We address the problem of building a map of the environment utilizing sensory depth information obtained from multiple viewpoints. The desired representation of the environment is in the form of a finite-resolution three-dimensional grid of voxels. Each voxel within the grid is assigned a binary value corresponding to its occupancy state. We present an approach for multi-sensory depth information assimilation based on the Dempster-Shafer theory for evidential reasoning. This approach provides a mechanism to explicitly model ignorance which is desirable when dealing with an unknown environment. We present results obtained from this approach on a laboratory stereo sequence and contrast these with results obtained from the traditional Bayesian approach.>

The quadratic filter for low-level vision applications is explored. The quadratic filter is the simplest nonlinear time-invariant filter and corresponds to the second term in the Volterra expansion. Concepts behind the quadratic filter are elaborated, and it is shown that it can be derived from fundamental properties of regions and the principle of model competition. Two properties of the filter are presented. It has better spatial localization than a linear filter, and it is insensitive to blurred boundaries.>

A nonparametric algorithm for edge localization is presented. When an edge detector is applied to the edge of interest, nearby edges introduce interference into the detection process and cause detected edge locations to differ from the true edge locations. The algorithm recovers the true edge location by removing the edge interference which is estimated by adapting nonparametric methods in statistics and employing robust statistics.>

A surface reconstruction method using multilayer feedforward neural networks is proposed. The parametric form represented by multilayer neural networks can model piecewise smooth surfaces in a way that is more general and flexible than many of the classical methods. The approximation method is based on a robust backpropagation (BP) algorithm, which extends the basic BP algorithm to handle errors, especially others, in the training data.>

A two-stage algorithm for visual surface reconstruction from scattered data while preserving discontinuities is presented. The first stage consists of a robust local approximation algorithm (the moving least median of squares (MLMS) of error) to clean the data and create a grid from the original scattered data points. This process is discontinuity preserving. The second stage introduces a weighted bicubic spline (WBS) as a surface descriptor. The WBS has a factor in the regularizing term that adapts the behavior of the spline across discontinuities. The weighted bicubic approximating spline can approximate data with step discontinuities with no discernible distortion in the approximating surface. The combination of robust surface fitting and WBSs removes outliers and reduces Gaussian noise. Either stage by itself would not effectively remove both kinds of noise. Experimental results with the two-stage algorithm are presented.>

An approach for incremental refinement of disparity maps obtained from a dynamic stereo sequence of a static scene is presented. The approach has been implemented using a binocular stereo vision system mounted on a mobile robot. A robust least median of squares based algorithm is given for recovering the camera motion between successive viewpoints, which provides a self-calibration mechanism. The recovered motion is utilized for recursive disparity prediction and refinement using a robust Kalman filter model.>

An optimal deformable contour approximation algorithm using a cardinal-form piecewise cubic spline (PCS) curve representation is presented. The approximation is optimal in the sense of least square errors in both location and orientation. The knots are set automatically at high curvature positions. The sample data are generated by a robust edge fragment detection algorithm which is optimal in the sense of a weighted absolute error. An initial contour placement algorithm uses a penalized maximum likelihood algorithm to group the edge fragments together for an initial contour. A controlled deformable contour algorithm refines the initial contour to cover meaningful edge features.>

A multidimensional edge model is established and a first-order estimation for multidimensional edge profiles is proposed. An optimal edge location detection algorithm is developed. The advantages of the algorithm are that (1) it has little dependence on assumptions of edge models, noise models, or smoothing filters, (2) it has better abilities for detecting very weak edges and making less edge orientation errors than other edge detectors, (3) it can handle corners and complicated multidimensional image structures, and (4) it detects different edge types at the same time.>

The surface reconstruction problem is formulated as a two-stage reconstruction procedure. The first stage is a robust local fit to the data in a multiresolution scheme and the second is a regularized least squares fit, with the addition of an adaptive mechanism in the smoothness functional in order to make the solution well behaved. The authors present the details of the second stage in which they use the weighted bicubic spline as a surface representation in a regularization framework, with a Tikhonov stabilizer, as the smoothness norm. It is shown how the adaptive weights, in the stabilizer help the surface bend across discontinuities by varying the energy of the surface.>

