Showing papers in "International Journal of Imaging Systems and Technology in 1990"

NOSER: An algorithm for solving the inverse conductivity problem

Abstract: The inverse conductivity problem is the mathematical problem that must be solved in order for electrical impedance tomography systems to be able to make images. Here we show how this inverse conductivity problem is related to a number of other inverse problem. We then explain the workings of an algorithm that we have used to make images from electrical impedance data measured on the boundary of a circle in two dimensions. This algorithm is based on the method of least squares. It takes one step of a Newton's method, using a constant conductivity as an initial guess. Most of the calculations can therefore be done analytically. The resulting code is named NOSER, for Newton's One-Step Error Reconstructor. It provides a reconstruction with 496 degrees of freedom. The code does not reproduce the conductivity accurately (unless it differs very little from a constant), but it yields useful images. This is illustrated by images reconstructed from numerical and experimental data, including data from a human chest.

Aspect graphs: An introduction and survey of recent results

Abstract: The study of the aspect graph of a three-dimensional object has recently become an active area of research in computer vision. The aspect graph provides a complete enumeration of all possible distinct views of an object, given a model for viewpoint space and a definition for “distinct.” This article presents a tutorial introduction to the aspect graph, surveys the current state of the art in algorithms for automatically constructing aspect graphs, and describes some possible applications of aspect graphs in computer vision and computer graphics.

Microwave tomography: From theory to practical imaging systems

Abstract: This paper deals with numerical processing techniques and practical applications of active microwave imaging. Different wavefront processing are presented, from an immediate use of measured projections to more complex procedures. Both spectral approaches to diffraction tomography and spatial iterative methods for generalized imaging are considered using multi-incidence of multifrequency techniques for 3D and/or 2D objects. The technology of the so-called microwave camera is presented for the fast recording of the scattered field with arrays of probes involving one- or two-dimensional sensors at a single frequency or in a broad-frequency band. Three different systems are depicted: a single-frequency linear sensor devoted to industrial applications (on-line transverse control of conveyed products), a single-frequency planar microwave camera for biomedical applications and research, and a broad-frequency linear microwave camera for civil engineering applications (detection of the rebars in reinforced concrete strctures). Microwave images obtained experimentally with the three systems are presented on configurations of practical interest for each field of application.

Visual language and software development environment for image processing

Abstract: The Khoros system integrates multiple user interface modes, code generators, instructional aids, data visualization, and information processing to produce a comprehensive image processing research tool. This system can easily be tailored to other application domains because the tools of the system can modify themselves as well as the system. This attribute is important in a system that is designed to be extensible and portable. The Khoros infrastructure consists of three major components: a high-level user interface specification, methods of software development embedded in a code generation tool set, and an interoperable data exchange format and algorithm library. These basic facilities have been used to build a set of applications for performing image processing research, algorithm development, and data visualization. One of the most powerful features of the system is its high-level abstract visual language. Khoros is a successful demonstration of how development programming, end-user applications programming, information processing, data display, instruction, documentation, and maintenance can be integrated to build a state-of-the-art image/data processing and visualization software environment.

Image estimation from scattered field data

Abstract: The purpose of this paper is to reappraise the linearizing methods frequently used to solve inverse scattering problems. We describe inversion algorithms based on the Born and the Rytov approximations and the nature of the distortions obtained in the reconstructions when using them. We present extensions of these methods, namely, the distorted-wave Born and the distorted-wave Rytov approximations, which incorporate prior knowledge about part of the scattering structure. A method for inverting scattered field data using these distorted-wave approximations is described, which retains the computational simplicity of the Born and the Rytov techniques. Some examples of their use with simulated and real data are given. A further extension of our distorted-wave formalism, which leads to improvements of the reconstructed image, is suggested. This entails a spectral estimation procedure also based on the incorporation of prior knowledge about the scatterer. This spectral estimation procedure can be useful for interpolation of scattered field data as well as resolution enhancement.

