Image Geometric Transformation Research Articles

A stereo vision-based obstacle detecting method for mobile robot navigation

SUMMARYThis paper presents a computationally simple stereo vision method for detecting useful features of obstacles on the ground relevant to a mobile robot's navigation in an indoor environment. Enhanced time efficiency and reliability is achieved by introducing a geometrical image transformation and a frame-wise iterative edge image comparison scheme. The image transformation used in this paper relates each constant disparity value to an oblique plane at an elevation from the floor. The stereo correspondence method is devised by implementing a frame-wise AND operation based upon edge orientation and a subsequent pixel wise intensity correlation checking. This method is efficient in terms of computation time and capable of identifying isodisparity points, so that the height information of all the obstacle points above the floor can be determined. The obtained disparities are recorded on a local map to give complete obstacle features for mobile robot's path planning. Through a series of experiments performed under various environmental conditions, it is found that the proposed method can effectively be applied for locating obstacles of various heights in indoor navigation of mobile robots.

Efficient image representation using binary space partitioning trees

Images are traditionally represented by a set of picture elements, or pixels, defined over a discrete two or three-dimensional lattice. Pixel-based representation of images, however, requires a large amount of storage memory and processing power when performing complex image operations. Several image processing, computer vision, and computer graphics applications have resorted to employing more efficient representations of images. Tree-based representations, such as quadtrees and octrees, have received a great deal of attention by researchers in many imaging, vision and graphics areas. Binary Space Partitioning (BSP) trees have been used in computer graphics as an efficient representation of objects with planar faces (i.e., polyhedra). In this dissertation we propose using BSP trees as an efficient representation of images for image compression and geometric transformation applications. The BSP tree approach partitions the image domain, in a recursive manner, using arbitrarily oriented lines. The result of this partitioning is a set of convex (unpartitioned) regions, known as the BSP tree cells. In order to generate an efficient segmentation of the image, the number of cells has to be as small as possible such that the image signal within each cell is smooth. Therefore, the most critical aspect of a BSP tree construction method is the criterion used for selecting the partitioning lines. Here, we introduce a boundary-based approach and an optimization method for selecting the lines of a BSP tree. Under the former approach, the partitionings are based on the boundaries of the objects within the image under consideration. By using an optimization method, the lines are selected based on a Least-Square-Error (LSE) criterion. As demonstrated in this work, both the boundarybased and LSE methods provide efficient segmentation when applied to complex images. In addition, we develop a multiresolution algorithm for constructing a multiresolution BSP tree. In this case, the coarse (high frequency) information of the image is represented by the nodes close to the root node, and the fine (low frequency) details are contained within the nodes close to the leaves of the BSP tree. Based on these BSP tree construction methods, a coding system is proposed for compressing still images. A hierarchical method for coding the partitioning lines of the tree is developed. Meanwhile, the image signal within the unpartitioned regions (cells) is coded using low order polynomials (zero and first order). Moreover, an optimum pruning algorithm is used to reduce the number of bits required for encoding the BSP tree representation while minimizing distortion. By employing this BSP tree-based compression method on typical images (of human faces), high compression ratios in the range of 50-100 were obtained. Unlike other tree-based representations (e.g. quadtrees), and due to the flexible representation of the BSP tree approach (namely, the use of arbitrarily oriented lines), line-preserving transformations can be applied very efficiently to BSP trees without the need for reconstructing the tree under consideration. In here, we show the result of performing affine and perspective projection transformations on the BSP tree representation of images. These geometric manipulations were achieved by performing parametric transformations on the partitioning lines of the tree.

Avoidance of additional aliasing in multipass image rotations

The two-pass (or multipass) image geometric transformation algorithm is ideally suited to real-time, parallel implementation, but is known to introduce frequency aliasing during rotation, over and above any aliasing which may result from the usual one-pass algorithm. We develop a unified framework and theory that precisely explains this added-aliasing for many of the well-known multipass algorithms, and show that it is usually less than might be expected at first sight. In some cases, the aliasing occurs in nondestructive, and therefore, theoretically recoverable, forms. We also show that the aliasing is very easily reduced, or avoided altogether, while commenting that this problem should be considered as a special case of a general alias-avoidance strategy in geometric transformation. Finally, we include some examples of multipass image rotations which seem to confirm our predictions.

