This paper is concerned with the inference of marginal densities based on MRF models. The optimization algorithms for continuous variables are only applicable to a limited number of problems, whereas those for discrete variables are versatile. Thus, it is quite common to convert the continuous variables into discrete ones for the problems that ideally should be solved in the continuous domain, such as stereo matching and optical flow estimation. In this paper, we show a novel formulation for this continuous-discrete conversion. The key idea is to estimate the marginal densities in the continuous domain by approximating them with mixtures of rectangular densities. Based on this formulation, we derive a mean field (MF) algorithm and a belief propagation (BP) algorithm. These algorithms can correctly handle the case where the variable space is discretized in a non-uniform manner. By intentionally using such a non-uniform discretization, a higher balance between computational efficiency and accuracy of marginal density estimates could be achieved. We present a method for actually doing this, which dynamically discretizes the variable space in a coarse-to-fine manner in the course of the computation. Experimental results show the effectiveness of our approach.

This paper proposes a method for detecting temporal changes of the three-dimensional structure of an outdoor scene from its multi-view images captured at two separate times. For the images, we consider those captured by a camera mounted on a vehicle running in a city street. The method estimates scene structures probabilistically, not deterministically, and based on their estimates, it evaluates the probability of structural changes in the scene, where the inputs are the similarity of the local image patches among the multi-view images. The aim of the probabilistic treatment is to maximize the accuracy of change detection, behind which there is our conjecture that although it is difficult to estimate the scene structures deterministically, it should be easier to detect their changes. The proposed method is compared with the methods that use multi-view stereo (MVS) to reconstruct the scene structures of the two time points and then differentiate them to detect changes. The experimental results show that the proposed method outperforms such MVS-based methods.

In this paper, we present a method for accurately estimating the shape of an object by integrating the surface orientation measured by photometric stereo and the position measured by some range-measuring method. We first show that even if the knowledge of the reflectance/illumination is inaccurate, the first derivatives of the photometrically measured orientation can be accurately estimated at the surface points where they have small values. We propose a probabilistic framework to quantitate the (in)accuracy of the knowledge and connect it to the estimation accuracy of these derivatives. Based on this framework, we consider optimally integrating the surface orientation and position to obtain the object shape with higher accuracy. The integration reduces to an optimization problem, and it is efficiently solved by belief propagation. We present several experimental results showing the effectiveness of the proposed approach.

The mean field (MF) methods are an energy optimization method for Markov random fields (MRFs). These methods, which have their root in solid state physics, estimate the marginal density of each site of an MRF graph by iterative computation, similarly to loopy belief propagation (LBP). It appears that, being shadowed by LBP, the MF methods have not been seriously considered in the computer vision community. This study investigates whether these methods are useful for practical problems, particularly MPM (Maximum Posterior Marginal) inference, in computer vision. To be specific, we apply the naive MF equations and the TAP (Thouless-Anderson-Palmer) equations to interactive segmentation and stereo matching. In this paper, firstly, we show implementation of these methods for computer vision problems. Next, we discuss advantages of the MF methods to LBP. Finally, we present experimental results that the MF methods are well comparable to LBP in terms of accuracy and global convergence; furthermore, the 3rd-order TAP equation often outperforms LBP in terms of accuracy.

In recent years, tactile sensors have become an important interface for information devices. Our goal is to develop a simple and sensitive tactile sensor. We have proposed a reflection-image-based tactile sensor. The key points of this sensor were its simplicity and use of an optical device. In this study, we propose a design of a distributed-force sensitive touch panel following the previous developments. We employ an LED (light emitting diode) and PDs (photo diodes) in the new reflection-type tactile sensor. We investigate the illumination distribution and its changes under some simple deformation of the sensor surface with a ray-trace simulation. Then, based on the results of the experimental simulations, we also propose a method for estimating a given deformation from the illumination distribution.