Nonlinearized approach to profile inversion

Abstract: A method for reconstructing the index of refraction of a bounded inhomogeneous object of known geometric configuration from measured far-field scattering data is presented. This work is an extension of recent results on the direct scattering problem wherein the governing domain integral equation was solved iteratively by a successive relaxation technique. The relaxation parameters were chosen to minimize the residual error at each step. Convergence of this process was established for indices of refraction much larger than required for convergence of the Born approximation. For the inverse problem, the same technique is applied, except is this case both the index of refraction and the field are unknown. Iterative solutions for both unknowns are postulated with two relaxation parameters at each step. They are determined by simultaneously minimizing the residual errors in satisfying the domain integral equation and matching the measured data. This procedure retains the nonlinear relation between the two unknowns. Numerical results are presented for the dielectric slab. The algorithm is shown to be effective in cases where the iterative solution of the direct problem is rapidly convergent and outperforms the Born-based approaches.

Local fractal geometric features for image segmentation

Abstract: In this article, features based on fractal geometry are used for segmentation of synthetic and natural scenes. Assuming a fractional Brownian motion model of image regions, we extract, at each pixel, small, one-variable “slices” in each of four directions from which we estimate two features: the fractal dimension and the intercept. While the fractal dimension has received most attention recently as a scale-invariant feature, we show that the intercept is related to the dimension and possesses even better discriminatory power for segmentation purposes when calculations are made on small, one variable windows. These parameters are studied as segmentation features on both composite images of synthetically generated fractional Brownian motion surfaces and on intensity images of natural scenes.

Resolution analysis of tomographic reconstruction of electron density profiles in the Ionosphere

Abstract: Traditionally, knowledge of the ionospheric electron density is obtained using Faraday rotation or differential Doppler techniques which measure total electron content in columns of the ionosphere. Conventional data processing can only image the electron density in the direction perpendicular to these columns, thereby forming one-dimensional images. Because this data is proportional to line integrals through the region of interest, tomographic techniques may be used to reconstruct two-dimensional electron density images. In this paper, the resolution limit of the image reconstruction process is analyzed in terms of limited-angle tomography.

Properties of essential matrices

Abstract: We use essential matrices to show that if the recovery of camera displacement from image correspondences is unstable, then a small perturbation yields an ambiguous set of correspondences. We show that there are at most three camera displacements compatible with a dense set of correspondences, and we show that the symmetric and the antisymmetric parts of an essential matrix are related.

Limited‐Angle inverse scattering problems and their applications for geophysical explorations

Abstract: The effect of the limited-angle measurements on the nonlinear inverse scattering problem is investigated. Because of incomplete information obtained in the limited-angle inverse problem, the linearized system matrix in the inversion procedure becomes more ill-conditioned compared to that of the conventional inverse scattering problem where the receivers are placed in a circle that completely surrounds the object. Consequently, the quality of the reconstruction is considerably reduced, and sometimes it is almost impossible to reconstruct the profile because of the sparsity of the measurement data. To overcome the above difficulty, a boosting procedure, which will help us to obtain the maximum amount of information for an arbitrary predefined experimental setup, has been proposed based on a physical viewpoint. The results of the computer simulations for well-to-well tomography demonstrate that by applying the boosting procedure the quality of the reconstruction and the speed of the convergence are improved significantly. Furthermore, for subsurface detection where both the transmitters and receivers are confined to the ground, the reconstruction becomes possible after applying the boosting procedure.

Inverse scattering, seismic traveltime tomography, and neural networks

Abstract: Inverse scattering methods for reconstructing sound-wave-speed structure in the dimensions have been shown to be equivalent to inverting line integrals when the scattered field is of sufficiently high frequency and the scattering is sufficiently weak. Seismic traveltime tomography uses first arrival traveltime data to invert for wave-speed structure. Of course, the traveltime is itself a line integral along a refracting ray path through the medium being probed. The similarity between these two inversion problems is discussed. One type of neural network-the Hopfield net-may be used to improve the traveltime inversion. We find that, by taking advantage of the general relationship between least-squares solution and generalized inverses, the neural networks approach eliminates the need for inverting singular or poorly conditioned matrices and therefore also eliminates the need for the damping term often used to regularize such inversions. This procedure produces reconstructions with fewer artifacts and faster convergence than those attained previously using damped least-squares methods.