Restoration Over Fields of View Wider than the Isoplanatic Patch

This paper presents the results of a preliminary investigation into the problems in through-the-atmosphere image restoration which are more suited to data from a small telescope, i.e., one having a diameter of about 0.5 m, using techniques of image geometric transformation (and eventually, parallel image processing) in their solution. We have imaged bright objects, over fields of view which subtend angles greater than those in most “large” telescope experiments, i.e., between 40 and 100 arc sec, for example, where the isoplanatic assumptions are less valid.

Decomposition and parallel architecture for the geometric transformation of digital images

The decomposition and implementation of image geometric transformation algorithms is considered. An approach based upon parallel within-row and column operations on image data is developed along with a taskspecific (modular) hardware for implementation. The time and hardware (space) complexity of this approach is compared with alternative architectures. Future research directions are indicated.

Fast geometric transformation of scanner images for the operative tracking of surface currents in the ocean

A method for the fast transformation of initial images into preset map projections is suggested bases on the analysis of the NOAA satellite scanner images transmitted in the APT regime. The objective was to attain such an accuracy of the geographic reference which is necessary for the tracking of mesoscale phenomena in the ocean. Specific geometric distortions of the APT data are taken into consideration. The feasibility of the verification of the reference accuracy using the coastline contours bank is shown. As an example of the application of the above methods, an automatically plotted map of the surface current is supplied.

Comparison at high spatial frequencies of two-pass and one-pass geometric transformation algorithms

Two-pass image geometric transformation algorithms, in which an image is resampled first in one dimension, forming an intermediate image, then in the resulting orthogonal dimension, have many computational advantages over traditional, one-pass algorithms. For example, interpolation and anti-aliasing are easier to implement, being 1-dimensional operations; computer memory requirements are greatly reduced, with access to image data in external memory regularized; while pipelined parallel computation is greatly simplified. An apparent drawback of the two-pass algorithm which has tended to limit its universal adoption is a reported corruption at high spatial frequencies due to apparent undersampling, in certain cases, in the necessary intermediate image. This experimental study set out to resolve the question of possible corruption by computing the mean-square error when a sinusoidal grating test image is rotated, either by an efficient two-pass algorithm or by a traditional one-pass algorithm. It was found that the method used for interpolation has a major effect on the accuracy of the result, poorer methods accentuating differences between the two algorithms. A totally unexpected and fortuitous result is that, by using near-perfect interpolation (e.g., by the FFT), the two-pass algorithm is almost as accurate as one pleases, for rotations up to 45°, to very close to the Nyquist limit (as also is the one-pass algorithm, with near-perfect interpolation). For rotations of φ > 45°, the two-pass algorithm breaks down before the Nyquist limit, but these can be replaced by rotations of 90° - φ and transposition. Thus, the supposed drawback of the two-pass algorithm can be nullified by near-perfect interpolation, at least in the case of rotation, while a major bonus is the greater ease with which interpolation by the FFT may be implemented, in the two-pass case, leading to the possibility of highly faithful geometric transformation in practice, aided by the increasing availability of fast DSP and FFT microcircuits.

The existence of geometrical density-image transformations corresponding to object motion

Proofs are presented which show that under a few, easily realizable restrictions, there exists a geometrical image transformation that produces a change in a density image that is identical to the change that would be produced in the image by the motion of the objects being imaged. Both two and three-dimensional images of three-dimensional scenes are considered subject to restrictions that are appropriate to conventional radiography, computerized axial tomography, gamma-ray scintigraphy, and magnetic resonance imaging. There is no restriction on the motion of the objects being imaged except that they behave as a conserved medium. There is no restriction on formation of the image except that it include convolution with a differentiable point-function. The convolution can be the result of blurring inherent in the acquisition of the image or of explicit image processing. The results have special significance with regard to the problem of motion artifacts in digital subtraction angiography. The case of incompressible flow is considered and comparisons are made with problems in optical flow.

Geometrical image transformations as a means to improve the quality of high-energy pictures

The human perception of high-energy pictures may be considerably facilitated if one enhances the interesting features of the image by modifying its geometry. Several examples for such an improvement are shown for pictures from bubble chambers, for a drawing of a fixed target experiment and for a simulated image from a collider experiment.