Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 1986"

Color constancy: a method for recovering surface spectral reflectance

Abstract: Human and machine visual sensing is enhanced when surface properties of objects in scenes, including color, can be reliably estimated despite changes in the ambient lighting conditions. We describe a computational method for estimating surface spectral reflectance when the spectral power distribution of the ambient light is not known.

Evaluation of linear models of surface spectral reflectance with small numbers of parameters

Abstract: Recent computational models of color vision demonstrate that it is possible to achieve exact color constancy over a limited range of lights and surfaces described by linear models. The success of these computational models hinges on whether any sizable range of surface spectral reflectances can be described by a linear model with about three parameters. In the first part of this paper, I analyze two large sets of empirical surface spectral reflectances and examine three conjectures concerning constraints on surface reflectance: that empirical surface reflectances fall within a linear model with a small number of parameters, that empirical surface reflectances fall within a linear model composed of band-limited functions with a small number of parameters, and that the shape of the spectral-sensitivity curves of human vision enhance the fit between empirical surface reflectances and a linear model. I conclude that the first and second conjectures hold for the two sets of spectral reflectances analyzed but that the number of parameters required to model the spectral reflectances is five to seven, not three. A reanalysis of the empirical data that takes human visual sensitivity into account gives more promising results. The linear models derived provide excellent fits to the data with as few as three or four parameters, confirming the third conjecture. The results suggest that constraints on possible surface-reflectance functions and the "filtering" properties of the shapes of the spectral-sensitivity curves of photoreceptors can both contribute to color constancy. In the last part of the paper I derive the relation between the number of photoreceptor classes present in vision and the "filtering" properties of each class. The results of this analysis reverse a conclusion reached by Barlow: the "filtering" properties of human photoreceptors are consistent with a trichromatic visual system that is color constant.

Rigorous coupled-wave analysis of metallic surface-relief gratings

Abstract: A rigorous coupled-wave analysis for metallic surface-relief gratings is presented. This approach allows an arbitrary complex permittivity to be used for the material and thus avoids the infinite conductivity (perfect-conductor) approximation. Both TE and TM polarizations and arbitrary angles of incidence are treated. Diffraction characteristics for rectangular-groove gold gratings with equal groove and ridge widths are presented for free-space wavelengths of 0.5, 1.0 and 10.0 μm for all diffracted orders as a function of period, groove depth, polarization, and angle of incidence. Results include the following: (1) TM-polarization diffraction characteristics vary more rapidly than do those for TE polarization, (2) 95% first-order diffraction efficiency occurs for TM polarization at 10.0 μm, (3) 50% absorption of incident power occurs at 0.5 μm, and (5) the perfect-conductor approximation is not valid for TM polarization at any of the wavelengths and is not valid for TE polarization at 0.5 μm.

Phase-retrieval stagnation problems and solutions

Abstract: The iterative Fourier-transform algorithm has been demonstrated to be a practical method for reconstructing an object from the modulus of its Fourier transform (i.e., solving the problem of recovering phase from a single intensity measurement). In some circumstances the algorithm may stagnate. New methods are described that allow the algorithm to overcome three different modes of stagnation: those characterized by (1) twin images, (2) stripes, and (3) truncation of the image by the support constraint. Curious properties of Fourier transforms of images are also described: the zero reversal for the striped images and the relationship between the zero lines of the real and imaginary parts of the Fourier transform. A detailed description of the reconstruction method is given to aid those employing the iterative transform algorithm.

Analysis of the retinex theory of color vision.

Abstract: If color appearance is to be a useful feature in identifying an object, then color appearance must remain roughly constant when the object is viewed in different contexts. People maintain approximate color constancy despite variation in the color of nearby objects and despite variation in the spectral power distribution of the ambient light. Land's retinex algorithm is a model of human color constancy. We analyze the retinex algorithm and discuss its general properties. We show that the algorithm is too sensitive to changes in the color of nearby objects to serve as an adequate model of human color constancy.