In recent years, many tactile sensors have been developed for the practical use in robotics and to meet the increasing demand for intuitive interfaces. However, the implementation of conventional tactile sensors is very complex. We develop a simple total-internal-reflection based tactile sensor that measures the shape of the sensor surface from a reflection image of the surface and evaluate its performance. We previously proposed a reconstruction method which solves geometric optical constraints of the sensor surface by optimization, however this method could not meet real-time and accurate reconstruction simultaneously. To solve this problem, in this paper, we propose a new reconstruction method based on the previously proposed one. By reconstruction experiments with simulated reflection images, we found that the proposed method could perform real-time and accurate reconstruction and was applicable to various sensor shapes and robust to feature tracking error and the presence of contact areas on the sensor surface without total-internal-reflection property. Then, we implemented the proposed method on the actual sensor and confirmed that the sensor could perform real-time reconstruction.

This paper examines numerical algorithms for factorization of a low-rank matrix with missing components. We first propose a new method that incorporates a damping factor into the Wiberg method to solve the problem. The new method is characterized by the way it constrains the ambiguity of the matrix factorization, which helps improve both the global convergence ability and the local convergence speed. We then present experimental comparisons with the latest methods used to solve the problem. No comprehensive comparison of the methods that have been proposed recently has yet been reported in literature. In our experiments, we prioritize the assessment of the global convergence performance of each method, that is, how often and how fast the method can reach the global optimum starting from random initial values. Our conclusion is that top performance is achieved by a group of methods based on Newton-family minimization with damping factor that reduce the problem by eliminating either of the two factored matrices. Our method, which belongs to this group, consistently shows a 100% global convergence rate for different types of affine structure from motion data with a very high population of missing components.

It is one of the central issues in augmented reality and computer vision to track a planar object moving relatively to a camera in an accurate and robust manner. In previous studies, it was pointed out that there are several factors making the tracking difficult, such as illumination change and motion blur, and effective solutions were proposed for them. In this paper, we point out that degradation in effective image resolution can also deteriorate tracking performance, which typically occurs when the plane being tracked has an oblique pose with respect to the viewing direction, or when it moves to a distant location from the camera. The deterioration tends to become significantly large for extreme configurations, e.g., when the planar object has nearly a right angle with the viewing direction. Such configurations can frequently occur in AR applications targeted at ordinary users. To cope with this problem, we model the sampling and reconstruction process of images, and present a tracking algorithm that incorporates the model to correctly handle these configurations. We show through several experiments that the proposed method shows better performance than conventional methods.

Maximum likelihood (ML) estimation is widely used in many computer vision problems involving the estimation of geometric parameters, from conic fitting to bundle adjustment for structure and motion. This paper presents a detailed discussion on the bias of ML estimates derived for these problems. Statistical theory states that although ML estimates attain maximum accuracy in the limit as the sample size goes to infinity, they can have non-negligible bias with small sample sizes. In the case of computer vision problems, the ML optimality holds when regarding variance in observation errors as the sample size. A natural question is how large the bias will be for a given strength of observation errors. To answer this for a general class of problems, we analyze the mechanism of how the bias of ML estimates emerges, and show that the differential geometric properties of geometric constraints used in the problems determines the magnitude of bias. Based on this result, we present a numerical method of computing bias-corrected estimates.

A fundamental problem in computer vision (CV) is the estimation of geometric parameters from multiple observations obtained from images; examples of such problems range from ellipse fitting to multi-view structure from motion (SFM). The maximum likelihood (ML) method is widely used to estimate the parameters in such problems, assuming Gaussian noises to be present in the observations, for example, bundle adjustment for SFM. According to the theory of statistics, the ML estimates are nearly optimal for these problems, provided that the variance of the observation noises is sufficiently small. This implies that when noises are not small, more accurate estimates can be derived as compared to the ML estimates. In this study, we propose the application of a method called the projected score method, developed in statistics for computing higher-accuracy estimates, to the CV problems. We describe how it can be customized to solve the CV problems and propose a numerical algorithm to implement the method. We show that the method works effectively for such problems.

