A brief review of the state-of-the-art in digital image processing is given. Wide-spread applications of digital image processing will require maximum computing power at cost less than that of the large-scale computers often used in image processing research. Increased sophistication in processing algorithms will also create a need for even more computing power. The potential for mini-computer and/or special-purpose computers to fill this need is discussed, and features of needed computer architecture are considered.

An image enhancement technique called "Noise Cheating" allows the detection of low contrast objects in a noisy background. This technique has been applied to imagery degraded by blur and by noise. The technique is reviewed in this paper, and the results of its application are compared to the results using Wiener filtering. Comparisons are made on both computer simulated and laboratory-generated imagery. The results indicate that subjectively preferable restorations are achieved by Wiener filtering when blur, rather than image noise, is the dominant degrading factor, while noise cheating produces preferable results when noise is predominant.

Taking into account the chemical and optical degrading factors as well as the granularity noise results in a subjectively reasonable mathematical model for the formation and recording of photographic images. This model represents highly nonlinear observations, making the subsequent restoration difficult. When images are scanned with very small apertures on a microdensitometer, the noise is so severe that conventional estimators do not perform well. In these cases detection schemes suited to individual degraded pictures are much more effective. When the noise is not so severe, an adaptive minimum mean square error filter can be applied. This filter explicitly includes the nonlinear image formation effects and does not require the assumption of stationary image statistics.

Spline functions, because of their highly desirable interpolating and approximating characteristics, are an interesting alternative to the conventional pulse approximation method in digital image modeling. For uniformly spaced knots, a class of spline functions called B-splines is used as a basis in a linear imaging system. A controllable smoothing criteria based on the local statistics and minimization of the second derivative is defined, and the corresponding filter is obtained for restoration of noisy blurred images.

Medical applications have vigorously stimulated image processing. Subjects range from sub-cellular entities to whole organs. End goals include enhanced objectivity, repeatability, throughput, and vali-dity.

A process is described for digitally reconstructing images of gamma-ray emitting organs recorded through an off-axis Fresnel zone plate aperture. This technique produces image cross sections for given depths which contain both quantitative and qualitative information about the source. The practicality of digital decoding is demonstrated experimentally by comparing the digital and optical reconstructions of images of a multi-plane gamma-ray source. Specifically, the multiplane source consists of numerals one, two and three located in three distinct planes at successive depths from the detector. The digital method of reconstruction has the following advantages over a method employing optical reconstruction. A quasi-real time system capable of recording and producing images can be assembled using components currently available. Quantitative data such as the source size and depth are readily determined. Digital image processing can be easily implemented to reduce the effect of artifacts and noise. Unlike the case using optical re-construction, the image depth dimension is not distorted in comparison with the source depth. Nonlinearity and film noise associated with the photographic process of obtaining a reduced transparency are avoided.

We present here a new restoring algorithm that, it is believed, puts edge images on a par with point images with regard to their ability to be enhanced. It is based on use of a "median-window filter." This is a mathematical window of length N, which, when placed on N consecutive image values, replaces the value at its mid-point position by the median of the N intensity values within the window. Used sequentially across an image, the filter tends to completely obliterate oscillations whose period is less than N while simultaneously passing unchanged any monotonically increasing or decreasing image regions (as occur at edges.) This is intrinsically a nonlinear effect. When cyclically used with any linear restoring algorithm, edge-gradient enhancements on the order of 5:1 over that in the image can frequently be obtained, depending on the noise level in the image data. The method is tested on computer-simulated imagery and a photographic image.

A space-variant or invariant point spread function of an imaging system is used to generate the grammian matrix from a continuous-discrete imaging model. If in) is a point in the continuous aperture of of the object plane and the i-th sample of the image array is given by gi = Is hi( )f(, )ddri (1) then the grammian matrix of the point spread function becomes [V] = s Toht(, (2a) where v. = ST h.(, )h..( (2b) The properties of [V] of interest are the singular values which define both the entropy and degrees of freedom of the imaging system. Using physical constraints on the point spread function, i. e. 0 < h. ( ) 1 (3a) N2 E) = 1 (3b) i= 1 1 we develop a set of experimental curves relating entropy and degrees of freedom. In addition a variable sampling procedure is hypothesized to increase the degrees of freedom for a fixed number of samples (Nx N= N2) to improve the data acquisition and processing efficiency and approach the fundamental limitations of the imaging system.

