Steganalysis is used to detect hidden content in innocuous images. Many successful steganalysis algorithms use
a large number of features relative to the size of the training set and suffer from a "curse of dimensionality":
large number of feature values relative to training data size. High dimensionality of the feature space can reduce
classification accuracy, obscure important features for classification, and increase computational complexity. This
paper presents a filter-type feature selection algorithm that selects reduced feature sets using the Mahalanobis
distance measure, and develops classifiers from the sets. The experiment is applied to a well-known JPEG
steganalyzer, and shows that using our approach, reduced-feature steganalyzers can be obtained that perform as
well as the original steganalyzer. The steganalyzer is that of Pevn´y et al. (SPIE, 2007) that combines DCT-based
feature values and calibrated Markov features. Five embedding algorithms are used. Our results demonstrate
that as few as 10-60 features at various levels of embedding can be used to create a classifier that gives comparable
results to the full suite of 274 features.
Steganography is the study of hiding information within a covert channel in order to transmit a secret message. Any public media such as image data, audio data, or even file packets, can be used as a covert channel. This paper presents an embedding algorithm that hides a message in an image using a technique based on a nonlinear matrix transform called the minimax eigenvector decomposition (MED). The MED is a minimax algebra version of the well-known singular value decomposition (SVD). Minimax algebra is a matrix algebra based on the algebraic operations of maximum and addition, developed initially for use in operations research and extended later to represent a class of nonlinear image processing operations. The discrete mathematical morphology operations of dilation and erosion, for example, are contained within minimax algebra. The MED is much quicker to compute than the SVD and avoids the numerical computational issues of the SVD because the operations involved only integer addition, subtraction, and compare. We present the algorithm to embed data using the MED, show examples applied to image data, and discuss limitations and advantages as compared with another similar algorithm.
Hiding messages in image data, called steganography, is used for both legal and illicit purposes. The detection of hidden messages in image data stored on websites and computers, called steganalysis, is of prime importance to cyber forensics personnel. Automating the detection of hidden messages is a requirement, since the shear amount of image data stored on computers or websites makes it impossible for a person to investigate each image separately. This paper describes research on a prototype software system that automatically classifies an image as having hidden information or not, using a sophisticated artificial neural network (ANN) system. An ANN software package, the ISU ACL NetWorks Toolkit, is trained on a selection of image features that distinguish between stego and nonstego images. The novelty of this ANN is that it is a blind classifier that gives more accurate results than previous systems. It can detect messages hidden using a variety of different types of embedding algorithms. A Graphical User Interface (GUI) combines the ANN, feature selection, and embedding algorithms into a prototype software package that is not currently available to the cyber forensics community.
Steganography is the study of data hiding for the purpose of covert communication. A secret message is inserted into a cover file so that the very existence of the message is not apparent. Most current steganography algorithms insert data in the spatial or transform domains; common transforms include the discrete cosine transform, the discrete Fourier transform, and discrete wavelet transform. In this paper, we present a data-hiding algorithm that exploits a decomposition representation of the data instead of a frequency-based transformation of the data. The decomposition transform used is the singular value decomposition (SVD). The SVD of a matrix A is a decomposition A= USV' in which S is a nonnegative diagonal matrix and U and V are orthogonal matrices. We show how to use the orthogonal matrices in the SVD as a vessel in which to embed information. Several challenges were presented in order to accomplish this, and we give effective information-hiding using the SVD can be just as effective as using transform-based techniques. Furthermore, different problems arise when using the SVD than using a transform-based technique. We have applied the SVD to image data, but the technique can be formulated for other data types such as audio and video.