Today there are many tactile sensors in the world. Though there is few sensor whose characteristics are similar to cutaneous sensation of human. If we want to measure the tactile information of human we have to use human-like tactile sensor. Here we have developed a reflection-type tactile sensor by using imaging device. This sensor employs a simple total reflection characteristic, so it has many degrees of freedom of selecting sensing units, and designing layer structures. This paper describes the design of the sensing unit and the structure of layers which has similar characteristics of human. First we compare the temporal frequency of the proposed sensor and human skin. Second we estimate the required spatial density of sensing units by simulation. Then we compare the total ability of proposed reflection-type sensor and cutaneous sensation of human.

In this correspondence, we discuss the quality of images realized by a recently proposed method of generating a high-resolution image by superimposing multiple low-resolution images projected by different projectors. We show several fundamental properties of this method: 1) the accuracy of the image realization (e.g., resolution of the realized image) is heavily affected by the structures of the images to be realized, and 2) there is a tradeoff between the image quality and the maximum brightness of the images to be realized. These are properties peculiar to multiprojector super-resolution and are in contrast with multicamera super-resolution. The results will be helpful in evaluating the usefulness of the method.

This paper proposes a novel concept for the image based visual control, which is called the goal-oriented just-in-time visual servoing. We apply this control to ball catching task by a robot arm. This approach contains the processes: 1. To achieve the control of robot arm 3D motion using visual observation, we employ no information to reconstruct 3D space from the 2D images, and only define the goal of the task in the image planes. 2. Then we apply the control to achieve all the 2D defined tasks simultaneously. 3. If all the respective goal defined in images are accomplished simultaneously, the 3D task can be interpreted to be achieved. Further more, in the proposed method, we estimate the Jacobian on-line to combine the image motion and 3D motion of the robot arm without the prior knowledge of the arm and camera structures for hand-eye and camera calibrations. The actual experiments show the feasibility of the proposed method for visual control of the ball catching robot.

This paper presents a new algorithm for the problem of robust subspace learning (RSL), i.e., the estimation of linear subspace parameters from a set of data points in the presence of outliers (and missing data). The algorithm is derived on the basis of the variational Bayes (VB) method, which is a Bayesian generalization of the EM algorithm. For the purpose of the derivation of the algorithm as well as the comparison with existing algorithms, we present two formulations of the EM algorithm for RSL. One yields a variant of the IRLS algorithm, which is the standard algorithm for RSL. The other is an extension of Roweis's formulation of an EM algorithm for PCA, which yields a robust version of the alternated least squares (ALS) algorithm. This ALS-based algorithm can only deal with a certain type of outliers (termed vector-wise outliers). The VB method is used to resolve this limitation, which results in the proposed algorithm. Experimental results using synthetic data show that the proposed algorithm outperforms the IRLS algorithm in terms of the convergence property and the computational time.

Using an imaging system in which the image plane can be tilted with respect to the optical axis of the lens, the image of a large-scale scene that appears to be a miniature to human eyes can be captured. This phenomenon suggests that the image contains information regarding the scale of the scene and that human vision can extract this information and recognize the scene scale from a single image. In this study, we consider how human vision can perform this single-view scale estimation. Although it is obvious that the existence of defocus blur in the image that simulates a shallow DOF plays an essential role in the scale estimation, we propose that this alone is not sufficient to explain the estimation mechanism. By incorporating a few assumptions, we theoretically show that scale estimation is made possible when (1) the 3D structure of the scene can be recovered from the image and furthermore, (2) the structure is combined with the defocus blur. Further, we present a simple algorithm for scale recognition and demonstrate its working using a real image.