Coherent optical feedback systems always use a pair of tilted mirrors that physically separate the forward path and the feedback path, one of which is at an off-axis position. This paper introduces an on-axis configuration with two parallel mirrors. The application of the system to contrast enhancement and image restoration is presented.

The optical processor for a direction independent differential operation ∂/∂x +i∂/∂y is described and feasibility studies for filter fabrication are reported. The resulting intensity distribution of the filterfunction can be generated by superimposing periodic time dependent pulse functions which modulate a writing beam (flying spot, monitor). Hence the filter transmission can be registered on a photographic film or by real time processing on an electro-coherent optical converter. This kind of filter generation allows to change the filterparameters with high speed, controlled by computer. The application of this processor to medical and biological images will be demonstrated.

We are interested in making computer generated holographic spatial filters on a graphics device which can plot only a limited number of points (such as a storage-tube terminal). The Generalized Binary Computer Generated Hologram is an algorithm which makes efficient use of available plotting points, thus making it attractive for use with these limited plotters. In this paper we study the nature of the set of complex amplitudes one can code with this algorithm. Our main topic is amplitude quantization noise. We show that, since the quantization steps vary in size, the optimum signal normalization is not necessarily that which uses all the quantization steps. We analyze the amplitude quantization noise in several types of real-valued holograms to demonstrate this behavior. We give the results of a measurement of errors in dot size and dot position on a storage tube terminal, and relate this noise to our analysis of amplitude quantization noise.

An objective and automatic method for quality control in a production line has been investigated. The proposed technique is an optical correlation in which the dimensional information of a master piece is stored in a hologram. A real time signal, which is a measure of the similarity between the master and the tested piece is obtained by integrating the correlation distribution over a small area on a photo detector. The necessity of an accurate positionment and orientation of each piece, which would be essential for high precision control can be eliminated by scanning the detector area. Synthetic holograms were found particularly helpful to adapt the response curve to practical requirements (sensitivity, dynamic range, ...) and to enhance some critical features of the work piece. Simple examples show the possibility of detecting shape errors of a few microns (less than 1% of the dimensions of the piece under test).

An analytical model of the synthetic aperture radar system is outlined. This model describes the radar image as a spatial two-dimensional band-pass filtering of the radar scene reflectivity density. The offset of the pass-band along the range frequency axis determines the major wavelength and geometrical properties of the simulated radar image. Through the use of a Fourier optical system, the photographs of radar target models and an aerial scene were band-pass filtered. The resulting images exhibit the characteristics of radar imagery, including texture (fading) and image dependence on object orientation. Use of the model and optical processing to simulate radar imagery from aerial photographs is discussed.

When halftone screens are used to realize monotonic or non-monotonic nonlinear point transfer functions in a coherent optical system, the screens are usually composed of periodically repeated cells which are themselves monotonic in density. This is not necessary, and an algorithm for generating non-monotonic cells yielding a desired transfer function in the first diffraction order is described. In practice, the photographic operations are non-ideal and change the nonlinear characteristics from input to output. The effects of low film gamma and low film saturation density can be calculated, and, to some extent, compensated a priori.

Research activities in analogue image processing in Japan are reviewed according to the technique mainly used. Several recent achievements in optical Fourier analysis, preparation of spatial filters, and non-linear filtering as coherent filtering, and those in electro-optical processing as incoherent processing are introduced.

Orthogonalized components of images are provided by the association of digital procedures and pure optical processing, in order to achieve classifying mappings. In a first step preprocessed data are optically delivered - typically by sampling of Fourier spectra. They satisfy both orthonormal and dimensionally reduced description of the considered images, which have not to be entirely digitized. The feature extraction consists of computing the dominant eigenvectors of the data covariance matrix or the Fourier descriptors of differences between spectra. The data are classifyied in the reduced space defined by the dominant eigen-vectors or Fourier descriptors. Applications to handwriting recognition and clustering are presented, starting from series of complete pages.

