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.

We show that moving objects can be detected from optical flow without using any knowledge about the magnitude of the noise in the flow or any thresholds to be adjusted empirically. The underlying principle is viewing a particular interpretation about the flow as a geometric model and comparing the relative "goodness" of candidate models measured by the geometric AIC.

In the usual optical flow detection, the gradient constraint, which expresses the relationship between the gradient of the image intensity and its motion, is combined with the least-squares criterion. This criterion means assuming that only the time derivative of the image intensity contains noise. In this paper, we assume that all image derivatives contain noise and derive a new optical flow detection technique. Since this method requires the knowledge about the covariance matrix of the noise, we also discuss a method for its estimation. Our experiments show that the proposed method can compute optical flow more accurately than the conventional method.

The uncertainty involved in the gradient constraint for optical flow detection is often modeled as constant Gaussian noise added to the time-derivative of the image intensity. In this paper, we examine this modeling closely and investigate the error behavior by experiments. Our result indicates that the error depends on both the spatial derivatives and the image motion. We propose alternative uncertainty models based on our experiments. It is shown that the optical flow computation algorithms based on them can detect more accurate optical flow than the conventional least-squares method.

We discuss optimal estimation of the current location of a mobile robot by matching an image of the scene taken by the robot with the model of the environment. We first present a theoretical accuracy bound and then give a method that attains that bound, which can be viewed as describing the probability distribution of the current location. Using real images, we demonstrate that our method is superior to the naive least-squares method. We also confirm the theoretical predictions of our theory by applying the bootstrap procedure.

Optical flow is usually computed only on the basis of intensity information of images. Therefore, if we use color information in addition to the intensity, it is expected that more accurate optical flow can be computed. However, this intuition will be correct only when the following conditions are satisfied. First, the images should contain rich color variations. Moreover, it is also required that the image gradient of each color band differs in its direction. In this report, we empirically examined the difference of gradient directions on each band using 500 images, and evaluated quantitatively the advantage of using color information for optical flow computation.

We implement a graphical interface that automatically transforms a figure input by a mouse into a regular figure which the system infers is the closest to the input. The difficulty lies in the fact that the classes into which the input is to be classified have inclusion relations, which prohibit us from using a simple distance criterion. In this letter, we show that this problem can be resolved by introducing the geometric AIC.

Anomaly detection has several practical applications in different areas, including intrusion detection, image processing, and behavior analysis among others. Several approaches have been developed for this task such as detection by classification, nearest neighbor approach, and clustering. This paper proposes alternative clustering algorithms for the task of anomaly detection. By employing a weighted kernel extension of the least squares fitting of linear manifolds, we develop fuzzy clustering algorithms for kernel manifolds. Experimental results show that the proposed algorithms achieve promising performances compared to hard clustering techniques.

Recently, cameras are equipped on cars in order to assist their drivers. These cameras often have a severe radial distortion because of their wide view angle, and sometimes it is necessary to compensate it in a fully automatic way in the field. We have proposed such a method, which uses the entropy of the histogram of oriented gradient (HOG) to evaluate the goodness of the compensation. Its performance was satisfactory, but the computational burden was too heavy to be executed by drive assistance devices. In this report, we discuss a method to speed up the algorithm, and obtain a new light algorithm feasible for such devices. We also show more comprehensive performance evaluation results then those in the previous reports.

This paper presents a new method for solving the structure-from-motion problem for optical flow. The fact that the structure-from-motion problem can be simplified by using the linearization technique is well known. However, it has been pointed out that the linearization technique reduces the accuracy of the computation. In this paper, we overcome this disadvantage by correcting the linearized solution in a statistically optimal way. Computer simulation experiments show that our method yields an unbiased estimator of the motion parameters which almost attains the theoretical bound on accuracy. Our method also enables us to evaluate the reliability of the reconstructed structure in the form of the covariance matrix. Real-image experiments are conducted to demonstrate the effectiveness of our method.

There is one method, called the block gradient method here, whereby to detect image movements from an imagesequence. In this method, a relation between image derivatives and a movement is used with an assumption that movements in a block have the same values. This method has an advantage over the computing cost, compared with other methods, such as the block matching method. However, it also involves a general problem, which is that the reliability of a detected movement varies with varying conditions. Therefore, it is important to obtain some indices indicating the reliability of the detected movements. The reason is that, without such information, it is impossible to make good use of the movements. In this paper, the reliability of a movement detected by the block gradient method is discussed and indices indicating it are proposed. One index indicates the support level for the assumption used in the block gradient method. Two other indices indicate the image pattern condition, or the aperture problem level, in other words. The detected movement accuracy is rather directly related to this condition. The indices effectiveness is shown by experiments. The indices are expected to offer helpful information to the sequential processes using the movements. In addition, a movement stabilization process is described. This process smooths a movement field in the image, using the detected movements and two of the three indices. It is useful, when the movement detection process is used independently.

We discuss optimal rotation estimation from two sets of 3-D points in the presence of anisotropic and inhomogeneous noise. We first present a theoretical accuracy bound and then give a method that attains that bound, which can be viewed as describing the reliability of the solution. We also show that an efficient computational scheme can be obtained by using quaternions and applying renormalization. Using real stereo images for 3-D reconstruction, we demonstrate that our method is superior to the least-squares method and confirm the theoretical predictions of our theory by applying bootstrap procedure.