Three-dimensional measurement methods using structured light projection enable accurate depth measurements by decoding the disparity between the projector-camera pair from an observed pattern. However, actual projection devices have various systematic error sources that distort the structured light pattern, directly affecting the accuracy of 3-D measurements. We propose a new method of measuring depth that is not affected by the systematic errors in the projected pattern. In our method, the image of a pattern projected onto a plane is referenced to cancel errors. Based on the invariance of the cross-ratio under perspective projections, depth is obtained from the disparity determined on the referenced image. In experiments, our method removed the systematic errors and improved the accuracy of depth measurement without any extra calibration or measurement.

We are motivated to deal with a biped robot by the existence of an almighty powerful control mechanism of a human. Although a visual information, in particular, plays an important role in order to realize admirable intelligence in a humanoid robot, we must assert a vision to be one of the developing sensors. In fact, there are many difficulties of both aspects of restrictive hardware resources for a vision and real-time image processing for motor control. In this paper, we clarify a structure and a nature of a visual information processing system which should be equipped with a biped robot. For this purpose, a human eye structure and its movements, and brain motor control through a central nervous system are considered as an analogy with robotics. We shall show that a gaze control mechanism like human is absolutely indispensable for a vision system of a biped robot. Furthermore, we investigate considerable differences between the human eyes and the biped robot ones. This allows us to propose a new, simple and intuitively understandable criteria, called stably gazing scope, for evaluating gaze control performance in the sense of availability of visual information for robot motion control

In order to keep intended distance and direction to a target object, our biped robot modifies its movements based on visual information. To detect the target direction, we stabilize gaze of the robot by 2-DOF controller, using a scheduled robot motion plan for the feedforward one and the image information for the feedback one. Then, we stabilize the robot motion with the stabilized gaze. In this control scheme, parameters of the feedforward controller is modified on-line by using an adaptive law of model reference adaptive control (MRAC).

This paper presents a method for calibrating a projector-camera system that consists of multiple projectors (or multiple poses of a single projector), a camera, and a planar screen. We consider the problem of estimating the homography between the screen and the image plane of the camera or the screen-camera homography, in the case where there is no prior knowledge regarding the screen surface that enables the direct computation of the homography. It is assumed that the pose of each projector is unknown while its internal geometry is known. Subsequently, it is shown that the screen-camera homography can be determined from only the images projected by the projectors and then obtained by the camera, up to a transformation with four degrees of freedom. This transformation corresponds to arbitrariness in choosing a two-dimensional coordinate system on the screen surface and when this coordinate system is chosen in some manner, the screen-camera homography as well as the unknown poses of the projectors can be uniquely determined. A noniterative algorithm is presented, which computes the homography from three or more images. Several experimental results on synthetic as well as real images are shown to demonstrate the effectiveness of the method.

In this paper, we propose an active vision strategy for the construction of a 3D map in a robot brain from its stereo eye images. We show that, by the direct combination of its action and image change caused by the action, the robot can acquires a 3D accurate map in his brain. If the robot stereo cameras and his motion parameters have been calibrated, the obtained reconstruction of the static scene stays stationary. But, if not, the reconstructed scene changes according to the robot action. We utilise this change to correct the robot parameters so as to obtain stationary scene in his 3D map under the action. We show the feasibility of this idea as an auto-calibration of robot vision with some simulation experiments and implementation on actual robots.

In this paper, a method for real-time tracking of moving objects or pedestrians is proposed. Especially, we tackled to track an object whose part was temporally occluded or which traversed in front of the cluttered background. Furthermore, we tried to obtain the accurate trajectory of the center of it stably even then. For the problems, we present a probabilistic color-based tracking. In our proposed method, we incorporated particle filtering into graphical models and applied it to the color-based tracking. When the color histogram of the tracked object was made, we used not one region of the whole of the object but the multi-part region of it if it was divided in some parts (e.g. the head and the body of a pedestrian). We treated the multi-part region as a graphical model. In the graphical model, messages about the state of the parts are sent to other parts. As the result., even when the tracked object has occluded part, our proposed method can track it stably and infer the state (e.g. position) of the occluded part. We made experiments to confirm effectiveness of this proposed method.