In the United States and in many other parts of the world, there is a rapidly increasing need for information as to the amount and condition of such earth resources as timber, forage, soils, water, minerals and agricultural crops. Usually because of the vastness of the geographic areas which must be covered, the needed information is best obtained, not by direct observation on the ground, but through the analysis of photographs, thermographs and other forms of remote sensing imagery acquired from high-flying aircraft, and/or earth-orbiting spacecraft. The amount of useful information that can be obtained by the image analyst often is increased substantially if the imagery is first "enhanced" by such means as density slicing, color coding, improving the signal-to-noise ratio, and combining multiple images into a single composite. Some scientists advocate the use of multiple lantern slide projectors or other optical devices for this purpose. Others advocate the use of closed-circuit color television equipment or other electronic devices. A combination of optical and electronic devices, however, usually produces the greatest amount of useful information, especially when several multidate and/or multiband images of the same area are available, each capable of providing certain unique kinds of information. Based on representative examples, mainly of the authors' NASA-funded test sites in California, the use and limitations of various optical and electronic image-enhancement devices and techniques are illustrated.

Most image enhancement techniques are not suitable for real-time applications. This paper presents two contrast enhancement techniques that can work at TV rates with fairly simple hardware.

A hybrid optical-electronic method for the display of large variation phase objects is described. It displays a conventional image whose local irradiance (or density) is proportional to the phase of the object. The method requires a much simpler optical system than previously proposed methods.

An optical/video processing system is described together with applications to satellite and aerial survey imagery. Diffraction pattern sampling, spatial filtering and holographic filtering can be implemented. The optical system is of very high quality, with diffraction limited performance for LANDSAT format transparencies and negligible coherent noise. The use of CCTV equipment in both diffraction and image planes allows interactive processing to be carried out together with further simple non-linear operations, such as grey level slicing and contouring.

Descriptions of the structure of a picture or scene generally refer to objects or regions in the scene. Thus, to construct a description, it is generally necessary to segment the scene into meaningful parts. When the parts have gray levels (or colors) that lie in different ranges, this is easy to do by simple thresholding, or by edge detection using simple differencing operations. When the parts differ in texture, rather than in gray level, the thresholding and edge detection approaches can be generalized to work in a variety of cases; the basic approach involves preprocessing and averaging prior to the thresholding or differencing step. This approach is based on the assumption that textural differences between regions are generally associated with differences in the average values of some simple local property. Examples of segmenta-tions obtained by these methods will be given.

A review of activities in digital image processing in Japan is presented, with concen-tration upon image restoration and image synthesis. Effects of the experimental errors on the restored images are examined through computer simulation of Wiener filtering and an experimental result considering these effects is shown. An optimum filter to restore the degraded image due to blurring of the system and signal-dependent noise is obtained, based on the theory of linear least-squares filtering. Utility of the method of least-squares to suppress the noise amplification during restoration process will be demonstrated through on-line digital image restoration of the motion blurred image by use of a mini-computer system and restoration of diffraction-limited noisy image. Technique of digital image synthesis is applied to evaluate the image of a complex object formed by a partially coherent optical system.

We compare two methods of restoring images with linear spatially-varying degradations: the singular value decomputation method, and the projection iterative method. Our tentative conclusion is that: (1) they give restorations of comparable quality; (2) the projection iterative method requires less computation time.

This paper treats the restoration of images degraded by noise and spatially varying blur. It is shown that such restoration problems can be formulated as linear programming problems and solved by standard algorithms. The feasibility of this technique is demonstrated by two-dimensional computer simulations , and the results of Fourier-domain restoration and LP-restoration are compared.

Until recently, the maximum entropy (ME) restoring method required too much computer time to be implemented on two-dimensional pictures. Additionally, it was originally derived assuming specifically additive noise in the image, whereas in many cases Poisson noise is a more realistic model. In this paper we show how a ME method may be derived on the basis of maximum likelihood and Poisson statistics for the image data, along with "maximum ignorance" for the object statistics. Interestingly, the new object estimate retains the old form of e to a series, while the noise estimate is now of a multiplicative form, i.e., proportional to the signal image. Also, although the old approach required knowledge of a parameter B, the most negative noise value, the new approach does not require this input. The new ME algorithm was applied to two 23 x 33 data point images of Ganymede. These were acquired by the NASA Pioneer 10 mission. By programming the restoring algorithm with close to maximal efficiency with regard to speed, we were able to bring CDC 6400 computer time down to about 30 sec for each restoration. We also restored the two images linearly, so as to compare performance of the ME algorithm with a standard method. The usual resolution advantages of the ME approach are observed in the outputs.

