Showing papers by "Alan C. Bovik published in 1988"

On detecting edges in speckle imagery

Abstract: Methods for detecting sustained intensity changes in images corrupted by speckle are analyzed. The problem is complicated by the nature of the speckle, which is characterized by a high degree of correlation and (approximately multiplicative) signal dependence. These characteristics make the automated extraction of edges in speckle very difficult for applications requiring the location and identifications of objects (e.g., synthetic aperture radar). In particular, the Laplacian-of-a-Gaussian (LoG) edge detector for this problem is analyzed. While the LoG is found to be effective for detecting meaningful edges, use of the LoG also gives rise to numerous extraneous edges having no physical correlate. To alleviate these effects, a ratio-of-averages edge detector is used in conjunction with the LoG. The combined scheme is found to be much more effective than either of the individual edge detectors. Actual SEASAT synthetic aperture radar (SAR) images are used to demonstrate the effectiveness of each technique. >

Adaptive trimmed mean filters for image restoration

Abstract: An adaptive smoothing filter is proposed for reducing noise in digital signals of any dimensionality. The adaptive procedure is based on the selection of an appropriate inner or outer trimmed mean filter according to local measurements of the tail behavior (impulsivity) of the noise process. The set of trimmed means used provides robustness against a wide range of noise possibilities ranging from very shallow tailed to very heavy tailed. A Monte Carlo analysis using a family of generalized exponential distributions supports the choice of the trimmed mean selected for measured values of an impulsivity statistic. The assumption underlying the definition of the filter is that the signal to be filtered is locally smoothly varying, and that the noise process is uncorrelated and derives from an unknown, unimodal symmetric distribution. For image-processing applications, a second statistic is used to mark the location of abrupt intensity changes, or edges; in the vicinity of an edge, the trend-preserving median filter is used. Since the impulsivity and edge statistics used in defining the adaptive filter are both functions of order statistics, the extra computation required for their calculation is minimal. Examples are provided of the filter as applied to images corrupted by a variety of noises. >

Digital reconstruction of three-dimensional serially sectioned optical images

Abstract: The nature of out-of-focus noise is analyzed and linear filtering approaches are demonstrated for minimizing its effect. The analysis is based on concepts of geometrical optics, and takes into account the passage of light through the object. The object is assumed to be nondiffractive and to have low contrast. These assumptions, although not usually met in practice, are not overly restrictive. Experience shows that even dark, diffractive objects show substantial improvement after filtering. Sample images of a pollen grain and a rat pancreas islet are used to demonstrate the efficacy of the technique. >

The missing cone problem and low-pass distortion in optical serial sectioning microscopy

Abstract: In optical serial sectioning, the 3-D structure of a microscopic specimen is observed by incrementing the focusing plane of a light microscope through the specimen. If the depth of field of the microscope is infinitesimal, the image obtained from each focusing plane is an in-focus slice of the optical density of the specimen. The authors show that the finite aperture of any practical microscope inevitably results in the loss of a biconic region of frequencies in the 3-D Fourier spectrum of the optical density, oriented in the direction of the optical axis. Thus, the resolution along this axis is severely reduced. Outside the missing cone of frequencies, the spectrum is distorted by a strong low-pass effect. A closed form expression is obtained for the overall distortion function using principles of geometric optics, and by assuming that the absorption of the specimen is linear and nondiffractive. Methods for restoring the 3-D images obtained through optical serial sectioning are considered, and several examples are provided. >

Missing Cone Of Frequencies And Low-Pass Distortion In Three-Dimensional Microscopic Images

Abstract: Optical serial sectioning is a technique by which the 3-D structure of a microscopic specimen is observed by incrementing the plane of focus of a light microscope through the specimen. Ideally, if the depth of field of the microscope is sufficiently shallow, the image at each focusing plane is an in-focus rendition of the specimen containing structural information from that plane only. Unfortunately, the limited aperture of any practical light microscope makes this unfeasible; at each focusing plane, the 2-D image obtained contains unfocused information from planes above and below the focusing plane. In this paper, the nature of the distortion of the light microscope is analyzed using principles of geometric optics, where it is assumed that the absorption of the specimen is linear and nondiffractive. It is found that the limited aperture of the microscope results in the loss of a biconic region of frequencies in the Fourier spectrum of the specimen along the optical axis, resulting in a severe loss of resolution along the axis; outside the missing cone of frequencies, the spectrum is distorted by a strong low-pass effect, further reducing the resolution of the image observed at each plane of focus.

Optimal order statistic filters with coefficient censoring

Abstract: Order statistic (OS) filters are noted for their robust properties for smoothing or estimating signals immersed in noise. The effect of coefficient censoring on the smoothing performance of OS filters is considered. Coefficient censoring can be effected either by adding zero coefficients to an existing filter, or by computing the optimal (MSE) censored coefficients for a set filter span. The second possibility is considered. In both cases, censoring can yield increased robustness and improved edge retention. OS filters in common use which can be interpreted as censored OS filters include the median filter, rank-order filters, and the trimmed mean filters. While optimal censored filters are generally suboptimal relative to optimal uncensored filters, they often yield superior performance for signals containing edge discontinuities. >

