We present an alternative approach to what we call the "standard optimization", which minimizes a cost function by searching a parameter space. Instead, our approach "projects" in the joint observation space onto the manifold defined by the "consistency constraint", which demands that any minimal subset of observations produce the same result. This approach avoids many difficulties encountered in the standard optimization. As typical examples, we apply it to line fitting and multiview triangulation. The latter produces a new algorithm far more efficient than existing methods. We also discuss the optimality of our approach.

This paper presents a pilot-aided channel estimation method which is particularly suitable for mobile WiMAX 802.16e Downlink Partial Usage of Subchannel mode. Based on this mode, several commonly used channel estimation methods are studied and the method of least squares line fitting is proposed. As data of users are distributed onto permuted clusters of subcarriers in the transmitted OFDMA symbol, the proposed channel estimation method utilizes these advantages to provide better performance than conventional approaches while offering remarkably low complexity in practical implementation. Simulation results with different ITU-channels for mobile environments show that depending on situations, enhancement of 5 dB or more in term of SNR can be achieved.

This paper describes a cumulative distribution function (CDF) of edge direction for detecting road lanes. Based on the assumptions that there are no abrupt changes in the direction and location of road lanes and that the intensity of lane boundaries differs from that of the background, the CDF is formulated, which accumulates the edge magnitude for edge directions. The CDF has distinctive peak points at the vicinity of lane directions due to the directional and the positional continuities of a lane. To obtain lane-related information, we construct a scatter diagram by collecting edge pixels, of which the direction corresponds to the peak point of the CDF, then perform the principal axis-based line fitting for the scatter diagram. Because noises can cause many similar features appear or disappear in an image, to prevent false alarms or miss detection, a recursive estimator of the CDF was introduced, and also a scene understanding index (SUI) was formulated by the statistical parameters of the CDF. The proposed algorithm has been implemented in real time on video data obtained from a test vehicle driven on a typical highway.

Introducing a mathematical model of image noise, we formalize the problem of fitting a line to point data as statistical estimation. It is shown that the reliability of the fitted line can be evaluated quantitatively in the form of the covariance matrix of the parameters. We present a numerical scheme called renormalization for computing an optimal fit and at the same time evaluating its reliability. We also present a scheme for visualizing the reliability of the fit by means of the primary deviation pair and derive an analytical expression for the reliability of a line fitted to an edge segment by using an asymptotic approximation. Our method is illustrated by showing simulations and real-image examples.

Based on a simple model for the statistical error characteristics of range sensing, a numerical scheme called renormalization is presented for optimally fitting a planar surface to data points obtained by range sensing. The renormalization method has the advantage that not only an optimal fit is computed but also its reliability is automatically evaluated in the form of the covariance matrix. Its effectiveness is demonstrated by numerical simulation. A scheme for visualizing the reliability of computation by means of the primary deviation pair is also presented.

The Paper describes a comprehensive system for image recognition based on the technique of boundary spline matching. It can be used to accurately compare two objects and determine whether they are identical or not. The result is extremely satisfactory for comparing planar objects as revealed from the illustrative example presented in this paper. In real practice, images of the same scene object can easily be considered as belonging to different objects if the objects are viewed from different orientations and ranges. Thus, image recognition calls for choosing the proper geometric transformation functions to match images as the initial step so that recognition by template matching can be done as the second step. However, there are a large variety of transformation functions available and the subsequent evaluation of transformation parameters is a highly nonlinear optimisation procedure which is both time consuming and not solution guaranteed, making real-time estimation impossible. This paper describes a new method that represents the boundary of each of two image objects by B-splines and matches the B-splines of two image objects to determine whether they belong to the same scene object. The algorithm developed in this paper concentrates on solving linear simultaneous equations only when handling the geometric transformation functions, which takes almost negligible computational time by using the standard Gaussian Elimination. Representation of the image boundary by B-splines provides a flexible and continuous matching environment so that the level of accuracy can be freely adjusted subject to the requirement of the user. The non-linear optimisation involves only one parameter, i.e. the starting point of each boundary under B-spline simulation, thus guaranteeing a very high speed computational system. The real time operation is deemed possible even there is a wide choice of proper transformation functions.

This paper presents a new line extraction method to capture vectors based on contours and skeletons from line drawing raster images in which the lines are touched by characters or other lines. Conventionally, two line extraction methods have generally been used. One is a thinning method. The other is a medial line extraction method based on parallel pairs of contours. The thinning method tends to distort the extracted lines, especially at intersections and corners. On the other hand, the medial line extraction method has a poor capability as regards capturing correct lines at intersections. Contours are able to maintain edge shapes well, while skeletons preserve topological features; thus, a combination of these features effectively leads to the best fitting line. In the proposed method, the line which best fits the original image is selected from among various candidate lines. The candidates are created from several merged short skeleton fragments located between pairs of short contour fragments. The method is also extended to circular arc fitting. Experimental results show that the proposed line fitting method is effective.