A two dimensional diffractographic technique has been developed, the purpose of which is to determine exactly the displacement and profile changes of the test object as a function of time To illustrate this process we have mapped continuously until failure the profile of a cylindrical rock sample. The resulting diffraction patterns have been recorded on film and processed digitally. It is shown that under certain conditions the interpretation of the two dimensional patterns is a spatial Fourier transform in the small dimension, amplitude modulated by Fresnel diffraction of the large one. This interpretation results in efficient and simple digital processing using conventional interpolation and filtering techniqueso thus reconstructing the profile and time history of the event with a typical strain resolution of 10^-5.

A state-of-the-art survey of digital image coding techniques is presented. Performance analyses are given for pulse code modulation, statistical, frame replenishment, predictive, interpolative, and transform coding methods.

A restoration technique is derived that can simultaneously reduce the degrading effects of a digital image coding operation and mitigate the effects of channel errors that arise when the encoded information is transmitted. The technique optimally reduces these degradations with respect to a mean-square-error criterion and is applied entirely a posteriori to a received visual signal. The restoration is based upon four factors--the multidimensional probability density function of a typical undegraded image, parameters of the encoding operation, the structure of the channel and its error probabilities, and the received visual signal. The technique is applied to the restoration of DPCM coded images which have been transmitted over a binary symmetric channel. The restored images which result exhibit a decrease in mean-square error and a subjective improvement in visual quality.

One definition of image enhancement is - a process which causes selected components of an image to be made stronger with respect to other components. Since this definition involves a measure of strength, a space in which that measure can be made is implied. Such spaces must logically involve the human visual system and its image processing characteristics.

Sample spacing and quantization levels are usually chosen for digitizing images such that the eye should not see degradations due to either process. Sample spacing is chosen based on the resolution (or high frequency) limit of the eye and quantization is based on perception of low contrast differences at lower frequencies. This process results in about 8 bit/pixel, 20 pixel/mm digitization, but, being based on two different visual limits, the total number of bits is an overestimate of the information perceived by the eye. The visual MTF can be interpreted in terms of perceptible levels as a function of spatial frequency. We show by this interpretation that the total information perceived by the eye is much less than 8 bits times the number of pixels. We consider the classic halftone as an image coding process, yielding 1 bit/ pixel. This approach indicates that halftones approximate the proper distribution of levels as a function of spatial frequency; therefore we have a possible explanation of why halftone images retain most of the visual quality of the original.

The objective of this study was to investigate the effects of certain sensor parameters upon the ability to extract useful information from image data gathered by current and future earth-orbiting satellites. The basic method used was to select representative images; scan and digitize them; process the digital data to simulate the effects of presampling filters, instantaneous field of view (IFOV) size and shape, sampling rates, noise, and word length; record the processed data on film; have the film images evaluated by experienced photointerpreters; and draw conclusions from those evaluations. The study concluded that presampling filters are not required for the suppression of aliasing, and the choice between square and circular IFOV shapes is not important. Increased horizontal and vertical sampling rates produced an increase in apparent resolution. The work with low-contrast targets demonstrated a definite maximum in the tradeoff between IFOV size and signal-to-noise ratio. Image data quantization (linear) to six bits was determined to be sufficient, with lower radiometric resolution producing visible contouring, and higher resolution producing no observable improvement in image quality.

Visual interpretation of multispectral images can be facilitated by suitable representations in color space. Continuous transformation possibilities and their application-oriented choice are discussed.

Visual detection of complex patterns consisting of repeated stripes of random texture was studied. Such patterns are of interest because they are environmentally relevant and because they have a relatively simple description in terms of the two-dimensional Fourier spectrum. Visibility of the patterns predicted from signal-detection analysis of the Fourier spectrum gave a good fit to the empirical data, supporting the use of Fourier analysis in the study of complex two-dimensional pattern perception.

Techniques have been developed which allow nearly all phases of the image forming process for turbulence degraded images to be computer simulated. The simulation includes generation of turbulence de-graded wavefronts, the degrading point spread function, and the sensor properties. Pre detection compensation of the wavefront and post detection compensation of the image can likewise be simulated. These simulation techniques have been used to determine fundamental limits of pre detection and post detection processing. Results of the application of these techniques to sun-illuminated objects will be presented in this paper.