In many problems of computer vision we have to estimate parameters in the presence of nuisance parameters increasing with the amount of data. It is known that, unlike in the cases without nuisance parameters, maximum likelihood estimation (MLE) is not optimal in the presence of nuisance parameters. By optimal we mean that the resulting estimate is unbiased and its variance attains the theoretical lower bound in an asymptotic sense. Thus, naive application of MLE to computer vision has a potential problem. This applies to a wide range of problems from conic fitting to bundle adjustment. For this nuisance parameter problem, studies have been conducted in statistics for a long time, whereas they have hardly been studied in the computer vision community. We cast light on the methods developed in statistics for obtaining optimal estimates and explore the possibility of applying them to computer vision problems. In this paper we focus on the cases where data and nuisance parameters are linearly connected. As examples, optical flow estimation and affine structure and motion problems are considered. Through experiments, we show that the estimation accuracy is improved in several cases.

This paper deals with the autocalibration of a system that consists of a planar screen, multiple projectors, and a camera. In the system, either multiple projectors or a single moving projector projects patterns on a screen while a stationary camera placed in front of the screen takes images of the patterns. We treat the case in which the patterns that the projectors project toward space are assumed to be known (i.e., the projectors are calibrated), whereas poses of the projectors are unknown. Under these conditions, we consider the problem of estimating screen-to-camera homography from the images alone. This is intended for cases where there is no clue on the screen surface that enables direct estimation of the screen-to-camera homography. One application is a 6DOF input device; poses of a multibeam projector freely moving in space are computed from the images of beam spots on the screen. The primary contribution of the paper is theoretical results on the uniqueness of solutions and a noniterative algorithm for the problem. The effectiveness of the method is shown by experimental results on synthetic as well as on real images.

In this paper we present a system for tracking objects' 3D motions by using sampling algorithm. The system consists of three cameras and 1 PC. We modified the condensation algorithm [M.A. Isard et al., 1998] to track objects' 3D positions. The condensation algorithm is a kind of "factored sampling" and it can easily cope with multi-modal probability density of objects' positions. We track objects not in images but in 3D space. We use a condensation particle-set as a tracker and represent a position of a moving object by a center of tracker. Since we don't track directly in images, a great advantage of this method is not to need to deal with occlusions or objects' mutual interferences which happen in images.

We propose a binocular motion tracking system by reconstructing the 3D shape of moving objects. This system has a pair of active cameras mounted on the robot arm. The 3D shape is an important feature to track a moving object. To track the moving object, the cameras fixate a point on the object and reconstruct the 3D shape of the object around the fixation point of the two images with the principle of spatio-temporal differentiation analysis. The 3D shape is fed back for the control of the active cameras and the robot arm for motion tracking. The system realizes an accurate and stable tracking of the moving object.

Several imaging systems called catadioptric cameras have been developed that use a combination of lenses and mirrors to obtain wide fields of view. Geometric aspects have been well studied. This paper focuses on photometric aspects of catadioptric cameras. We discuss how geometric distortion of images of catadioptric cameras resulting from curvature of the mirror affects image irradiance. We show that image irradiance is determined only by the nature of lenses comprising the cameras and is independent of mirror shape. This is because an increase in the solid angle of space per single image pixel is canceled out by a decrease in the apparent solid angle of the lens aperture viewed from a scene point via the mirror. Thus, image irradiance of catadioptric cameras is not affected by geometric distortion due to mirror curvature. This is in contrast to cameras with ordinary lenses alone, especially fisheye lenses, in which image irradiance is actually affected by image distortion. Theoretical results as well as results of numerical simulations are presented.