Digital holographic interference-phase measurement using the Fourier-transform method

Abstract: A method for accurate phase determination in holographic interferometry using a one- or two-dimensional Fourier transform is described. The method calculates the interference phase pointwise, even between fringe extrema, and thus has advantages over conventional fringe-finding and -tracking methods. Only one interference pattern may be used, although the use of two patterns reconstructed with a mutual phase shift permits an easier phase unwrapping and determination of nonmonotonic fringe-order variations. Additionally, the method offers a means for filtering out disturbances such as speckle noise and background variations.

Simultaneous color constancy.

Abstract: Observers matched patches (simulated Munsell papers) in two simultaneously presented computer-controlled displays, a standard array presented under 6500-K illumination and a test array under 4000 or 10,000 K. Adaptation to the test illuminants was limited. The adjusted patch was surrounded by a single color (annulus display) or by many colors (Mondrian display). Observers either matched hue and saturation or made surface-color (paper) matches in which the subject was asked to make the test patch look as if it were cut from the same piece of paper as the standard patch. For two of the three subjects, the paper matches were approximately color constant. The hue-saturation matches showed little color constancy. Moreover, the illumination difference between the two displays was always visible. Our data show that simultaneous mechanisms alone (e.g., simultaneous color contrast) alter hues and saturations too little to produce hue constancy.

Mechanisms of color constancy.

Abstract: We develop a model of how the visual system finds the colors of objects that have unknown shapes and positions. The model relies on mechanisms of light adaptation, coupled with eye movements, to recover three descriptors of surface reflectance that are represented in the signals of an achromatic mechanism and two color-opponent mechanisms. These descriptors are transformed to yield estimates of hue, the dimension of surface color that is independent of object shape and viewing geometry.

Minimum-variance synthetic discriminant functions

Abstract: The conventional synthetic discriminant functions (SDF’s) determine a filter matched to a linear combination of the available training images such that the resulting cross-correlation output is constant for all training images. We remove the constraint that the filter must be matched to a linear combination of training images and consider a general solution. This general solution is, however, still a linear combination of modified training images. We investigate the effects of noise in input training images and prove that the conventional SDF’s provide minimum output variance when the input noise is white. We provide the design equations for minimum-variance synthetic discriminant functions (MVSDF’s) when the input noise is colored. General expressions are also provided to characterize the loss of optimality when conventional SDF’s are used instead of optimal MVSDF’s.

Method for computing the scene-illuminant chromaticity from specular highlights

Abstract: The perception of an unchanging surface color under different illuminations requires the computation of the scene-illuminant color either directly or indirectly. A possible source for the computation is the specular highlight of the surface reflection. Some issues related to color constancy are discussed, and a theory for computing the scene-illuminant chromaticity from specular highlight is described. An interesting result of the theory is that in an ideal situation, two surfaces of different colors will be sufficient for the computation.

Application of the Wigner distribution function to partially coherent light

Abstract: The paper presents a review of the Wigner distribution function (WDF) and of some of its applications to optical problems, especially in the field of partial coherence. The WDF describes a signal in space and in spatial frequency simultaneously and can be considered the local spatial-frequency spectrum of the signal. Although derived in terms of Fourier optics, the description of an optical signal by means of its WDF closely resembles the ray concept in geometrical optics; the WDF thus presents a link between partial coherence and radiometry. Properties of the WDF and its propagation through linear optical systems are considered; again, the description of systems by WDF’s can be interpreted directly in geometric-optical terms. Some examples are included to show how the WDF can be applied to practical problems that arise in the field of partial coherence.

Visual localization: age and practice.

Abstract: Older people seem to be highly susceptible to the distracting effects of irrelevant or interfering visual stimuli, We studied this susceptibility using visual displays in which observers had to localize the position of a face. When a face appeared in isolation, observers of all ages did equally well; when distracting stimuli surrounded the face, older observers alone performed poorly. Brief periods of practice produce substantial and long-lasting improvement in performance.

