Norman S. Kopeika

Direct method for restoration of motion-blurred images

We deal with the problem of restoration of images blurred by relative motion between the camera and the object of interest. This problem is common when the imaging system is in moving vehicles or held by human hands, and in robot vision. For correct restoration of the degraded image, it is useful to know the point-spread function (PSF) of the blurring system. We propose a straightforward method to restore motion-blurred images given only the blurred image itself. The method first identifies the PSF of the blur and then uses it to restore the blurred image. The blur identification here is based on the concept that image characteristics along the direction of motion are affected mostly by the blur and are different from the characteristics in other directions. By filtering the blurred image, we emphasize the PSF correlation properties at the expense of those of the original image. Experimental results for image restoration are presented for both synthetic and real motion blur.

Identification of blur parameters from motion blurred images

The problem of restoration of images blurred by relative motion between the camera and the object scene is important in a large number of applications. The solution proposed here identifies important parameters with which to characterize the point spread function (PSF) of the blur, given only the blurred image itself. This identification method is based on the concept that image characteristics along the direction of motion are different from the characteristics in other directions. Depending on the PSF shape, the homogeneity and the smoothness of the blurred image in the motion direction are greater than in other directions. Furthermore, in this direction correlation exists between the pixels forming the blur of the original unblurred objects. By filtering the blurred image we emphasize the PSF characteristics at the expense of the image characteristics. The method proposed here identifies the direction and the extent of the PSF of the blur and evaluates its shape which depends on the type of motion during the exposure. Correct identification of the PSF parameters permits fast high resolution restoration of the blurred image.

Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model

Turbulence properties of communication links (optical and microwave) in terms of log-amplitude variance are studied on the basis of a three-layer model of refractive index fluctuation spectrum in the free atmosphere. We suggest a model of turbulence spectra (Kolmogorov and non-Kolmogorov) changing with altitude on the basis of obtained experimental and theoretical data for turbulence profile in the troposphere and lower stratosphere.

Image resolution limits resulting from mechanical vibrations. Part IV: real-time numerical calculation of optical transfer functions and experimental verification

A method of calculating numerically the optical transfer function appropriate to any type of image motion and vibration, including random ones, has been developed. We compare the numerical calculation method to the experimental measurement; the close agreement justifies implementation in image restoration for blurring from any type of image motion. In addition, statistics regarding the limitation of resolution as a function of relative exposure time for low-frequency vibrations involving random blur are described. An analytical approximation to the probability density function for random blur has been obtained. This can be used for the determination of target acquisition probability. A comparison of image quality is presented for three different types of motion: linear, acceleration, and high-frequency vibration for the same blur radius. The parameter considered is the power spectrum of the picture.

Identification of blur parameters from motion-blurred images

A difficult problem in imaging systems is degradation of images caused by motion. This problem is common when the imaging system is in moving vehicles such as tanks or planes and even when the camera is held by human hands. For correct restoration of the degraded image we need to know the point spread function (PSF) of the blurring system. In this paper we propose a method to identify important parameters with which to characterize the PSF of the blur, given only the blurred image itself. A first step of this method has been suggested in a former paper where only the blur extent parameter was considered. The identification method here is based on the concept that image characteristics along the direction of motion are different than the characteristics in other directions. Depending on the PSF shape, the homogeneity and the smoothness of the blurred image in the motion direction are higher than in other directions. Furthermore, in the motion direction correlation exists between the pixels forming the blur of the original unblurred objects. The method proposed here identifies the direction and the extent of the PSF of the blur and evaluates its shape which depends on the type of motion during the exposure. Correct identification of the PSF parameters permits fast high resolution restoration of the blurred image.

Restoration of atmospherically blurred images according to weather-predicted atmospheric modulation transfer functions

Restoration for actual atmospherically blurred images is per- formed using an atmospheric Wiener filter that corrects simultaneously for both turbulence and aerosol blur by enhancing the image spectrum primarily at those high frequencies least affected by the jitter or random- ness in a turbulence modulation transfer function (MTF). The correction is based on weather-predicted rather than measured atmospheric MTFs. Both turbulence and aerosol MTFs are predicted using meteorological parameters measured with standard weather stations at the time and location where the image was recorded. A variety of weather conditions and seasons are considered. Past results have shown good correlation between measured and predicted atmospheric MTFs. Here, the pre- dicted MTFs are implemented in actual image restoration and quantita- tive analysis of the MTF improvement is presented. Corrections are shown also for turbulence blur alone, for aerosol blur alone, and for both together.

Background noise in optical communication systems

The origin and magnitude of the several kinds of background noise that perturb optical communication receivers are discussed, including background radiation sources viewed directly, radiation reflected from background objects, and radiation scattered by the atmosphere into the receiver field of view. An extensive bibliography on this topic is presented.

Forecasting optical turbulence strength on the basis of macroscale meteorology and aerosols: models and validation

Although optical turbulence is usually modeled with micrometeorology, it is shown here that this can be done successfully too with macrometeorology using meteorological parameters measured with standard weather stations and predicted in standard weather forecasts. This makes it possible to predict C2n according to weather forecast. Two experimentally derived models are developed-one for practical use and the other for scientific understanding. Correlation of prediction with measurement is on the order of 90% or more, over large dynamic ranges of meteorological parameters. One interesting aspect of these measurements is the statistical evidence that scintillations are affected by aerosols, particularly under conditions of high total aerosol cross-sectional area. Various explanations for effects of aerosols on C2n and its measurement are suggested. In addition, validity of the models was examined, and experimental comparisons in two very different climates and surface conditions are presented. High correlation is found in both cases between prediction and measurement.

Behavior of structure function of refraction coefficients in different turbulent fields

Deviations of experimental data on the effect of atmospheric turbulence on electromagnetic wave propagation from a standard Kolmogorov (or Obukhov-Kolmogorov) model are examined from the standpoint of the behavior of atmospheric passive scalar spectrum. It is pointed out that these deviations are not random and can be explained on the basis of todays ideas of passive scalar behavior in the atmosphere. This approach allows us to view electromagnetic radiation transfer in random media in a new way and to make the necessary steps for developing a generalized model of this phenomenon.

Comparison of direct blind deconvolution methods for motion-blurred images

Direct methods for restoration of images blurred by motion are analyzed and compared. The term direct means that the considered methods are performed in a one-step fashion without any iterative technique. The blurring point-spread function is assumed to be unknown, and therefore the image restoration process is called blind deconvolution. What is believed to be a new direct method, here called the whitening method, was recently developed. This method and other existing direct methods such as the homomorphic and the cepstral techniques are studied and compared for a variety of motion types. Various criteria such as quality of restoration, sensitivity to noise, and computation requirements are considered. It appears that the recently developed method shows some improvements over other older methods. The research presented here clarifies the differences among the direct methods and offers an experimental basis for choosing which blind deconvolution method to use. In addition, some improvements on the methods are suggested.