Information contained in the motion field of lines and the cooperation between motion and stereo

Abstract: We investigate the relationships that exist between the three-dimensional structure and kinematics of a line moving rigidly in space and the two-dimensional structure and kinematics (motion field) of its image in one or two cameras We establish the fundamental equations that relate its three-dimensional motion to its observed image motion We show how this motion field can be estimated from a line-based token tracker We then assume that stereo matches have been established between image segments and show how the estimation of the motion field in the two images can be used to compute part of the kinematic screw of the corresponding 3D line The equations are linear and if several lines belong to the same object provide a very simple way to estimate the full kinematic screw of that object Finally, we show how the motion field can constrain the stereo matches by establishing necessary conditions that must be satisfied by the motion field of segments which are images of lines belonging to the same object Only part of this theory has been implemented yet This part uses Kalman filtering Several experimental results using synthetic and real data are presented

Nonrigid object motion and deformation estimation from three‐dimensional data

Abstract: This article presents a model-based approach for nonrigid object motion and deformation analysis from 3D data. The modeling primitives used in this research are the superquadrics, which have already been proven useful in describing a variety of natural and man-made objects. This model-based approach is not only in accordance with the human visual perception process but also able to decouple the large and unstructured nonrigid motion estimation system into simple and well structured subsystems. We develop a recursive algorithm for estimating global motion and object shape, which effectively incorporates a priori knowledge of the object into the estimation procedure and obtains a good estimate of the global motion and object shape even if the given 3D points are distributed bias. After compensating for the global motion of the object a tensor model of local deformation is introduced and a spherical harmonic surface-fitting algorithm is described such that the localized deformations of the object surface can be characterized. The local deformations of the object are then estimated using tensor-description-based analysis and parametrized by the directions and magnitudes of the extreme deformations in a localized surface element. To illustrate the potential of this model-based approach for nonrigid motion analysis, a real data example is presented using the proposed approach. This example involves estimating the left ventricle motion and deformations from a time sequence of 3D coordinates of coronary artery bifurcation points. The estimation results show the success of the model-based approach even when the given bifurcation points are distributed only on half of the left ventricle surface.

Superhigh image resolution for microwave imaging

Abstract: Algorithms for extrapolating the scattered field along the frequency direction and the azimuthal direction are developed and analyzed. Their effects on the image resolution for polar format processing and rectangular format processing are discussed. Simulation and experimental results show that extrapolation along the frequency direction does increase the range resolution. While extrapolation along the azimuthal direction improves the cross-range resolution for small angle imaging, it does not improve image resolution of complex-shaped objects for wide angle imaging. Both range and cross-range resolutions can be improved simultaneously for small angle imaging using rectangular format processing if the angular interval and the resolution cells are suitably chosen. A promising application for the algorithms developed is in microwave dynamic imaging.

Microwave imaging of moving objects

Abstract: Microwave images for objects in motion can be obtained with quality as good as those obtained in the stationary case if the signal waveforms, data acquisition systems, and image reconstruction algorithms are cleverly designed. The principle of imaging for objects in motion is to eliminate the gross Doppler effect of the echo signals and only reserve the differential Doppler information to reconstruct the image. Accordingly, requirements for parameters of the signal waveform are established. Two steps are involved in the image reconstruction algorithm: range alignment and phase compensation. Focused images of complex-shaped targets with simulated motion have been obtained experimentally.

Terrain analysis from curvature profiles

Abstract: This paper describes a new algorithm which uses Gaussian and mean curvature values of the terrain surface to extract feature points. These points are then used for recognition of particular subregions of the terrain and in estimating relative positions of these subregions in the terrain. The Gaussian and mean curvatures are chosen because they are invariant under rotation and translation. In the Gaussian and mean curvature images, the points of maximum and minimum curvatures are extracted and used for matching. The stability of the position of these points in the presence of noise and with resampling is investigated. The input for this algorithm is 3D digital terrain data. Curvature values are calculated from the data by fitting a quadratic surface over a square window and calculating directional derivatives of this surface. A method of surface fitting that is invariant to sensor-centered coordinate system transformation is suggested and implemented. Real terrain data are used in our experiments. The algorithm is tested with and without the presence of noise, and its performance is described.

