In this paper, we propose a global image registration method using a sparse dictionary. For global image registration, template images are registered to a pregenerated image stored in a dictionary. Finding the closest image in the dictionary, we obtain a geometric transform between a template image and a reference image. To achieve robustly accurate registration, a large number of transformed images are prepared and stored in the dictionary. To reduce the spacial complexities of this image dictionary, we introduce a method to generate a new template image from a collection of images stored in the image dictionary. This generated template image allows us to achieve accurate image registration, even if the population of image dictionary is relatively small. To the generation of new entry in the dictionary, we use geometrical and topological properties of images in the neighbourhood of a template. This process is achieved using nearest neighbour method. Therefore, to reduce the temporal and spacial complexities of matching pairs in registration, we use a random projection to reduce the size of both template and reference images. Since the random projection approximately preserves topology of a metric space, we compute a matching process in a low-dimensional Euclidean space without significant loss of matching accuracy.

Super resolution is a technique to recover a high resolution image from a low resolution image. We develop a variational super resolution method for the subpixel accurate optical flow computation using variational optimisation. We combine variational super resolution and the variational optical flow computation for the super resolution optical flow computation.

In this paper, we present an algorithm for the hierarchical recognition of an environment using independent components of optical flow fields for the visual navigation of a mobile robot. For the computation of optical flow, the pyramid transform of an image sequence is used for the analysis of global and local motion. Our algorithm detects the planar region and obstacles in the image from optical flow fields at each layer in the pyramid. Therefore, our algorithm allows us to achieve both global perception and local perception for robot vision. We show experimental results for both test image sequences and real image sequences captured by a mobile robot. Furthermore, we show some aspects of this work from the viewpoint of information theory.

Introduction In this paper, we develop an algorithm for the detection of circles from an image captured by a monocular omnidirectional camera system. We assume that an image captured by an omnidirectional camera system is normalised to a spherical image, the image on the unit sphere. Using this geometrical property of the omnidirectional images, we introduce a method for marker-based positioning and navigation of autonomous mobile robots which mounts a monocular omnidirectional camera system. We first clarify the geometric properties of the spherical image of a circle marker placed on the ground plane, and we show that, for the detection of a plane from circle markers, we are required to capture at least two coplanar circle markers. We prove that the image of a circle on the spherical image is a fourth-order algebraic curve, which is the intersection of a sphere and an oblique elliptic cone. For the detection of marker images on the spherical images, we introduce a method for transforming the detection of this fourth-order algebraic curve to the detection of a spatial conic, which is quadric. Second, we develop a voting method for the extraction of images of planar circle markers on a spherical image, using the spatial-quadric detection strategy. Finally, using the assumption for the geometrical configuration of the camera system and the circle markers on the plane on which the robot moves, we derive a positioning algorithm. This positioning method for the robot mounting a monocular omnidirectional camera system allows us to navigate a robot using our circle-detection algorithm. We show some numerical examples both for synthetic and real images.

In this paper, we aim to develop an algorithm for featureless navigation of an autonomous robot using optical flow observed through a vision system mounted on a mobile robot. Furthermore, we show that this optical flow observed from a mobile robot for navigation of it is also used in the construction of environmental maps. Our algorithm first detects an area corresponding to the dominant plane from a sequence of images employing optical flow and, second, backprojects the dominant plane to the environment for the construction of the environmental map. Moreover, our algorithm estimates ego-motion of the mobile robot using projected optical flow. The planar area detection by our method does not require any physical assumptions concerning the robot motion of any camera calibration. Therefore, our algorithm allows obstacles to be detected without using any feature in the environment and any heuristics rule. We show the results of the construction of an environmental map using the mobile robot.

Symmetry of an object on a plane and in a space is an important geometric feature for biology, chemistry, and the understanding of human perception of figures. We propose a randomized method for the detection of symmetry in planar polygons and polyhedrons without assuming the predetermination of the centroids of the objects. Using a voting process, which is the main concept of the Hough transform in image processing, we transform the geometric computation for symmetry detection which is usually based on graph theory and combinatorial optimization, to the peak detection problem in a voting space in the context of the Hough transform. Our algorithm detects the centroid after detecting symmetry of an object for both planar and spatial objects.

In this paper, we solve the topological problem of isosurfaces generated by the marching cubes method using the approach of combinatorial topology. For each marching cube, we examine the connectivity of polyhedral configuration in the sense of combinatorial topology. For the cubes where the connectivities are not considered, we modify the polyhedral configurations with the connectivity and construct polyhedral isosurfaces with the correct topologies.

We introduce a method for the estimation of parameters of a tree from an orthographic view, and we define a distance measure of trees. First we introduce the iterative function systems for trees. Second, we show that a set of parameters of a tree can be determined from an orthographic view. Third, we define a metric of trees using the matrix norm of matrices of the iterative function systems which describe growth grammars of trees. Thus, we can discriminate trees from their single orthographic views. Our method provides possibility for studying reconstruction, recognition, and representation in the same context.

A tomographic reconstruction technique for a moving image produced by a rotating camera is presented. Projections of the moving image are degraded because of image movement. It is clarified that projection of a moving image are convolved by the kernel function defined by the angular velocity of an image. A reconstruction method is derived for a clear image from degraded projections. An estimation method of the angular velocity is also proposed.>

This paper proposes a new signal smoothing method which is applicable to any type of signal. This method is a direct extension of the Lanczos signal smoothing method for the truncated Fourier series. The method coincides with the classical Lanczos method if basis functions of a signal space are trigonometric functions. The proposed method is applied to the smoothing for the truncated series of the Hermite functions which are the eigenfunctions of the Fourier transformation.