Experiments on pattern recognition using invariant Fourier-Mellin descriptors.

Abstract: Image descriptors based on the circular-Fourier-radial-Mellin transform are used for position-, rotation-, scale-, and intensity-invariant multiclass pattern recognition. The orders of the radial moments and of the circular harmonics are chosen to obtain an efficient image description. The first-order radial moments of three circular harmonics are sufficient to obtain a satisfactory recognition performance. The influence of additive noise is investigated. Experimental results are shown.

Formal connections between lightness algorithms.

Abstract: The computational problem underlying color vision is to recover the invariant surface-spectral-reflectance properties of an object. Lightness algorithms, which recover an approximation to surface reflectance in independent wavelength channels, have been proposed as one method to compute color. This paper clarifies and formalizes the lightness problem by proposing a new formulation of the intensity equation on which lightness algorithms are based and by identifying and discussing two basic subproblems of lightness and color computation: spatial decomposition and spectral normalization of the intensity signal. Several lightness algorithms are reviewed, and a new extension (the multiple-scales algorithm) of one of them is proposed. The main computational result is that each of the lightness algorithms may be derived from a single mathematical formula, under different conditions, which, in turn, imply limitations for the implementation of lightness algorithms by man or machine. In particular, the algorithms share certain limitations on their implementation that follow from the physical constraints imposed on the statement of the problem and the boundary conditions applied in its solution.

Window of visibility: a psychophysical theory of fidelity in time-sampled visual motion displays

Abstract: Many visual displays, such as movies and television, rely on sampling in the time domain. We derive the spatiotemporal-frequency spectra for some simple moving images and illustrate how these spectra are altered by sampling in the time domain. We construct a simple model of the human perceiver that predicts the critical sample rate required to render sampled and continuous moving images indistinguishable. The rate is shown to depend on the spatial and the temporal acuity of the observer and on the velocity and spatial-frequency content of the image. Several predictions of this model are tested and confirmed. The model is offered as an explanation of many of the phenomena known as apparent motion. Finally, the implications of the model for computer-generated imagery are discussed.

Information capacity and resolution in an optical system

Abstract: The concept of invariance of information capacity is discussed and applied to the resolution of an optical system. Methods of obtaining superresolution in microscopy are discussed, and scanning microscopy has many distinct advantages for such applications.

Statistical properties of dynamic speckles

Abstract: The statistical properties of dynamic speckles produced by a moving diffuse object were reviewed by providing the space–time correlation function and the power spectrum of speckle-intensity fluctuation for five combined cases of both the optical configuration and the illumination light. In the optical configuration, three kinds of geometry (free-space, single-lens, and double-lens) were taken, and three kinds of illumination light (a Gaussian beam, a plane-wave beam, and a Gaussian Schell-model beam) were used. Consequently, it was shown that the cross-correlation function and the power spectrum are both Gaussian under some assumptions. From the dynamic properties, two types of speckle motion, boiling and translation, were also evaluated for various conditions of object motion, optical configuration, and illumination light.

Modal estimation of a wave front from difference measurements using the discrete Fourier transform

Abstract: It is shown that a wave front, or in general any scalar two-dimensional function, can be reconstructed from its discrete differences by a simple multiplicative filtering operation in the spatial-frequency domain by using complex exponentials as basis functions in a modal expansion. Various difference-sampling geometries are analyzed. The difference data are assumed to be corrupted by random, additive noise of zero mean. The derived algorithms yield unbiased reconstructions for finite data arrays. The error propagation from the noise on the difference data to the reconstructed wave fronts is minimal in a least-squares sense. The spatial distribution of the reconstruction error over the array and the dependence of the mean reconstruction error on the array size are determined. The algorithms are computationally efficient, noniterative, and suitable for large arrays since the required number of mathematical operations for a reconstruction is approximately proportional to the number of data points if fast-Fourier-transform algorithms are employed.

