Nonlinear restoration of noisy images

The restoration of images degraded by an additive white noise is performed by nonlinearly filtering a noisy image. The standard Wiener approach to this problem is modified to take into account the edge information of the image. Various filters of increasing complexity are derived. Experimental results are shown and compared to the standard Wiener filter results and other earlier attempts involving nonstationary filters.     

Optimal structuring elements for the morphological patternrestoration of binary images

In this paper, we derive the optimal structuring elements of morphological filters in image restoration. The expected pattern transformation of random sets is presented. An estimation theory framework for random sets is subsequently proposed. This framework is based on the least mean difference (LMD) estimator. The LMD estimator is defined to minimize the cardinality of the expected pattern transformation of the set-difference of the parameter and the estimate. Several important results for the determination of the LMD estimator are derived. The LMD structuring elements of morphological filters in image restoration are finally derived     

Linear granulometric moments of noisy binary images

The first and second moments of the granulometric pattern spectrum are expressed for a random binary image that is formed either as the union of a deterministic signal with random point noise or as the set subtraction of random point noise from a deterministic signal. The granulometry is generated by a vertical (or horizontal) linear structuring element, and there are no constraints placed on the structure of the uncorrupted signal. Because the noise is random, the image on which the granulometry is run is random. Hence the pattern spectrum is a random function with random-variable moments. For both the union and subtractive cases, expressions are found for the expectation of the pattern-spectrum mean and variance, where the expectation is relative to the noise intensity. In each case a recursive formula is obtained for the key expression.     

Hole-spectrum representation and model-based optimal morphological restoration of binary images degraded by subtractive noise

A shape-based image representation grounded on the distribution of holes within an image is developed, and the manner in which this representation can be used to design optimal morphological filters to restore images suffering from subtractive-noise degradation is investigated. The image and noise models are predicated on the existence of some class of shape primitives into which both image and noise can be decomposed (relative to union), and this decomposition is developed within the framework of a general algebraic paradigm for component-based filtering that does not depend on the linear-space structure typically used in spectral representations. Both deterministic and nondeterministic models are considered, and in each case the necessary model constraints are fully explored. Moreover, the type of filters that are naturally compatible with the image-noise models are analyzed. Specifically, optimal morphological filter design is studied in terms of the shape-based hole spectrum (as linear filter design is studied in terms of the frequency spectrum). Various forms of a design algorithm are discussed, the particulars depending on a symmetric-difference error analysis yielding approximate error expressions in terms of the spectral decomposition and the geometry of the underlying shape primitives. Finally, the statistical estimation procedures required for practical implementation of the entire spectrum-filter paradigm are explained.     

Point reconstruction from noisy images

In this paper we treat the problem of determining optimally (in the least-squares sense) the 3D coordinates of a point, given its noisy images formed by any number of cameras of known geometry. The optimality criterion is determined by the covariance matrices associated with the images of the point. The covariance matrices are not restricted to be positive definite but are allowed to be singular. Thus, image points constrained to lie along straight lines can be handled as well. Estimation of the covariance of the reconstructed point is provided.The often appearing two-camera stereo case is treated in detail. It is shown in this case that, under reasonable conditions, the main step of the reconstruction reduces to finding the unique zero of a sixth degree polynomial in the interval (0, 1).The authors are listed in random order.     

Two pyramid machine algorithms for edge detection in noisy binary images

This paper presents a pair of fast algorithms which detect edges in noisy binary images. The algorithms run on a parallel hierarchical cellular array processor called a pyramid machine. Example results are illustrated and the time required by each algorithm is discussed.     

Optimal mean-square N-observation digital morphological filters: I. Optimal binary filters

The present paper places binary morphological filtering into the framework of statistical estimation, the intent being to develop the theory of mean-square (MS) optimization. Classical binary morphological operations are interpreted as numerical functionals on binary N-vectors, so that in the random setting they can be treated as estimators dependent on N binary observation random variables. For single-erosion filters, optimization is achieved by finding the structuring element that minimizes MS error. Using the Matheron representation as a guide, we generalize the analysis to morphological filters given by unions of multiple erosions and optimize by minimizing MS error over all collections of erosions, or over a prefixed number of erosions. In all cases, MS error is relative to the estimation of an unobserved variable by a morphological function of observed variables. A key element in the method is use of the basis form of the Matheron expansion to reduce significantly the structuring-element search. The technique is adapted to special morphological filters by constraining the basis representation in accordance with the class of interest. It is demonstrated that optimization in terms of erosions is equivalent to optimization in terms of dilations.     

