The probabilistic framework of W.E. Grimson and D.P. Huttenlocher (1990, 1991) is adapted to evaluate analytically the probability of false alarm attached to a simple recognition algorithm, the PS-Matcher. The model is extended to anisotropic distributions image edge orientations. It provides a natural criterion for selecting automatically the major threshold in edge detection, namely, the gradient magnitude threshold, as a function of the scene complexity. The model provides a probabilistic justification to select the most reliable peak in the Hough accumulator. This analytic quantitative evaluation appears to be extremely important to discriminate between correct and wrong hypotheses, especially in the presence of clutter edges.>

The detection of edges is only one of many steps in the understanding of images. Further processing necessarily involves grouping operations between contours. We present a representation of edge contours by approximating B-splines and show that such a representation facilitates the extraction of symmetries between contours. Our representation is rich, compact, stable, and does not critically depend on feature extraction. We turn our attention to the detection of three types of symmetries: skew symmetries and parallel symmetries, which have proven to be of great importance in inferring shape from contour, and smooth local symmetries, which have been used for planar shape description. We show that our representation facilitates the computation of these symmetries.>

A method to smooth a signal while preserving discontinuities is presented. This is achieved by repeatedly convolving the signal with a very small averaging mask weighted by a measure of the signal continuity at each point. Edge detection can be performed after a few iterations, and features extracted from the smoothed signal are correctly localized (hence, no tracking is needed). This last property allows the derivation of a scale-space representation of a signal using the adaptive smoothing parameter k as the scale dimension. The relation of this process to anisotropic diffusion is shown. A scheme to preserve higher-order discontinuities and results on range images is proposed. Different implementations of adaptive smoothing are presented, first on a serial machine, for which a multigrid algorithm is proposed to speed up the smoothing effect, then on a single instruction multiple data (SIMD) parallel machine such as the Connection Machine. Various applications of adaptive smoothing such as edge detection, range image feature extraction, corner detection, and stereo matching are discussed.>

The authors present an active triangulation-based range finding system composed of an independent laser system generating a sheet of light projected on the object to be measured, which is placed on a linear or a rotary table driven by a personal computer. This computer includes a video digitizer board to which two cameras, looking at the scene from both sides of the sheet of light, are connected. Besides its low cost, this system has several advantages over similar systems. First of all, two cameras are used to limit the occlusion problem, and a method is proposed to integrate range data obtained from these cameras into a single range image. The calibration of each camera is very simple, provides subpixel accuracy, and is performed only once as the laser or the camera does not move. The data acquisition uses an interpolation technique that produces very accurate depth measurements. The system also provides intensity data in registration with the range data. The application of all these techniques is illustrated by showing numerous examples of the range and intensity data acquisition from various complex objects.>

The authors present a method to smooth a signal-whether it is an intensity image, a range image, or a contour-which preserves discontinuities and thus facilitates their detection. This is achieved by repeatedly convolving the signal with a very small averaging filter modulated by a measure of the signal discontinuity at each point. This process is related to the anisotropic diffusion reported by P. Perona and J. Malik (1987) but it has a much simpler formulation and is not subject to instability or divergence. Real examples show how this approach can be applied to the smoothing of various types of signals. The detected features do not move, and thus no tracking is needed. The last property makes it possible to derive a novel scale-space representation of a signal using a small number of scales. Finally, this process is easily implemented on parallel architectures: the running time on a 16 K connection machine is three orders of magnitude faster than on a serial machine.>

The authors discuss some of the issues that have to be tackled in order to perform geometric reasoning from range imagery. They begin by pointing out that a successful system must deal with real-world data, and therefore take into account the effects of noise and quantization. They suggest that adaptive smoothing may prove to be a helpful tool for such a task. The next stage of processing involves a symbolic representation of the original data. The authors spell out criteria for shape description, discuss current representation schemes and point out their limitations, and then propose some ideas for overcoming such limitations, illustrated on real examples. Finally, they look at the issues in recognition, and more specifically the matching part, with reference to different methodologies, tree search and constraint satisfaction network.>

The authors present an active triangulation range finding system composed of an independent laser system generating a plane of light projected on an object placed on a rotary table driven by a personal computer. This computer includes a video digitizer board connected to a camera looking at the scene. Besides its low cost, this system has other advantages over the comparable existing systems. First, the authors have designed a simple, fast and accurate calibration procedure which does not require any knowledge about the camera parameters or the relative position of the camera with the laser plane. Furthermore, this calibration procedure is performed only once, ensuring stable and accurate results. The result of the scanning of a given object is given in cylindrical coordinates. Choosing different viewpoints, Cartesian range images of the same object are computed in order to show, with shaded and perspective views of the scanned object, the quality of the results.>

A new and unified approach is proposed for ridge and contour points detection in textures. It involves a 3D-representation of a greylevel image and a description of the surface thus obtained, with local curvature properties. Some theoretical foundations are first recalled and used for the extraction of ridge and contour points from the convex domains of the image surface. Experimental results are given in the case of crystallization images of biological substratums, in which radiance centers are looked for.