Techniques developed for the planetary exploration program are being applied by the Image Processing Laboratory of JPL to other astronomical images. Plates of the galactic cluster Stephans Quintet were scanned and digitized. Faint nebulosity was enhanced by removing foreground stars and subjecting the resulting image to a high pass filter. Exaggerated true color images were generated by color representation of the ratios of calibrated images taken in red and blue light. Partial compensation for atmospheric degradation was accomplished with a positionally dependent convolution kernel based upon a Wiener noise-additive model. The signal to noise of the kernel was allowed to vary as a function of the local standard deviation. Photographs of Saturn were digitized and processed in an effort to obtain more information about the D-ring region. Because of the low signal level, straightforward enhancement techniques were not sufficient to bring out possible structure in this region. By transformation to a polar coordinate image, summation techniques were able to increase the apparent signal to noise of radially symmetric brightness elements. Spectra from several planets were digitized in an effort to quantify possible spectral shift as a function of position in the image. Each spectrum scan line was cross-correlated with the central scan line. From the results of this cross-correlation, a most probable spectral line tilt angle was determined.

Residual errors in the wavefront from an active wavefront compensation device cause image degradation, especially for extended objects. Even if these errors are as small as one-sixth wave rms, the image degradation can be significant enough that post-processing of the resulting imagery is justified. To analyze the degradation present in this imagery, the characteristics of the image of a point source are found in terms of the statistics of the residual wavefront errors. The image of an extended object can be described in terms of the characteristics of the point image. In recording the imagery with a view to post-processing, certain requirements must be met by the recording device in order for the processing to be successful. The signal-to-noise ratio of the detection device, its resolution, and the integration time necessary to achieve these requirements are discussed. It is shown how criteria for these requirements can be treated in terms of the statistics of the residual wavefront errors, the size of the optics, and the source radiance. A method of post-processing of the imagery is suggested that is based on the recording of images at two different focal planes simultaneously.

The presence of atmospheric turbulence degrades the angular resolution attainable using conventional photographic methods with an astronomical telescope. Near diffraction-limit resolution has been obtained using statistical measurements from short exposure photographs by Labeyrie. A signal processing method for the A posteriori restoration of atmospherically degraded images is developed. The emphasis is on near "optimal" processing of the measurements so that the images are restored without enhancing the unwanted noise effects. Short exposure images are used to "freeze" the motion caused by atmospheric turbulence. Multiframe imagery is used to obtain first and second order statistics of the degraded images. The integral equations relating the measured statistics to the underlying object and atmospheric characteristics are derived. A multi-step process is developed for solving these integral equations. An estimate of the Cartesian product of the object with itself is obtained from the second order statistics using Fourier methods. An estimate of the object is then derived from an eigen expansion of the Cartesian product. This estimate is augmented by an estimate from the first order statistics. The performance of this restoration method is illustrated by simulation results.

The fields near radiating antennas are useful for evaluating the effects of dielectric housings or nearby metallic objects. This paper describes the determination and processing of fields produced by a small antenna in a metallic cone and by another, array antenna. The procedure was to first compute the complex-valued, rectangular components of the electric and magnetic fields near a radiating antenna from data measured on a spherical surface, with radius large enough to eliminate probe effects. Resolution was about half a wave-length, and speckle was pronounced at low intensities. The spectra of the reconstructed fields were computed, filtered, and slightly extended beyond the visible region. Resolution was changed slightly. Speckle amplitude was reduced, and an induced source near the cone tip was made more visible. The processed nearfields gave more accurate farfields then the original nearfields. The basis for the theory was verified by considering linear antennas. From assumed current distributions and farfields we showed the reconstruction is a convolution. This justified filtering. The assumed nearfields were exactly reconstructed by continuing the spectra. Filtering functions for the apertures were derived from theoretical cases and applied to the spectra computed from measured data.

From the measurements of intensity distribution across an incident source, and the spatial variation of the mean phase difference (= effective retardation) of the light, respectively, at point r1 with respect to the light at r2, the image of the source can be constructed. Our phase measurable optical interferometer') measures completely the interference effect of the form r12 (T) so that the complex coherence function 112(t) of the inci-dent light is obtainable.