Methods for fast morphological image transforms using bitmapped binary images

In this paper we present new implementations for morphological binary image processing on a general-purpose computer, using a bitmap representation of binary images instead of representing binary images as bitplanes inserted in gray value images. The bitmap data representation is a very efficient one, both in terms of memory requirements and in terms of algorithmic efficiency because of the CPU operates on 32 pixels in parallel. The algorithms described in this paper are capable of performing the basic morphological image transforms using structuring elements of arbitrary size and shape. In order to speed up morphological operations with respect to commonly used, large, convex structuring elements, the logarithmic decomposition of structuring elements is used. Experiments indicate that the new algorithms are more than 30 times faster for pixelwise operations and about an order of magnitude faster for the basic morphological transforms than the fastest known software implementations.     

Optimal visibility algorithms for binary images on the hypercube

Consider an×n binary image. Given a directionD, the parallel visibility problem consists of determining for each pixel of the image the portion that is visible (i.e., not obstructed by any other black pixel of the image) in directionD from infinity. A related problem, referred to as point visibility, is to compute for each pixel the portion that is visible from a given pointp. In this paper, we deriveO(logn) time SIMD algorithms for each of these two problems on the hypercube, where one processor is assigned to every pixel of the image. Since the worst case communication distance of two processors in an ²-processor hypercube is 2 logn, it follows that both of the above algorithms are asymptotically optimal.This paper summarizes a preliminary version [Ref. 1] and short note on a possible improvement [Ref. 2] presented at the 1988IFIP WG 10.3. Working Conference on Parallel Processing and 1988Allerton Conference on Communication, Control and Computing, respectively. The first and third authors' research are partially supported by the Natural Sciences and Engineering Research Council of Canada.     

Estimation of object motion parameters from noisy images

An approach is presented for the estimation of object motion parameters based on a sequence of noisy images. The problem considered is that of a rigid body undergoing unknown rotational and translational motion. The measurement data consists of a sequence of noisy image coordinates of two or more object correspondence points. By modeling the object dynamics as a function of time, estimates of the model parameters (including motion parameters) can be extracted from the data using recursive and/or batch techniques. This permits a desired degree of smoothing to be achieved through the use of an arbitrarily large number of images. Some assumptions regarding object structure are presently made. Results are presented for a recursive estimation procedure: the case considered here is that of a sequence of one dimensional images of a two dimensional object. Thus, the object moves in one transverse dimension, and in depth, preserving the fundamental ambiguity of the central projection image model (loss of depth information). An iterated extended Kalman filter is used for the recursive solution. Noise levels of 5-10 percent of the object image size are used. Approximate Cramer-Rao lower bounds are derived for the model parameter estimates as a function of object trajectory and noise level. This approach may be of use in situations where it is difficult to resolve large numbers of object match points, but relatively long sequences of images (10 to 20 or more) are available.     

High-capacity reversible data hiding in binary images using pattern substitution

Data hiding, as the term itself suggests, means the hiding of secret data in a cover image. The result is a so-called stego-image. Reversible data hiding is technique, where not only the secret data can be extracted from the stego-image, but the cover image can be completely rebuilt after the extraction of secret data. Therefore, reversible data hiding is the choice in cases of secret data hiding, where the recovery of the cover image is required. In this paper, we propose a high-capacity reversible data hiding scheme based on pattern substitution. Our scheme gathers statistical data concerning the occurrence frequencies of various patterns and quantifies the occurrence frequency as it differs from pattern to pattern. In this way, some pattern exchange relationships can be established, and pattern substitution can thus be used for data hiding. In the extraction stage, we reverse these patterns to their original forms and rebuild an undistorted cover image. Our experimental results demonstrate the practicability of the proposed method. In fact, our new scheme gives a better performance than pair-wise logical computation (PWLC) in terms of both hiding capacity and stego-image visual quality.     

