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.>

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.>

The authors deal with the principal patch representation of visible surfaces in a scene, an algorithm for creating a stable surface model in this representation, and an algorithm for extending this model into subsequent views. The representation is based on the fact that the lines of minimum and maximum curvature on a generic smooth surface are orthogonal at almost every point. An engineering solution is presented for creating global principal patch networks. By computing the lines of curvature from a range image, it will be possible to construct a mesh data structure and repatch the surface with tensor product surfaces that are virtually free of tensor product artifacts and allow application of intersurface continuity algorithms. The authors focus on the computational difficulties encountered in building a quadrilateral mesh based on integrated lines of curvature.>

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.>

A new concept in passive ranging to moving objects is described which is based on the comparison of multiple image flows. It is well known that if a static scene is viewed by an observer undergoing a known relative translation through space, then the distance to objects in the scene can be easily obtained from the measured image velocities associated with features on the objects (i.e., motion stereo). But in general, individual objects are translating and rotating at unknown rates with respect to a moving observer whose own motion may not be accurately monitored. The net effect is a complicated image flow field in which absolute range information is lost. However, if a second image flow field is produced by a camera whose motion through space differs from that of the first camera by a known amount, the range information can be recovered by subtracting the first image flow from the second. This ``difference flow'' must then be corrected for the known relative rotation between the two cameras, resulting in a divergent relative flow from a known focus of expansion. This passive ranging process may be termed Dynamic Stereo, the known difference in camera motions playing the role of the stereo baseline. We present the basic theory of this ranging process, along with some examples for simulated scenes.

A modification over Sakoe and Chiba's dynamic time warping algorithm for isolated word recognition is proposed. It is shown that this modified algorithm works better without any slope constraint. Also, this algorithm not only consumes less computation time but also improves the word recognition accuracy.