Maximum likelihood for target location in the presence of substitutive noise.

We consider the optimal likelihood algorithm for the estimation of a target location when the images are corrupted by substitutive noise. We show the relationship between the optimal algorithm and the sliced orthogonal nonlinear generalized (SONG) correlation. The SONG correlation is based on the application of a linear correlation to corresponding binary slices of both the input scene and the reference object with appropriate weight factors. For a particular case, we show that the optimal strategy is a function of only the number of pixels for which the gray values in the noisy image match the ones of the reference image when the substitutive noise is uniformly distributed. This is exactly what a particular definition of the SONG correlation does.

Statistical techniques for target detection in polarization diversity images.

We address the problem of target detection in active polarimetric images. This technique, which has the appealing feature of revealing contrasts that do not appear in conventional intensity images, provides several images of the same scene. However, because of the presence of nonhomogeneity in the reflected intensity, it is preferable to perform target detection on the orthogonal-state contrast image, which is a measure of the degree of polarization of the reflected light when the coherency matrix is diagonal. We show that one can determine a simple nonlinear transformation of this orthogonal-state contrast image that leads to additive noise, and we then propose a simple and efficient technique for detecting targets in these images.

Minimal-complexity segmentation with a polygonal snake adapted to different optical noise models.

Polygonal active contours (snakes) have been used with success for target segmentation and tracking. We propose to adapt a technique based on the minimum description length principle to estimate the complexity (proportional to the number of nodes) of the polygon used for the segmentation. We demonstrate that, provided that an up-and-down multiresolution strategy is implemented, it is possible to estimate efficiently this number of nodes without a priori knowledge and with a fast algorithm, leading to a segmentation criterion without free parameters. We also show that, for polygonal-shaped objects, this new technique leads to better results than using a simple regularization strategy based on the smoothness of the contour.

Detection of multiregion objects embedded in nonoverlapping noise.

The concept of a statistical filter for objects that comprise several regions is introduced. The process is optimal in the presence of nonoverlapping noise for the target and may perform independently of variations in the mean value in every region. The basic performance of the filter is described, and a comparison with other types of processing is made.

Optical snake-based segmentation processor with a shadow-casting incoherent correlator.

What is believed to be the first incoherent snake-based optoelectronic processor that is able to segment an object in a real image is described. The process, based on active contours (snakes), consists of correlating adaptive binary references with the scene image. The proposed optical implementation of algorithms that are already operational numerically opens attractive possibilities for faster processing. Furthermore, this experiment has yielded a new, versatile application for optical processors.

Edge location in SAR images: performance of the likelihood ratio filter and accuracy improvement with an active contour approach.

The likelihood ratio edge detector is an efficient filter for the segmentation of synthetic aperture radar (SAR) images. We show that this filter provides biased location of the edge, when the window does not have the same orientation as the edge. A phenomenological model is proposed to characterize this bias. We then introduce an efficient technique to refine edge location: the statistical active contour. The combination of these two methods permits to achieve accurate and regularized edge location.

Statistical algorithms for target detection in coherent active polarimetric images.

We address the problem of small-target detection with a polarimetric imager that provides orthogonal state contrast images. Such active systems allow one to measure the degree of polarization of the light backscattered by purely depolarizing isotropic materials. To be independent of the spatial nonuniformities of the illumination beam, small-target detection on the orthogonal state contrast image must be performed without using the image of backscattered intensity. We thus propose and develop a simple and efficient target detection algorithm based on a nonlinear pointwise transformation of the orthogonal state contrast image followed by a maximum-likelihood algorithm optimal for additive Gaussian perturbations. We demonstrate the efficiency of this suboptimal technique in comparison with the optimal one, which, however, assumes a priori knowledge about the scene that is not available in practice. We illustrate the performance of this approach on both simulated and real polarimetric images.

Deconvolution of several versions of a scene perturbed by different defocus blurs: influence of kernel diameters on restoration quality and on robustness to kernel estimation.

It has been shown many times that using different versions of a scene perturbed with different blurs improved the quality of a restored image compared with using a single blurred image. We focus on large defocus blurs, and we first consider a case in which two different blurring kernels are used. We analyze with numerical simulations the influence of the relative diameter of both kernels on the quality of restoration. We then quantitatively evaluate how the two-kernel approach improves the robustness of restoration to a difference between the kernels used in designing the algorithm and the actual kernels that have perturbed the image. We finally show that using three different kernels may not improve the restoration performance compared with the two-kernel approach but still improves the robustness to kernel estimation.

Snake-based method for the segmentation of objects in multichannel images degraded by speckle.

We recently proposed a new approach for the segmentation of speckled images based on active contours (snakes) [e.g., Opt. Commun. 137, 382 (1997)]. We propose an extension of this approach to multichannel data. Two solutions are compared based on hypotheses on the possible mean intensity variation between the channels. Each solution is optimal for a certain class of input images, but one solution shows better or equivalent performance for both input image classes. This result opens new perspectives for the segmentation of multichannel images with the snake-based approach.