Bandwidth compression of noisy images

The effect of additive noise on Discrete Fourier Transform of pictorial data (2DFT) must be considered in several important problems such as filtering, enhancement and bandwidth compression. This paper investigates the statistical properties of the corrupted 2DFT coefficients, and the error involved in reconstruction when a subset of these coefficients is employed for the purpose. The latter being often the case, the present analysis provides a rational basis for frequency selection and filter specification. Application of an F-test quantifies the reliability of filtering or bandwidth compression.     

Neural edge enhancer for supervised edge enhancement from noisy images

We propose a new edge enhancer based on a modified multilayer neural network, which is called a neural edge enhancer (NEE), for enhancing the desired edges clearly from noisy images. The NEE is a supervised edge enhancer: Through training with a set of input noisy images and teaching edges, the NEE acquires the function of a desired edge enhancer. The input images are synthesized from noiseless images by addition of noise. The teaching edges are made from the noiseless images by performing the desired edge enhancer. To investigate the performance, we carried out experiments to enhance edges from noisy artificial and natural images. By comparison with conventional edge enhancers, the following was demonstrated: The NEE was robust against noise, was able to enhance continuous edges from noisy images, and was superior to the conventional edge enhancers in similarity to the desired edges. To gain insight into the nonlinear kernel of the NEE, we performed analyses on the trained NEE. The results suggested that the trained NEE acquired directional gradient operators with smoothing. Furthermore, we propose a method for edge localization for the NEE. We compared the NEE, together with the proposed edge localization method, with a leading edge detector. The NEE was proven to be useful for enhancing edges from noisy images.     

Bayesian image and pattern reconstruction from incomplete and noisy data

A Bayesian iterative method can be the basis for a wide range of technologies in the field of pattern recognition and image reconstruction. It involves finding the most probable solutions for images or patterns, if functionals describing the likelihood function and a priori information, respectively, are already known. The article describes the basic principles and recent advances in the development of BIM and its applications in various fields, mainly in tomography and restoration of functions from incomplete and noisy data.     

Inferring region salience from binary and gray-level images

We introduce a method that uses contour fragments to highlight regions of interest. Our method obtains as input either a binary image or the gradient map of a gray-level image. It produces a saliency map that reflects for every point in the image our belief that it belongs to a salient region. Saliency is determined by criteria such as closure, convexity, and size. In addition, gaps in the boundaries of regions diminish their saliency. Explicit scale parameter determines the size of interest. The method is implemented by a convolution of the input edge image with a linear filter that specifies the region of influence of a contour point over the image. Experiments demonstrate the utility of the method for saliency and segmentation.     

Retrieval of colour and texture images using local directional peak valley binary pattern

Pattern Analysis and Applications - Many content-based image retrieval (CBIR) methods are being developed to store more and more information about images in shorter feature vectors and to improve...     

An edge extraction technique for noisy images

Extracting edges from noisy images has an important significance in practical applications which utilize some type of visual input capability. This paper describes a new edge extraction technique specifically developed for noisy images which eliminates the necessity of noise removal preprocessing or postprocessing. The algorithm is based on parallel statistical tests for which indeterminate decisions are allowed. A number of well-chose examples are shown to demonstrate the capabilities of the new algorithm for noisy images as well as noise free images.     

Estimation-detection of object boundaries in noisy images

Estimation of boundaries of objects in noisy images is considered when the objects and the background are statistically characterized. The noise is assumed white, additive, and Gaussian. Optimal recursive estimators in a joint estimation-detection context are derived. Applications to binary pictures are illustrated.     

Towards reliable object detection in noisy images

Image noise is a common problem frequently caused by insufficient lighting, low-quality cameras, image compression and other factors. While low image quality is expected to degrade results of visual recognition, most of the current methods and benchmarks for object recognition, such as Pascal Visual Object Classes Challenge and Microsoft Common Objects in Context Challenge, focus on relatively high-quality images. Meanwhile, object recognition in noisy images is a common problem in surveillance and other domains. In this work we address object detection in noisy images and propose a novel low-cost method for image denoising. When combined with the standard Deformable Parts Model and Regions with Convolutional Neural Network object detectors, our method shows improvements of object detection under varying levels of image noise. We present a comprehensive experimental evaluation and compare our method to other denoising techniques as well as to standard detectors re-trained on noisy images. Results are presented for the common Pascal Visual Object Classes benchmark for object detection and KAIST Multispectral Pedestrian Detection Benchmark with the real noise presence in night images.