This paper proposes a method to reconstruct and display 3D fundus (inner bottom of eye-ball) pattern from a set of multiple partial images of fundus. They were taken from several different view angles by shifting fundus camera. Since they are distorted by eye lens, a simple stereo technique does not work for the 3D reconstruction from any pair of images. Moreover, every fundus image's distortions differ from each other. In this method, we utilize the fact that a fundus has a spherical shape and that the image of sphere by the eye lens results in a quadratic surface. First, we determine each camera's viewing position and pose relative to the eye-ball and the shape of the quadratic surface by matching feature points in every fundus image on the quadratic image surface. Then, we identify the eye lens parameters so that the quadratic surface should be originated from a spherical fundus surface. As the final result, we obtain a wide area 3D fundus pattern reconstructed from the set of fundus images.

We propose a method to generate primitive curves from a set of given contour figures. The primitive curve is a partial shape which is commonly seen in given contours, and describes total characteristic shape of them. The proposed method, first, approximates every given contour figure by smoothing out only small details. The amount of smoothing is determined adaptively with the size of the details. In order to detect the details and their sizes, we use the scale-space analysis. Then, each approximated contour is split at corner points into curves. Each split curve describes partial shape of each given contour. Scale-space analysis helps to detect the global corner points. Next, we make clusters of those split curves based on the shape similarity. Finally, we generate primitive curves by obtaining average curves of each cluster.

This paper presents a new method for fine registration of two range images from different viewpoints that have been roughly registered. Our method takes into account the properties of the measurement error of the range images. The error distribution is different for each point of the image and is usually dependent on the viewing direction and the distance to the object surface. We find the best transformation of two range images to align each measured point and reconstruct 3D total object shape. The alignment is according to the distribution of the measurement errors, and the amount of the point position correction is according to its variance. The best transformation is selected by the evaluation of the facility of this correction of each measured point. The experiments showed that our method produced better results than the conventional ICP methods.

A method has been proposed for acquiring an omnidirectional image of a scene using a specular sphere (namely a mirror ball). The method takes the reflected image on the specular sphere located at a desired position in a scene by an ordinary camera. This paper discusses the relation between the reflected image of the scene and the radiance of the scene. Due to the reflection on the sphere, the final image on the camera has geometric distortion. There are imaging systems covering a wide angle by the lens system itself, e.g., a fish-eye lens. The image obtained by such lens systems has similar geometrical distortion. However, the effect of the distortion on the image brightness is different. We point out that the image distortion due to the lens system affects the image brightness, while that due to the reflection on the specular sphere does not. Most of the discussion can be applied to the methods using a curved mirror to obtain a wide angle image.

We describe a new design of a recognition system for a single image of indoor scene including complex occlusions. In our system the system first estimates the 3D structure of an object by fitting a 3D structure model to the image qualitatively. Next, by checking the supporting relation between objects, it eliminates object candidates that are impossible to exist and estimates actual objects from their parts in the image. Finally, the system then recognizes the objects that are consistent with each other. We implemented the system as a multi-agent-based image understanding system. This paper describes an outline of the system and results of recognition experiments.

This paper reports a visual system that recognizes 3D shapes of high speed moving objects. In this system, an active camera fixates a point on the moving object at the center of the image and tracks it. In this tracking, other object points than the fixation point move in the image field depending on their relative depths to the fixated point. Based on this fact, we are able to reconstruct 3D object shape from the tracking images. We developed a simple algorithm to realize this reconstruction for real time processing. We utilize the relation between spatial and temporal change of image with respect to the object depths. For our purpose, it is important to obtain object shape quickly even if it will be a rough one. We constructed a system that does not need complex and difficult image processing.

This paper deals with the image-based simultaneous motion control of robot-arms mounted with cameras and target objects. Given a goal image, the control achieves to move the robots to the position where the given goal images were taken and, at the same time, target objects to the same position as in the goal images. Their motions are determined to reduce the difference between the goal images and the images taken at their current positions. We use the "eigenspace method" to obtain compact representations of the images. To relate the image differences to the robot-arm and target object motions, we re-arrange the eigenspace so that the representations and their motions become linearly dependent. Experiments to control real robots are shown with good performances.