KEYWORDS: Data storage, Steganography, Digital watermarking, Data hiding, Lithium, Information operations, Visualization, Data communications, Binary data, Reconstruction algorithms
This paper presents result of applying the minimax eigenvalue decomposition (MED), a morphology type transform, that hides data within digital images as part of a flexible, computationally robust algorithm. This new algorithm presents a general method for hiding information within an image, although the strength of this algorithm lies in authentication. Authentication is the establishment of ownership of digital information, and is a type of watermarking. While no self-authenticating techniques are currently known, the algorithm presented here provides a certain level of self-authentication regardless of the particular information embedded in the data. The algorithm is applied to ten different images acquired over the internet, three of which are included in this document. Information in the form of a binary bit stream is inserted into each image data. A measure is created to determine how close an image containing message data is to its original image. A visual comparison is also performed. Keys, or information separate from the message data that is generated by the embedding techniques, are used to establish authenticity of the image data. This is different from most current steganography techniques that rely on embedded data integrity to establish authenticity. An analysis of the results is presented.
This paper presents theory and experiment to perform a pattern recognition task. The task is to detect a mine in visual imagery, using a training algorithm. The marginal statistics for the data windows around potential targets are collected using a lexicode approach. Theoretical results supporting the lexicode's ability to perform such a task are presented. Preprocessing of the data is performed prior to the application of the lexicode. Discussion is given on the theoretical foundations and the preprocessing of the data, with future research activities outlined.
Detection of objects in images in an automated fashion is necessary for many applications, including automated target recognition. In this paper, we present results of an automated boundary detection procedure using a new subclass of Markov random fields (MRFs), called partially ordered Markov models (POMMs). POMMs offer computational advantages over general MRFs. We show how a POMM can model the boundaries in an image. Our algorithm for boundary detection uses a Bayesian approach to build a posterior boundary model that locates edges of objects having a closed-loop boundary. We apply our method to images of mines with very good results.
In this paper we demonstrate that a genetic algorithm can be used to produce collections of pixel locations termed foot patterns useful for distinguishing between different types of binary texture images. The genetic algorithm minimizes the entropy of empirical samples taken with a particular foot pattern on a training image. The resulting low entropy foot patterns for several texture types are then used to classify test images. In order to classify a given image, foot patterns for several texture types are applied to the image to obtain entropy scores. The lowest entropy foot patterns are then used in a vote with the majority among the ten lowest scoring being taken as the classification. On the original test set of sixty images, twelve each from five image types, the resulting classification was 98.3% accurate (one image was not classified). When a sixth texture type, picked specifically to confound the classification technique, was added to texture types in the original test the technique misclassified several images of the two similar types. This latter experiment helps explain much of the how and why of the texture classification technique. We discuss potential methods for overcoming limitations of the texture classification technique.
This paper presents research on texture modeling and regeneration. We view a texture as a large pattern created from regular repetitions of a small, basic texture element, or texel. Given a texture image, the problem was to find the 'best' texel for that data, regenerate the texture represented by that texel, and compare the original image and the regenerated one. The texel-finding problem was posed as an optimization procedure. We used a genetic algorithm to do the optimization. To regenerate the texture, we used a Metropolis-like algorithm. The textures regenerated from the texels found by the genetic algorithm were difficult to visually distinguish from the original data. Research efforts are continuing to improve the efficiency and accuracy of the method and to extend the method to different types of data.
When using approaches for solving imaging problems such as maximum likelihood or a Bayesian decision rule, massive amounts of data are involved. In order to make the implementation on computers attainable and not overly CPU-intensive, approximations to optimal solutions are often chosen, or nonoptimal solutions sought. In this paper we present a novel solution to the problem of solving for a maximum a posteriori estimator that uses genetic algorithms to search the solution space and a new statistical model called partially ordered Markov models (POMMs). We apply the procedure to the problem of parameter fitting to stochastic models for texture. POMMs are a subclass of Markov random fields that have been shown to offer computational advantages over general Markov rnadom fields. POMMs are based on partial orderings of the lattice array. Among other properties, these models have an exact closed-form joint distribution. We show that POMMs can be used successfully for parameter fitting to texture data. A genetic algorithm is used for approximation of a solution of the maximum likelihood estimator. We also show simulated textures representing samples of the solutions found.