Improved robustness of target location in nonhomogeneous backgrounds by use of the maximum-likelihood ratio test location algorithm.

We address the problem of localizing small targets with random gray levels that appear in random background clutter. We consider the recently proposed maximum-likelihood ratio test (MLRT) algorithm, which scans the observed scene with an estimation window in which the local statistics are estimated. In the presence of a spatially homogeneous background, we show that if the estimation window is a few times larger than the target itself, the MLRT is quasi-equivalent to the optimal maximum-likelihood (ML) algorithm, which uses the whole scene for estimating the background statistics. The MLRT thus constitutes an efficient alternative to the ML algorithm and is more robust in dealing with spatially nonhomogeneous clutter since it utilizes a small estimation window.

Unified statistically independent region processor for deterministic and fluctuating targets in nonoverlapping background.

Recently, new approaches for location of a target in nonoverlapping noise, which are optimal in the maximum-likelihood sense, have been proposed. In particular, different methods for deterministic or fluctuating targets have been developed. We propose a unified and optimal processor for a target with either known or unknown gray levels. We demonstrate the efficiency and robustness of this method in comparison with previously developed processors.

Improvement in robustness of the statistically independent region snake-based segmentation method of target-shape tracking.

We propose a technique to increase the robustness of a snake-based segmentation method originally introduced to track the shape of a target with random white Gaussian intensity upon a random white Gaussian background. Because these statistical conditions are not always fulfilled with optronic images, we describe two improvements that increase the field of application of this approach. We first show that regularized whitening preprocessing allows one to apply the original method successfully for a target with a correlated texture upon a correlated background. We then introduce a simple multiscale approach that increases the robustness of the segmentation against the initialization of the snake (i.e., the initial shape used for the segmentation). These results provide a robust and practical method for determination of the reference image for correlation techniques.

Optimal X(2) filtering method and application to targets and backgrounds with random correlated gray levels.

We describe a pattern recognition processor based on a new optimal x(2) filtering method that is designed to localize a target with unknown gray levels appearing on a random background. This processor consists of preprocessing of the analyzed image followed by correlations with binary masks.

Optimal correlation at low photon levels: study for astronomical images.

We consider the problem of determining the unknown translation between two images. We analyze the performance of the optimal technique in presence of Poisson noise in comparison with the classical linear intercorrelation method, and we apply this approach to astronomical images.

Detection theory approach to multichannel pattern location.

We propose and assess new algorithms for detecting and locating an object in multichannel images. These algorithms are optimal for additive Gaussian noise and maximize the likelihood of the observed images. We consider two cases, in which the illumination of the target and the variance of the noise in each channel are either known or unknown. We show that in the latter case the algorithm provides accurate estimates of variance and luminance. These algorithms can be viewed as postprocessed versions of the correlation of a reference with the scene image in each channel.

Multicriteria optimality for iterative encoding of computer-generated holograms.

We propose a new multicriteria method for the determination of computer-generated holograms (CGH's). For this purpose, the direct binary search (DBS) algorithm for computing CGH's has been modified to converge on a new error function that defines the optimal trade-off among different criteria. This approach allows us to control the trade-off between the amplitude error and the diffraction efficiency and to provide a rigorous figure of merit. Comparisons among different encoding methods show that the best results are obtained with a modified version of the DBS method combined with the iterative Fourier transform algorithm.

Fast algorithm for texture discrimination by use of a separable orthonormal decomposition of the co-occurrence matrix.

We consider the problem of texture analysis with a fast algorithm. For that purpose we propose to use coefficients of the decomposition of co-occurrence matrices on an orthonormal and separable basis. We apply this method for texture discrimination, and we thus demonstrate with some examples its efficiency in terms of rapidity, discrimination performance, and robustness. We compare this method with classifiers that use a Fisher linear discrimination on features a priori defined in the co-occurrence matrices.

Restoration of images degraded by atmospheric turbulence by a least-squares method and a Markov process.

We present a two-step deconvolution method for restoring images degraded by atmospheric turbulence. The first step is linear space-invariant filtering, and the second step is a nonhomogeneous Markov process. This nonhomogeneous method preserves the discontinuities of the original image better than the homogeneous method does.

Optimal detection of a target with random gray levels on a spatially disjoint background noise.

We describe a pattern-recognition processor that is optimal for detection and location of a target with white Gaussian random gray levels on a white random spatially disjoint background. We show that this algorithm consists of correlations of the silhouette of the reference object with preprocessed versions of the scene image. This result can provide a theoretical basis for pattern-recognition techniques that use nonlinear preprocessing of images before correlation.

Optimal snake-based segmentation of a random luminance target on a spatially disjoint background.

We describe a segmentation processor that is optimal for tracking the shape of a target with random white Gaussian intensity appearing on a random white Gaussian spatially disjoint background. This algorithm, based on an active contours model (snakes), consists of correlations of binary references with preprocessed versions of the scene image. This result can provide a practical method to adapt the reference image to correlation techniques.