We present a new form of least squares (LS), called "hyper LS", for geometric problems that frequently appear in computer vision applications. Doing rigorous error analysis, we maximize the accuracy by introducing a normalization that eliminates statistical bias up to second order noise terms. Our method yields a solution comparable to maximum likelihood (ML) without iterations, even in large noise situations where ML computation fails.

A higher order scheme is presented for the optimal correction method of Kanatani [5] for triangulation from two views and is compared with the method of Hartley and Sturm [3]. It is pointed out that the epipole is a singu-larity of the Hartley-Sturm method, while the proposed method has no singu-larity. Numerical simulation confirms that both compute identical solutions at other points. However, the proposed method is significantly faster. 1

A very compact algorithm is presented for fitting an ellipse to points in images by maximum likelihood (ML) in the strict sense. Although our algorithm produces the same solution as existing ML-based methods, it is probably the simplest and the smallest of all. By numerical experiments, we show that the strict ML solution practically coincides with the Sampson solution.

A new method is presented for computing the fundamental matrix from point correspondences: its singular value decomposition (SVD) is optimized by the Levenberg-Marquard (LM) method. The search is initialized by optimal correction of unconstrained ML. There is no need for tentative 3-D reconstruction. The accuracy achieves the theoretical bound (the KCR lower bound). 1

We compare the convergence performance of different numerical schemes for computing the fundamental matrix from point correspondences over two images. First, we state the problem and the associated KCR lower bound. Then, we describe the algorithms of three well-known methods: FNS, HEIV, and renormalization. We also introduce Gauss-Newton iterations as a new method for fundamental matrix computation. For initial values, we test random choice, least squares, and Taubin's method. Experiments using simulated and real images reveal different characteristics of each method. Overall, FNS exhibits the best convergence properties.

We propose a new technique for optimizing a triangular mesh for polyhedral representation of the scene in a video stream. We introduce a specially designed template that can effectively detect color and texture discontinuities. Using real images, we demonstrate that our method is superior to existing methods.

This paper proposes a polynocular stereo algorithm that is the integration of two algorithms with/without occlusion handling mechanism. The algorithm is useful to improve the sharpness of depth map at occluding boundaries obtained by video-rate stereo machines without occlusion handling capability. In order to realize the integration, we have developed an algorithm for detecting occlusion area and a correspondence algorithm with occlusion handling mechanism. Using the evaluation values that are computed in the correspondence search process without considering occlusion, occlusion area can be extracted with small additional computational cost. We have developed a polynocular stereo algorithm based on sort-oriented occlusion handling mechanism. Experimental results using ground-truthed stereo images show the effectiveness of the integration.