Detection of objects in images in an automated fashion is necessary for many applications, including automated target recognition. In this paper, we present results of boundary detection using Markov random fields. Once the boundaries of regions are detected, object recognition can be conducted to classify the regions within the boundaries. Thus, an approach that gives good boundary detection is very important in many automated target recognition systems. Our algorithm for boundary detection combines Bayesian approach with a histogram specification technique to locate edges of objects that have a closed-loop boundary. The boundary image is modeled by a Markov random field. The method is relatively insensitive to the input parameters required by the user and provides a fairly robust automated detection procedure that produces an image with closed one-pixel-wide boundaries. We apply our method to mine data with very good results.
This paper presents a neural network application to target classification using a new type of neural network called the Fuzzy Image Algebra Neural Network (FIANN). The FIANN is used in a heterogenous network structure. The first layer of the net performs feature extraction, while the remaining layers are used for classification. Generalized image algebra operations are used to obtain fuzzy morphological or linear operation. The parameters for the generalized operations are learned in a fashion similar to standard backpropagation, but with training rules based on a combination of stochastic learning and gradient descent techniques. The type of data used is the range data part of tank LADAR data. The objective is to classify the tanks by type. The range data is first converted to elevation data, which is input to the net for feature extraction and classification. A two tiered approach is used for training. The first layer learns image features, while the top layers perform classification.
The use of statistical pattern recognition techniques in image processing has led to simplifying assumptions on the statistical interdependence of the pixel value of an image, which allow theoretical analysis and/or computational implementation to be achieved. For instance, the assumption of statistical independence of the values or that their joint distributions are multivariate normal, simplifies the analysis enormously. However, these results are very limiting in representing models for data, and do not allow for analysis of arbitrary spatial dependencies, in the data. One method for modeling two-dimensional data on a lattice array has been developed by Abend et al. called the Markov mesh model, and is a generalization of the familiar 1D Markov chain. The Markov mesh model allows the use of a class of spatial dependencies that is popular in many 2D data processing schemes, including image processing. One advantage of using this model is that it allows a computationally attractive implementation of statistical procedures involving joint and conditional probabilities. In this paper, we generalize Abend et al.'s results to a more comprehensive model, which we call the Markov pyramid model, using the concept of partial ordering. We present the necessary background for this model and show that Abend's model is a special case of our model. Finally, we present a simple application of our results to texture modeling.
Artificial neural networks have proven to be quite useful for a variety of different applications. A recent addition to the arena of neural networks, morphology neural networks use a morphology-like operation as their basic nodal calculation, instead of the usual linear operation. Several morphology neural nets have been developed, and lattice-type learning rules have been used to train these networks. In this paper, we present a different kind of learning rule for morphology neural nets that is based on the simulated annealing algorithm. Simulated annealing has been applied to many different areas involving optimization.
A mathematical structure used to express image processing transforms, the AFATL image algebra has proven itself useful in a wide variety of applications. The theoretical foundation for the image algebra includes many important constructs for handling a wide variety of image processing problems: questions relating to linear and nonlinear transforms, including decomposition techniques; mapping of transformations to computer architectures; neural networks; recursive transforms; and data manipulation on hexagonal arrays. However, statistical notions have been included only on a very elementary level and on a more sophisticated level in the literature. This paper presents an extension of the current image algebra that includes a Bayesian statistical approach. It is shown how images are modeled as random vectors, probability functions or mass functions are modeled as images, and conditional probability functions are modeled as templates. The remainder of the paper gives a brief discussion of the current image algebra, an example of the use of image algebra to express high-level image processing transforms, and the presentation of the statistical development of the image algebra.
This paper presents an application of morphology neural networks to a template learning problem. Morphology neural networks are a nonlinear version of the familiar artificial neural networks. Typically, an artificial neural net is used to solve pattern classification problems One useful characterization of many neural network algorithms is the ability to 'learn' to respond correctly to new data based only on a selection of known data responses. For example, in the multilayer perceptron model, the 'learning' is a procedure whereby parameters are fed back from output to input neurons and the weights changed to give a better response. The morphological neural net in this paper solves a different type of image processing problem. Specifically, given an input image and an output image which corresponds to a dilated version of the input, one would like to determine what template produced the output. The problem corresponds to teaching the network to solve for the weights in a morphological net, as the weights are the template's values. A reasonable method has been investigated for the boolean case; in this paper results are presented for gray scale images. Image algebra has been shown to provide a succinct expression of neural networks algorithms and also to allow a generalization of neural networks, and thus the authors describe the algorithm in image algebra. The remainder of the paper gives a brief discussion of image algebra, the relationship of image algebra and neural networks, a recap of the dilation morphology neural network boolean for boolean images, and the generalization to grayscale data.
