the search space in the nonlinear optimization is drastically reduced by exploiting the relationship between structure and motion parameters; (2) the degree of reliability of the observations and estimates is effectively taken into account; (3) the proposed formulation allows arbitrary interframe motion; (4) the information about the structure of the scene, acquired from previous images, is systematically integrated into the new estimations; (5) the integration of multiple views using this method gives a large 2.5D visual map, much larger than that covered by any single view. It is shown also that the scale factor associated with any two consecutive images in a monocular sequence is determined by the scale factor of the first two images. Our simulation results and experiments with long image sequences of real world scenes indicate that the optimization method developed in this paper not only greatly reduces the computational complexity but also substantially improves the motion and structure estimates over those produced by the linear algorithms.
We present a new robust algorithm for edge detection. The algorithm detects both roof and step type edges. A pixel is declared as an edge pixel if there is a consensus between different processes that try to determine if the pixel lies on a discontinuity. We use robust estimation methods to estimate local fits to windows in the pixel′s neighborhood and accumulate votes from each fit. The use of robust estimators enables us to transform any window possibly containing a discontinuity to a binary window containing a step edge in the location of the discontinuity. We then employ conventional methods to detect this step edge. We show experimental results on simulated edges and synthetic images with varying Gaussian and random noise levels and analyze the probability of detection. The algorithm is also applied to several real intensity and range images and it is shown to perform well. A comparison with the Canny edge detector is given when applicable.
Many man-made objects such as industrial parts are partially constructed of surfaces of revolution, as well as planar surfaces. We have studied the problem of finding and recovering solids of revolution in range data which are potentially useful for modeling and recognizing 3D objects. We propose an approach to the problem which is based on the fact that at least one of two focal surfaces for a surface of revolution degenerates into the axis of rotation. First, by computing the surface normal and principal curvatures, the centers of principal curvature which construct the focal surfaces are obtained for each point in the range image. Then, using the Hough transform, the axes of rotation are detected by finding the centers of principal curvature which lie on straight lines in space. Finally, the solid of revolution is completely determined by estimating the radius function of cross-section along each rotational axis. The proposed method can be used even in situations where occlusion or truncation is a problem because it does not require the visibility of entire surfaces. Experiments have been successfully carried out with real range data obtained from laser rangefinders.
Many image analysis and computer vision problems have been expressed as the minimization of global energy functions describing the interactions between the observed data and the image representations to be extracted in a given task. In this note, we investigate a new comprehensive approach to minimize global energy functions using a multiscale relaxation algorithm. The energy function is minimized over nested subspaces of the original space of possible solutions. These subspaces consist of solutions which are constrained at different scales. The constrained relaxation is implemented via a coarse-to-fine multiresolution algorithm that yields fast convergence towards high quality estimates when compared to standard monoresolution or multigrid relaxation schemes. It also appears to be far less sensitive to local minima than standard relaxation algorithms. The efficiency of the approach is demonstrated on a highly nonlinear combinatorial problem which consists of estimating long-range motion in an image sequence on a discrete label space. The method is compared to standard relaxation algorithms on real world and synthetic image sequences.
The interpretation of the movements of articulated bodies in image sequences is one of the most challenging problems in computer vision. In this contribution, we introduce a model-based approach for the recognition of pedestrians. We represent the human body by a 3D-model consisting of cylinders, whereas for modelling the movement of walking we use data from medical motion studies. The estimation of model parameters in consecutive images is done by applying a Kalman filter. Experimental results are shown for synthetic as well as for real image data.
It has been proposed recently that the skeleton of a shape can be computed using the Voronoi diagram of a discrete sample set of the shape boundary. This method avoids many of the complications encountered when computing the skeleton directly from an image because it is based on a continuous-domain model for shapes. In order to make better use of this new approach, it is necessary to establish a bridge between the continuous domain skeleton and its approximation obtained from the discrete boundary sample set. In this paper, the skeleton and Voronoi diagram formulations are briefly reviewed and elaborated upon to establish criteria for the functions to be continuous. Then the new continuity results are related to the discrete sample set model in order to establish conditions under which the skeleton approximation converges to the exact continuous skeleton.