A method which detects the characteristic shapes and sizes of image structures is proposed. The method first blurs an image by Gaussian filters with various scales. Then, at every scale, principal curvatures of the image gray-level profile are calculated for every position. As the scale changes, the principal curvatures change. We detect the inherent shapes and sizes of the image structures by characterizing the type of the change of the principal curvatures. For the detection, we introduce the idea of principal curvature plane spanned by the two principal curvatures as its Cartesian coordinates.

The paper is concerned with the problem of identifying types of image singular points as either maxima, minima, or saddle points, especially for the case of unknown lighting direction. Singular points are defined as maximally bright points in the image whose corresponding surface normals coincide with the lighting direction. The identification of their type is the key to the global shape from shading problem, and it can be viewed as rough estimation of the object shape in itself. Using photometric invariants (e.g., extrema of the image grey level profile always lie on the parabolic curves of the object surface), it is shown that the two singular points which are connected by two steepest ascent curves starting from an image saddle point usually have different signs with each other. This constrains the possible combination of the types of the singular points in the global shape from shading problem.

An image understanding system for real world images, which has the ability to recognize various kinds of images, is proposed. We propose a multi-agent architecture to integrate object recognition modules for individual target objects. In our method, the recognition results by different agents are fused not only on the evaluations by each modules themselves but also on relations of object locations, sizes, etc. This is carried out autonomously between the agents concerned, and the most reliable result is selected after the arbitration between them. We implemented an experimental system on a parallel computer, and achieved recognition for both indoor and outdoor images.

Image-based visual servoing interprets image change directly to camera motion, and control the position and pose of a robot mounting a camera to reach the goal, where the camera obtains just the same image as a given goal image. Because its strategy is to simply minimize the differences between the goal image and the currently obtained image, trajectory of the robot motion cannot be estimated beforehand, and sometimes it results in largely inefficient motion. This paper points out that this inefficient motion is caused by interferences of translation and rotation of images. Then, we propose two algorithms to decouple them by using the homography and the epipolar condition held between the goal image and the current image, and to generate the optimal trajectory of the robot motion to reach the goal straightforwardly.

A general scheme to represent the relation between dynamic images and camera motion is presented, and its application to visual servoing proposed. For a specific object, the camera cannot obtain any arbitrary image, so that the possible combination of the camera pose and the obtained image should be constrained on a lower dimensional hyper surface within the product space of all the combinations. The visual servoing, for example, is interpreted as to find a path on this surface leading to a given goal image. Our approach is to analyse the properties of this surface and utilise its tangential property for visual servoing. We propose to use the principal component analysis and to represent images with a composition of small number of "eigen-images" by using the Karhunen-Loeve expansion. We describe that a normal vector of this surface is related to the so-called interaction matrix. We then present a dynamic estimation of the normal vectors to move the robot arm mounting a camera to a goal position where a given goal image will be obtained. Experimental results of visual servoing method show the feasibility and applicability of our proposed approach.

A new method for reconstructing three dimensional object from an endoscope image is presented. The proposed method uses image shading generated by a light source at the endoscope head. In this case, the light source is near to the object surface so that the image brightness depends on not only the surface gradients but also the distance from the light source to the surface point. To deal with this difficulty, we consider the imaging system of the endoscope as the system having a point light source at the projection center. The object surface is reconstructed by propagating equal-distance contours, spatial curves composed of points at an equal distance from the light source. The propagation is controlled by the image shading. We use the level-sets method for numerical computation. Experimental results for real medical images show feasibility of this method.

In this paper, we propose a new method for camera calibration that is an extension of the visual servoing technique. The basic objective of visual servoing is to control the camera motion so as to obtain the goal image which is given a priori. In this paper, we consider the case where intrinsic camera parameters are not known. First, we compose the goal image with initial guesses of the parameters. Then, in addition to the control of the camera motion, we dynamically modify the goal image according to the estimated intrinsic camera parameters. When the same image with the modified goal image is obtained, both the true intrinsic and extrinsic camera parameters are determined. We describe this new method with theoretical details and experiments using synthetic and real images.