Invariants under image perspective transformations: Theory and examples

Abstract: The objective of this work is to develop automated techniques for recognizing the same objects in images that differ in scale, tilt, and rotation. Such perspective transformations of images are produced when aerial images of the same scene are taken from different vantage points. The algebraic methods developed previously do not utilize the intensity values of the images, i.e., their pixel gray levels. Since image features essential for object recognition, such as edges and local image textures, may be described in terms of derivatives and integrals of the image intensity, it is necessary to investigate whether certain differential and integral operators applied to different perspective views of the same object are also invariant under the perspective transformation. We proceed to derive new differential operators and their corresponding integral invariants for curves and planar objects. We introduce a variant form of Fourier expansion specially adapted to the projective transformation. Extensions to three dimensions are discussed, as well as applications to other image formation models such as synthetic aperture radar (SAR). These results are steps toward a computational model for perspective-independent object recognition.

Imaging of earthquake sources

Abstract: Elastic waves, produced by temporally and spatially finite fault ruptures during earthquakes, propagate through the Earth. Recordings of these waves at the Earth's surface provide the data for reconstruction of the source properties, including location, spatial and temporal extents, and rupture velocities. A 2D finite-difference solution of the elastic wave equation is used to numerically extrapolate synthetic observations backward in time to create images of the energy release during an earthquake.

Imaging techniques for cable network structures

Abstract: Imaging techniques are presented for developing interactive computer display of cable network structures on a microcomputer such as the IBM PS/2® These structures create surfaces formed by an orthogonal mesh of cables and are primarily loaded normal to the surface A three-dimensional perspective representation of network structures is developed for fast drawing of cable structures on microcomputers

Knowledge-Based configuration of image segmentation processes

Abstract: The solution of an image interpretation problem using digital image analysis methods requires the configuration of an image analysis system to meet the requirements of this specific task the specific data material. This process includes the selection of the appropriate sequence of operators and the adaptation of the free parameters. A system has been developed and is described, which performs this configuration process automatically on the basis of a user-specified task definition, and general knowledge of an image analysis expert. The latter knowledge has been assessed, stored, and used by employing different paradigms of knowledge representation similar to expert systems.

Beam profiling by vibrating knife edge: Implications for near-field optical scanning microscopy

Abstract: We show theoretically and experimentally that beam profiling with a vibrating knife exhibits spatial resolution equal to the knife-edge excursion. We discuss the implications of this for near-field optical scanning microscopy, propose an extension of the method to two dimensions, and calculate impulse response, step response, and spatial frequency response.

Seismic imaging by shot record migration: A case study

Abstract: INTRODUCTION In echo-acoustical applications the medium under investigations is ‘illuminated’ from the surface with acoustic waves, The incident wave field is reflected at inhomogeneities in the medium. The reflected wave field is registered at the surface and yields information on the mechanical properties of the medium. Echo-acoustics is a fast growing field. Applications can be found in three main areas (Figure 1):

Estimating rigid‐body motion from three‐dimensional data without matching point correspondences

Abstract: The estimation of the three-dimensional (3-D) motion parameters of a rigid body is a very important subject in scene analysis and trajectory prediction. Motion parameters can be estimated from two sets of object feature points before and after the motion. In general, the matching correspondences of the feature points are available, and the motion parameters can be estimated by solving equations associated with the correspondences. In this paper, we present a new method for motion estimation from 3-D data without requiring the knowledge of matching correspondences. In the noise-free case, this approach identifies four candidates for the rotation matrix. The rotation matrix giving the best match of the point features can then be selected from the four candidates, and the matching correspondences are subsequently established. Possible ambiguities due to symmetrical feature points are also discussed in this paper. In the presence of noise, this method provides an initial estimate of the motion, which is then used to establish the matching correspondences. Subsequently, a new estimate of the motion parameters can be obtained with the established matching correspondence information. The effects of random zero-mean noise are studied. Simulated results are shown to demonstrate the effectiveness and accuracy of this technique.