Distribution of light at and near the focus of high-numerical-aperture objectives

Abstract: Classical diffraction theory is used to investigate the effects of high numerical aperture on the focusing of coherent light. By expanding the diffracted beam in plane waves, we show that the lens action can be expressed as a succession of three Fourier transforms. Furthermore, polarization effects are included in the model in a natural way. Some numerical results of the theory are also presented.

Complex argument Hermite–Gaussian and Laguerre–Gaussian beams

Abstract: Hermite–Gaussian and Laguerre–Gaussian beams with complex arguments of the type introduced by Siegman [ J. Opt. Soc. Am.63, 1093 ( 1973)] are shown to arise naturally in correction terms of a perturbation expansion whose leading term is the fundamental paraxial Gaussian beam. Additionally, they can all be expressed as derivatives of the fundamental Gaussian beam and as paraxial limits of multipole complex-source point solutions of the reduced-wave equation.

Reflection and refraction at the surface of a chiral medium: comparison of gyrotropic constitutive relations invariant or noninvariant under a duality transformation

Abstract: Fresnel amplitudes for specular reflection and refraction at the surface of an isotropic, intrinsically nonmagnetic chiral medium are derived for sets of constitutive relations that are invariant or noninvariant under a duality transformation of the electromagnetic fields. The invariant set leads to a differential reflection curve of incident left and right circularly polarized light that is null at normal incidence and peaks beyond Brewster’s angle; the noninvariant set leads to maximum differential reflection in the vicinity of normal incidence and extends over a wide range of incident angles. Both sets lead to effectively equivalent descriptions of standard optical rotation and circular dichroism.

Heuristic analysis of von Kries color constancy.

Abstract: The properties of constancy models based on the proportionality rule of von Kries are examined in a series of simplified examples. It is found that the breadth of receptor-sensitivity functions causes metamerism, thwarting color constancy. Overlap of these functions limits the accuracy of von Kries adaptation for a more subtle reason: it causes nonzero off-diagonal elements in the transformation matrix relating object reflectance to receptor stimulations. Such off-diagonal elements make von Kries adaptation an inexact color-constancy scheme, even when the illuminant is restricted to prevent metamerism.

New look at Bloch's law for contrast.

Abstract: It has been commonly reported that the temporal integration of grating contrast proceeds more slowly as spatial frequency is increased. Such results have been based on the critical duration for sensitivity to contrast pulses varying in duration, but the analyses have not assumed full integration at short durations and have neglected the effects of probability summation over time. To take such effects into account, we discuss a class of analytical models based on nonlinear temporal integration. On the assumption that the temporal impulse response of the visual system determines contrast integration over time, we develop both a high-threshold model and a signal-detection approach involving multiple and independent nonlinear signal detectors with a time-limited integration span. The redefined critical durations predicted by the models and verified by the data are about 35 msec and vary by no more than 10 msec across spatial frequency. This variation is entirely attributable to a change in the strength of inhibition with spatial frequency, and the analysis implies that the excitatory component is constant at all spatial frequencies, contrary to previous accounts.

Ambient illumination and the determination of material changes

Abstract: The task of distinguishing material changes from shadow boundaries in chromatic images is discussed. Although there have been previous attempts at providing solutions to this problem, the assumptions that were adopted were too restrictive. Using a simple reflection model, we show that the ambient illumination cannot be assumed to have the same spectral characteristics as the incident illumination, since it may lead to the classification of shadow boundaries as material changes. In such cases, we show that it is necessary to take into account the spectral properties of the ambient illumination in order to develop a technique that is more robust and stable than previous techniques. This technique uses a biologically motivated model of color vision and, in particular, a set of chromatic-opponent and double-opponent center-surround operators. We apply this technique to simulated test patterns as well as to a chromatic image. It is shown that, given some knowledge about the strength of the ambient illumination, this method provides a better classification of shadow boundaries and material changes.