Estimation of curvature from noisy sampled data is a fundamental problem in digital arc segmentation. The facet approach to curvature estimation involves least square fitting the observed data points to a parametric cubic polynomial and the calculation of the curvature analytically from the fitted parametric coefficients. Due to the fitting, there exists systematic error or bias between curvature which is calculated analytically from the parameterization of a circle and one which is calculated analytically based on the coefficients of the fitted cubic polynomial, even when the data are sampled from a noiseless circle. It is shown how to compensate this bias by estimating it with the coefficients of the fitted cubic polynomial, which gives more accurate curvature value. Small perturbations are introduced to the sampled data from a noiseless circle, and the authors analytically trace how the perturbation propagates through coefficients of the fitted polynomials and results in perturbation error of the curvature.>

Proposes a new method of active vision which recognizes the 3-D shape of objects without knowing camera motion parameters. The motion parameters are calculated from the optical flows and the depth of object points whose 3-D shape is already known. Then, using these calculated motion parameters and the optical flows, the 3-D position of unknown points are reconstructed, which, in turn, will be used as the known points in the next frame of image. These processes are iterated for a sequence of images to recognize the 3-D scene. In this method, the effects of quantization errors are overcome by two approaches. The errors of camera motion parameters are compensated by using a large number of points to calculate them. Then, the Kalman filtering method is applied to the sequence of images to reduce the 3-D position errors of each unknown point.>

Proposes a new application of Wu's (1978) mechanical theorem proving method for recognition of polyhedra in 3D space from the projection image. First, the authors set up a number of equations which express the vertices on plane segments, line segments, angles in 3D space and those on the image plane, and also the relations between the vertices in 3D space and those on the image plane. Next, they classify all the equations into two parts, a set of hypotheses and a conjecture. Then they obtain a pseudodivided remainder of the conjecture by Wu's method, which represents a relation of angles or a relation of lengths between the 3D space and its projected image. Also they show that by a stability analysis the remainder can be defined even in the case that vertices on the image plane are in unstable areas of hypotheses whose denumerators approach to zero, so that it cannot be defined by direct manipulations of the hypotheses and conjecture polynomials.>

A method for approximating contour figures with piecewise-linear polygons using a criterion function based on regularization theory is presented. In this method, it is possible to select the degree of fineness of the approximation to a given contour figure with a parameter in the criterion function, which represents a tradeoff between the fitness and the simplicity of the polygonal model. However, it is shown that, for a given figure, only a few types of stable models optimize the criterion with a variety of values of the parameter. This means that only a few types of polygons may be suitable approximations for representing the original characteristic features of the figure. This method derives such polygons automatically from the given figures. Thus, the approach shows potential as a powerful method for the analysis and interpretation of planar contour figures.>

Efficient image processing from a low level to a higher level on a PSM system is described. PSM is a multiprocessor system architecture with pipelined multiple-instruction multiple-data (MIMD) processors, shared memory, and a multistage interconnection network designed for high-speed parallel image processing. A parallel image processor, PSM-32, which is being constructed based on the PSM architecture, is discussed. To ensure total efficient instruction and data flows in the presence of the memory access delays commonly occurring on a multistage interconnection network machine, an architecture with a pipelined MIMD processor is proposed for the PSM system.>

A new approach to texture characterization and texture-based image partitioning is presented. In this approach the gray level of each pixel of an image is estimated from a weighted sum of gray levels of its neighbor pixels. The weight coefficients are determined so that the mean square estimation error is minimized. The obtained two-dimensional estimator characterizes the texture of the sample and can be used to discriminate other classes of textures. This texture characterization technique is applied to image partitioning, and two partitioning procedures are developed. Experimental results obtained by their application are also shown.