The development of a preprocessor for image algebra on the MasPar computer, a SIMD processor array, is discussed. One of the parallel languages used on the MasPar is MPL, a parallel version of the programming language C. This machine and language were chosen because of the close correspondence between MPL and image algebra and, as a result, MPL is easily extended to include image algebra. The preprocessor consists of three primary components: the lexical analyzer, the parser, and the code generator. The lexical analyzer converts the input stream into tokens the parser recognizes. The parser checks the program for syntax errors.The code generator produces MPL source code which is then compiled and run on the MasPar. The architecture of the MasPar computer is reviewed, and in particular the structures used for routing data through the array are examined. The parallel language MPL is also reviewed, with attention given to the methods in which the extensions to C in MPL interact with the MasPar architecture. The close correspondence between MPL and image algebra is specifically discussed. The authors present the structure and development of the image algebra preprocessor, including possible future extensions. Examples of image algebra preprocessor code and the corresponding MPL code produced by the preprocessor are given.
Recursion and feedback are two important processes in image processing. Image algebra, a unified algebraic structure
developed for use in image processing and image analysis, provides a common mathematical environment for expressing
image processing transforms. It is only recently that image algebra has been extended to include recursive operations [1].
Recently image algebra was shown to incorporate neural nets [2], including a new type of neural net, the morphological
neural net [3]. This paper presents the relationship of the recursive image algebra to the field of fractions of the ring of
matrices, and gives the two dimensional moving average filter as an example. Also, the popular multilayer perceptron
with back propagation and a morphology neural network with learning rule are presented in image algebra notation. These
examples show that image algebra can express these important feedback concepts in a succinct way.
Lattice transformations are a class of nonlinear image processing transforms that include mathematical morphology transforms as a subclass. By using a matrix representation lattice transforms may apply results established in minimax algebra a matrix algebra originally developed for operations research. This paper presents a strong decomposition technique for a translation invariant template that is a lattice transform using a minimax matrix approach. The factors of the decomposition correspond to variant templates. This method is particularly suited for implementation on multiple-instruction multiple-data (MIMD) architectures. Since the minimax algebra is a subalgebra of the Air Force image algebra which in turn encompasses mathematical morphology this technique provides another tool for template decomposition which in particular can be applied to morphology transforms.
Commercial hardware for neural network implementations is becoming more readily available. However as yet there exists no hardware- or software-independant environments in which to compare neural net chips. This paper presents a comparison of the Hamming net modeled on two neural net chips using image algebra a mathematical structure developed for use in image processing and related fields. The two chips used in the comparison are the Electrically Trainable Analog Neural Network (ETANN) from Intel and the Neural Bit Slice (NBS) from Micro Devices and are on opposite ends of the spectrum of available neural network hardware. The ETANN is almost entirely analog while the NBS is an all-digital device. The image algebra pseudocode modeled well not only the internals of the chips but the external logic and control as well.
The theory of classical artificial neural networks has been used to solve pattern recognition problems
in image processing that is different from traditional pattern recognition approaches. In standard
neural network theory, the first step in performing a neural network calculation involves the linear
operation of multiplying neural values by their synaptic strengths and adding the results. Thresholding
usually follows the linear operation in order to provide for non-linearity of the network. This
paper presents the fundamental theory for a morphological neural network which, instead of multiplication
and summation, uses the non-linear operation of addition and maximum. Several basic applications
which are distinctly different from pattern recognition techniques are given, including a net which
performs a sieving algorithm.
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