Nonspecular phenomena in beam fields reflected by multilayered media

Abstract: Past studies have shown that beams reflected by a single dielectric interface exhibit lateral and focal shifts under total-reflection conditions or angular shifts if a partial reflection regime is maintained. We investigate these effects for Gaussian beams incident upon multilayered media by using an analysis that treats the three beam-shifting phenomena in a unified manner. This approach reveals a novel fourth effect that manifests itself as an expansion or a reduction of the beam waist. All the four nonspecular phenomena are evaluated for typical layered configurations, and simple approximate relations are derived. The results show that the reflected beam fields may be considerably different from those predicted by geometrical optics if incidence occurs at an angle around which the reflectance function varies rapidly.

Superresolving filters in confocally scanned imaging systems

Abstract: The limitations of superresolving filters in imaging systems are investigated. The constraints on such filters in the nonscanning imaging mode are discussed. The possible advantages of such filters in confocal scanning imaging are highlighted. It is shown theoretically and verified experimentally that simply designed complex-amplitude filters can be used effectively to double the exit pupil of a confocal imaging system and thus improve resolution. Superresolution can be achieved with acceptable energy losses and manufacturing tolerances.

New theory of partial coherence in the space-frequency domain. Part II: Steady-state fields and higher-order correlations

Abstract: In Part I of this investigation [ WolfE., J. Opt. Soc. Am.72. 343 ( 1982)] new representations were introduced for the cross-spectral density of a steady-state source of any state of coherence. The central concept in that formulation was the notion of a coherent source mode (a natural mode of oscillation). In the present paper the theory is developed further and new representations are obtained for the cross-spectral densities of all orders, both of the source and of the field that the source generates. These representations involve only the previously introduced coherent source modes and the moments of certain random coefficients that characterize the statistical properties of the source. The results provide a new mathematical framework for analyzing coherence properties of all orders of stationary sources and of stationary fields. Some potential applications of the theory are mentioned.

Gabor representation and aperture theory

Abstract: The analytical properties and computational implications of the Gabor representation are investigated within the context of aperture theory. The radiation field in the pertinent half-space is represented by a discrete set of linearly shifted and spatially rotated elementary beams that fall into two distinct categories, the propagating (characterized by real rotation angles) and evanescent beams. The representation may be considered a generalization in the sense that both the classical plane wave and Kirchhoff’s spatial-convolution forms are directly recoverable as limiting cases. The choice of a specific window function [w(x)] and the corresponding characteristic width (L) are, expectedly, cardinal decisions affecting the analytical complexity and the convergence rate of the Gabor series. The significant spectral compression achievable by an appropriate selection of w(x) and L is demonstrated numerically, and simple selection guidelines are derived. Two specific window functions possessing opposite characteristics are considered, the uniformly pulsed and the Gaussian distributions. These are studied analytically and numerically, highlighting several outstanding advantages of the latter. Consequently, the primary attention is focused on Gaussian elementary beams in their paraxial and their far-field estimates. Although the main effort is devoted to aperture analysis, demonstrating the advantages and limitations of the proposed approach, reference is also made to its potential when applied to aperture-synthesis and spatial-filtering problems. The quantitative effects of basic filtering in the discrete Gabor space are depicted.

Origins of linear and nonlinear recursive restoration algorithms

Abstract: Linear and nonlinear image restoration methods have been studied in depth but have always been treated separately. In this paper several well-known linear and nonlinear restoration methods are written as recursive algorithms, and some new recursive algorithms are developed. The nonlinear restoration algorithms are based on the assumption that the noise is either a Poisson or a Gaussian process. The linear algorithms are shown to be related to the nonlinear methods through the partial derivative, with respect to the object, of a Poisson or a Gaussian likelihood function. A table of results is given, along with applications to real imagery.