It is shown how a contour can be estimated from a few edge positions. The technique fits a cubic spline to edges using the position and orientations of edges (tangent slopes) and computes tangent magnitudes by a minimization based on the second derivatives. Cubic splines (piecewise third-order polynomials) are used because they are the lowest-order polynomials that can deal with inflection points. For assuring a smooth overall contour, the polynomial segments are joined such that the continuity of the first derivative is preserved and discontinuity in the second derivative is minimized. This technique can be used as an efficient means for entering and editing contours which are tied to the underlying data through the edge orientations. The time required for computing the edge orientations and the time for finding the curve parameters are linearly proportional to the number of edge fragments. The algorithm was applied to medical images, and the results are compared with the conic splines and the B-splines and the distance approximation to the cubic splines.>

Dynamic stereo is useful for constructing a complete map of the environment as only a portion of the actual environment is visible from each viewpoint. In addition, there is usually an overlap between the portions of the environment visible from two successive viewpoints. It is then feasible to utilize a prediction-verification approach to combine the individual depth estimates of features visible from both viewpoints to obtain a more accurate estimate. A fundamental requirement for such an approach to be used is accurate knowledge of the camera motion between the two viewpoints. A robust least median of squares (LMS)-based algorithm to recover this motion which provides a self-calibration mechanism is presented. The recovered motion is utilized for recursive disparity prediction and refinement using a robustified Kalman filter formulation. Results are presented for a laboratory stereo sequence.>

An algorithm for the optimal edge contour estimation in medical images without a priori shape models is described. The proposed method is an intermediate-level approach compared with the usual low-level edge-detection operators. An optimal and robust contour estimator is derived by the minimization of a risk function which measures the error from both an inappropriate choice of edge contour and an inappropriate choice of the noise model in the image. The result includes Huber's function. If a parametric statistical noise model and the Neyman-Pearson criterion are used, the result is an extension of maximum-likelihood function. A recursive formulation can be implemented by assuming an independent random field and a Markov path model. The assumption of independent statistics can be satisfied by the use of an autoregressive moving-average preprocessor. The problem of varying edge strength is lessened using an adaptive trimmed mean. The robust algorithm is implemented using a priority-tree (stack) structure. The system's performance is illustrated by estimation of lesion boundaries in medical images.>

A novel algorithm for computing the orientation field for a flowlike texture is presented. The basic idea behind the algorithm is to use an oriented filter, namely the gradient of the Gaussian, and perform manipulations on the resulting gradient vector field. The most important aspect of the algorithm is that it is provably optimal in estimating the local orientations of an oriented texture. An added strength of the algorithm is that it is simpler and has a better signal-to-noise ratio than previous approaches, because it utilizes fewer derivative operations. Also proposed is a measure of coherence which is based on the use of the angle and coherence images as intrinsic images. An analysis of oriented textures requires the computation of these intrinsic images as a first step. In this sense, the computation of the orientation field, resulting in the intrinsic images, is indispensable in the analysis of oriented textures. Results from a number of experiments indicate the usefulness of the angle and coherence intrinsic images.>

A two-stage algorithm for visual surface reconstruction while preserving discontinuities is presented. The primary contribution is the second stage, a weighted bicubic spline as a surface descriptor. The weighted bicubic spline has a factor in the regularizing term that adapts the behavior of the spline across the discontinuity. The weighted bicubic interpolating spline is able to interpolate data with step discontinuities with no discernible distortion (such as Gibbs phenomena) in the interpolated surface. Since regularization is related to spline approximation, extensions to this work should suggest ideas for solving ill-posed problems in vision. Experiments with weighted bicubic spline interpolation are presented.>

Image flow is the velocity field in the image plane caused by the motion of the observer, objects in the scene, or apparent motion, and can contain discontinuities due to object occlusion in the scene. An algorithm that can estimate the image flow velocity field when there are discontinuities due to occlusions is described. The constraint line clustering algorithm uses a statistical test to estimate the image flow velocity field in the presence of step discontinuities in the image irradiance or velocity field. Particular emphasis is placed on motion estimation and segmentation in situations such as random dot patterns where motion is the only cue to segmentation. Experimental results on a demanding synthetic test case and a real image are presented. A smoothing algorithm for improving the velocity field estimate is also described. The smoothing algorithm constructs a smooth estimate of the velocity field by approximating a surface between step discontinuities. It is noted that the velocity field estimate can be improved using surface reconstruction between velocity field boundaries.>