Chromatic edge detection: Idealization and reality

Abstract: Chromatic edges are edges that correspond to large changes of red, green, and blue signals in unequal proportions. They are often, but not always, caused by changes in surface material. In this article, the theoretical and practical problems of chromatic edge detection are examined in detail.

Maximum entropy methods in coherent radar imaging

Abstract: There are some compelling reasons for viewing the problem of image reconstruction from noisy or incomplete data as one of statistical estimation, i.e., of choosing, from the infinity of images consistent with the data, that image which, in some statistical sense, is most plausible. Among these reasons are the soundness of the philosophical underpinning of the resulting image reconstruction process, a greater realization of the image resolution which is inherent in the data, and freedom from many of the artifacts encountered in commonly used ad hoc reconstruction schemes. One successful technique employing a principle of statistical inference is the maximum entropy technique, in which the data-consistent image with maximum configurational entropy is chosen. It is a computationally intensive approach involving a conjugate gradient search over a convex function of a vector in a space of dimensionality equal to the number of image pixels. This technique has been employed with success in situations where the data samples are modeled as linearly related to a real non-negative object. We investigate application of maximum entropy image reconstruction to the problem of high-resolution radar diagnostic imaging. The problem differs from others in which maximum entropy has been applied in that the object to be imaged is complex. Although the desired image is of the magnitude of the complex object and is thus real and non-negative, there is no linear relationship beween object magnitude and data. Rather, the data are linearly related to the complex object. Several earlier proposed methods for applying the maximum entropy principle to this problem are identified and analyzed. A method that more closely approximates true Bayesian estimation is proposed.

The nuclear magnetic resonance imaging of short t2 material using solid echoes

Abstract: The application of solid echoes to the nuclear magnetic resonance (NMR) imaging of short T2 materials is demonstrated by means of two-dimensional (19F) images. A closed-form, exact and generally applicable expression for solid echo imaging is derived and a procedure for on-the-fly data analysis given.

Contour reconstruction in diffraction tomography

Abstract: We address the problem of reconstructing the directional derivative and/or the Laplacian of an object function f characterizing a weakly inhomogeneous scatterer directly from data collected in a set of scattering experiments. We employ the Rytov approximation to model the complex phase of the scattered wavefields and show that a minimum-norm least-squares solution can be obtained from the well known filtered backpropagation algorithm of diffraction tomography with appropriate modification of the tomographic filters employed in the filtering step of the algorithm. The procedure is illustrated by a computer simulation study.

Feature classification techniques in model-based object recognition

Abstract: We describe a system that performs model-based recognition of the projections of generalized cylinders, and present new results on the final classification of the feature data. Two classification methods are proposed and compared. The first is a Bayesian technique that ranks the object space according to estimated conditional probability distributions. The second technique is a new feed-forward “neural” implementation that utilizes the back-propagation learning algorithm. The neural approach yields a 31.8% reduction in classification error for a database of twenty models relative to the Bayesian approach, although it does not provide an ordered ranking of the object space. The accuracy results of the neural approach represent a significant performance advance in feature-based recognition by perceptual organization without the use of depth information. Examples are provided using the results of a simple segmentation system applied to real image data.

Image motion estimation by clustering

Abstract: Image motion is estimated by matching feature “interest” points in different frames of video image sequences. The matching is based on local similarity of the displacement vectors. Clustering in the displacement vector space is used to determine the set of plausible match vectors. Subsequently, a similarity-based algorithm performs the actual matching. The feature points are computed using a multiple-filter image decomposition operator. The algorithm has been tested on synthetic as well as real video images. The novelty of the approach is that it handles multiple motions and performs motion segmentation.

Tomographic reconstruction of multiple‐layer specimens with the scanning tomographic acoustic microscope

Abstract: In this article we report the recent results of tomographic image reconstructions of multiple‐layer specimens at 100 MHz with the Scanning Tomographic Acoustic Microscope (STAM) system. The experiment utilizes 12 uniformly spaced projections and the results show significant improvement over the holographic images.