This paper presents an RK-means clustering algorithm which is developed for reliable data grouping by introducing a new reliability evaluation to the K-means clustering algorithm. The conventional K-means clustering algorithm has two shortfalls: 1) the clustering result will become unreliable if the assumed number of the clusters is incorrect; 2) during the update of a cluster center, all the data points belong to that cluster are used equally without considering how distant they are to the cluster center. In this paper, we introduce a new reliability evaluation to K-means clustering algorithm by considering the triangular relationship among each data point and its two nearest cluster centers. We applied the proposed algorithm to track objects in video sequence and confirmed its effectiveness and advantages.

With a view to virtual studio applications, we design an optimal grid pattern such that the observed image of a small portion of it can be matched to its corresponding position in the pattern easily. The grid shape is so determined that the cross ratio of adjacent intervals is different everywhere. The cross ratios are generated by an optimal Markov process that maximizes the accuracy of matching. We test our camera calibration system using the resulting grid pattern in a realistic setting and show that the performance is greatly improved by applying techniques derived from the designed properties of the pattern.

We describe a theoretically optimal algorithm for computing the homography between two images. First, we derive a theoretical accuracy bound based on a mathematical model of image noise and do simulation to confirm that our renormalization technique effectively attains that bound. Then, we apply our technique to mosaicing of images with small overlaps. By using real images, we show how our algorithm reduces the instability of the image mapping.

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.

Introducing a mathematical model of image noise, we formalize the problem of fitting a conic to point data as statistical estimation. It is shown that the reliability of the fitted conic can be evaluated quantitatively in the form of the covariance tensor. 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. Our method is illustrated by showing simulations and real-image examples.