Improving visible-surface reconstruction

Abstract: Techniques are described for improving the speed and accuracy of iterative visible-surface reconstruction algorithms. In particular, the importance of obtaining accurate early information is emphasized, both in the initial surface approximation and in the early localization of surface discontinuities. The first of these goals is attained using a simple technique known as constraint expansion, which yields a good initial approximation while accounting for detected discontinuities. The second goal is attained by using the locations of the image intensity edges as a guide in locating potential discontinuities. >

Relating analog and digital order statistic filters

Abstract: Recent efforts have been directed towards the development of analog versions of the digital median filter. Here, the concept is extended to the more general rank-order and order statistic (OS) filters. By identifying analog and digital signals that are in some sense equivalent, such that the outputs of analog and digital OS filters applied to equivalent analog and digital signals are also equivalent, the properties of discrete-time and continuous-time OS filters can be related, making possible a richer mathematical framework for analysis and design of rank-order and OS filters in both domains. While some theory for digital rank-order and OS filters has been developed, the definition of the analog versions is nontrivial. Suitable definitions are offered for analog versions of the rank-order and OS filters, and a formalism is developed for relating the analog and digital filters. >

On the generation of random numbers from heavy-tailed distributions

Abstract: A method is described for the generation of random numbers using a modification of the rejection technique, which is useful when the inverse of the underlying probability distribution function is inexpressable or is expensive to compute. However, the rejection technique can also be expensive if the underlying distribution has heavy tails. The method proposed reduces this expense by computing the random variate from a subinterval of the range space which is chosen randomly. The method is illustrated for a set of parameterized density functions. This technique has proven to be effective for investigating the robust smoothing properties of a class of nonlinear digital filters by Monte Carlo simulation. >

Determining the 3-D structure of serial-sectioned microscopic objects: analysis and limitations

Abstract: The limited aperture of an optical system has the effect of zeroing a biconic portion of the 3-D spectrum of the specimen oriented along the optical axis; elsewhere, the spectrum is distorted by a low-pass function The planar resolution of the serial sections can be improved by inverse filtering; however, the missing information cannot be recovered directly In the absence of these effects, the sections can be processed to delineate significant changes in image intensity, or edges The edges can be aggregated using morphology and other region correction procedures from which a 3-D representation of the specimen can be generated >

Computing shape changes in SOLANUM tuberosa slices viewed through a stereo microscope

Abstract: A research effort is described to compute the 3-D shape parameters of biological objects observed through a stereoscope light microscope. An algorithm for computing global shape parameters from microscopic images is presented. Algorithms for computation of global shape parameters from images obtained through a stereo light microscope are developed and applied to characterize the shape parameters of small piece of potato slices when exposed to hyperosmotic sugar solutions. >

Robust detection of object boundaries in Weibull radar imagery

Abstract: Radar image speckle is often modeled as having a negative-exponential, or more generally, gamma distribution. However, studies of noise in coherent radar systems suggest that the first-order statistics may be more accurately modeled using the two-parameter Weibull density, the parameters of which vary with the surface being imaged. Techniques for detecting object boundaries in noisy radar images are proposed and compared. The images are assumed to be coarsely sampled, so that the (multiplicative) radar noise can be modeled as uncorrelated and identically distributed. Edge detection in multiplicative noise is effectively accomplished by thresholding ratios of locally adjacent image estimates. The efficacies of edge detectors defined as ratios of single order statistics, ratios of averages and ratios of best linear unbiased estimators (BLUEs) are compared. The comparisons are based on computed error probabilities as the Weibull parameters are varied. Several example images are provided for empirical comparison as well. >

In weibull radar imagery

Abstract: Radar image speckle is often modeled as having a negative-exponential, or more generally, gamma distribution. However, studies of noise in coherent radar systems suggest that the first-order statistics may be more accurately modeled using the two-parameter Weibull density , f(x) = uxp-lexp(axP), the parameters of which vary with the surface being imaged. In this paper, techniques for detecting object boundaries in noisy radar images are proposed and compared. The images are assumed to be coarsely sampled, so that the (multiplicative) radar noise can be modeled as uncorrelated and identically distributed. Edge detection in multiplicative noise is effectively accomplished by thresholding ratios of locally adjacent image estimates. In this paper, the efficacies of edge detectors defined as ratios of single order statistics, ratios of averages and ratios of best linear unbiased estimators (BLUES) are compared. The comparisons are based on computed error probabilities as the Weibull parameters are varied. Several example images are provided for empirical comparison as well.

D5a.3 RELATING ANALOG AND DIGITAL ORDER STATISTIC FILTERS

Abstract: Recent efforts have been directed towards the development of analog versions of the digital median filter. In this paper, the concept is extended to the more general rank- order and order sfatistic (OS) filters. By identifying analog and digital signals that are in some sense "equivalent," such that the outputs of analog and digital OS filters applied to "equivalent" analog and digital signals are also "equivalent." the properties of discrete-time and continuous-time OS filters can be related, making possible a richer mathematical framework for the analyis and design of rank-order and OS filters in both domains. While some theory for digital rank-order and OS filters has been developed, the definition of the analog versions is nontrivial. Here, suitable definitions are offered for analog versions of the rank-order and OS filters, and a formalism is developed for relating the analog and digital filters.

Acknowledgement of priority spectral properties of moving L-estimates of independent data

Abstract: Professor H.A. David has kindly pointed out that an expression for the joint probability distribution function of order statistics from overlapping samples, similar to equation (3) in our paper, had been previously given in the reference cited below. This expression could also have been used in deriving the results obtained later in our paper.