Adrian G. Bors

Image watermarking using DCT domain constraints

Watermarking algorithms are used for image copyright protection. The algorithms proposed select certain blocks in the image based on a Gaussian network classifier. The pixel values of the selected blocks are modified such that their discrete cosine transform (DCT) coefficients fulfil a constraint imposed by the watermark code. Two different constraints are considered. The first approach consists of embedding a linear constraint among selected DCT coefficients and the second one defines circular detection regions in the DCT domain. A rule for generating the DCT parameters of distinct watermarks is provided. The watermarks embedded by the proposed algorithms are resistant to JPEG compression.

Multimodal decision-level fusion for person authentication

The use of clustering algorithms for decision-level data fusion is proposed. Person authentication results coming from several modalities (e.g., still image, speech), are combined by using fuzzy k-means (FKM) and fuzzy vector quantization (FVQ) algorithms, and a median radial basis function (MRBF) network. The quality measure of the modalities data is used for fuzzification. Two modifications of the FKM and FVQ algorithms, based on a fuzzy vector distance definition, are proposed to handle the fuzzy data and utilize the quality measure. Simulations show that fuzzy clustering algorithms have better performance compared to the classical clustering algorithms and other known fusion algorithms. MRBF has better performance especially when two modalities are combined. Moreover, the use of the quality via the proposed modified algorithms increases the performance of the fusion system.

Median radial basis function neural network

Radial basis functions (RBFs) consist of a two-layer neural network, where each hidden unit implements a kernel function. Each kernel is associated with an activation region from the input space and its output is fed to an output unit. In order to find the parameters of a neural network which embeds this structure we take into consideration two different statistical approaches. The first approach uses classical estimation in the learning stage and it is based on the learning vector quantization algorithm and its second-order statistics extension. After the presentation of this approach, we introduce the median radial basis function (MRBF) algorithm based on robust estimation of the hidden unit parameters. The proposed algorithm employs the marginal median for kernel location estimation and the median of the absolute deviations for the scale parameter estimation. A histogram-based fast implementation is provided for the MRBF algorithm. The theoretical performance of the two training algorithms is comparatively evaluated when estimating the network weights. The network is applied in pattern classification problems and in optical flow segmentation.

Optical flow estimation and moving object segmentation based on median radial basis function network

Various approaches have been proposed for simultaneous optical flow estimation and segmentation in image sequences. In this study, the moving scene is decomposed into different regions with respect to their motion, by means of a pattern recognition scheme. The inputs of the proposed scheme are the feature vectors representing still image and motion information. Each class corresponds to a moving object. The classifier employed is the median radial basis function (MRBF) neural network. An error criterion function derived from the probability estimation theory and expressed as a function of the moving scene model is used as the cost function. Each basis function is activated by a certain image region. Marginal median and median of the absolute deviations from the median (MAD) estimators are employed for estimating the basis function parameters. The image regions associated with the basis functions are merged by the output units in order to identify moving objects.

Watermarking mesh-based representations of 3-D objects using local moments

A new methodology for fingerprinting and watermarking three-dimensional (3-D) graphical objects is proposed in this paper. The 3-D graphical objects are described by means of polygonal meshes. The information to be embedded is provided as a binary code. A watermarking methodology has two stages: embedding and detecting the information that has been embedded in the given media. The information is embedded by means of local geometrical perturbations while maintaining the local connectivity. A neighborhood localized measure is used for selecting appropriate vertices for watermarking. A study is undertaken in order to verify the suitability of this measure for selecting vertices from regions where geometrical perturbations are less perceptible. Two different watermarking algorithms, that do not require the original 3-D graphical object in the detection stage, are proposed. The two algorithms differ with respect to the type of constraint to be embedded in the local structure: by using parallel planes and bounding ellipsoids, respectively. The information capacity of various 3-D meshes is analyzed when using the proposed 3-D watermarking algorithms. The robustness of the 3-D watermarking algorithms is tested to noise perturbation and to object cropping.

Variational learning for Gaussian mixture models

This paper proposes a joint maximum likelihood and Bayesian methodology for estimating Gaussian mixture models. In Bayesian inference, the distributions of parameters are modeled, characterized by hyperparameters. In the case of Gaussian mixtures, the distributions of parameters are considered as Gaussian for the mean, Wishart for the covariance, and Dirichlet for the mixing probability. The learning task consists of estimating the hyperparameters characterizing these distributions. The integration in the parameter space is decoupled using an unsupervised variational methodology entitled variational expectation-maximization (VEM). This paper introduces a hyperparameter initialization procedure for the training algorithm. In the first stage, distributions of parameters resulting from successive runs of the expectation-maximization algorithm are formed. Afterward, maximum-likelihood estimators are applied to find appropriate initial values for the hyperparameters. The proposed initialization provides faster convergence, more accurate hyperparameter estimates, and better generalization for the VEM training algorithm. The proposed methodology is applied in blind signal detection and in color image segmentation

Watermarking 3D models

Copyright protection of graphical objects and models is important for protecting author rights in animation, multimedia, computer-aided design (CAD), virtual reality, medical imaging, etc. We suggest a blind watermarking algorithm for 3D models and objects. A string of bits, generated according to a key, is embedded in the geometrical structure of the graphical object by changing the locations of certain vertices. The criterion to choose these vertices ensures a minimal visibility of the distortions in the watermarked object. A bit encoding 1 is associated with positioning a vertex inside a volume modelled by the geometry of its neighbourhood, while a bit encoding 0 positions the vertex outside such a volume. The proposed watermarking algorithm is applied on various 3D models.

Terrain analysis using radar shape-from-shading

This paper develops a maximum a posteriori (MAP) probability estimation framework for shape-from-shading (SFS) from synthetic aperture radar (SAR) images. The aim is to use this method to reconstruct surface topography from a single radar image of relatively complex terrain. Our MAP framework makes explicit how the recovery of local surface orientation depends on the whereabouts of terrain edge features and the available radar reflectance information. To apply the resulting process to real world radar data, we require probabilistic models for the appearance of terrain features and the relationship between the orientation of surface normals and the radar reflectance. We show that the SAR data can be modeled using a Rayleigh-Bessel distribution and use this distribution to develop a maximum likelihood algorithm for detecting and labeling terrain edge features. Moreover, we show how robust statistics can be used to estimate the characteristic parameters of this distribution. We also develop an empirical model for the SAR reflectance function. Using the reflectance model, we perform Lambertian correction so that a conventional SFS algorithm can be applied to the radar data. The initial surface normal direction is constrained to point in the direction of the nearest ridge or ravine feature. Each surface normal must fall within a conical envelope whose axis is in the direction of the radar illuminant. The extent of the envelope depends on the corrected radar reflectance and the variance of the radar signal statistics. We explore various ways of smoothing the field of surface normals using robust statistics. Finally, we show how to reconstruct the terrain surface from the smoothed field of surface normal vectors. The proposed algorithm is applied to various SAR data sets containing relatively complex terrain structure.

Binary morphological shape-based interpolation applied to 3-D tooth reconstruction

In this paper, we propose an interpolation algorithm using a mathematical morphology morphing approach. The aim of this algorithm is to reconstruct the n-dimensional object from a group of (n-1)-dimensional sets representing sections of that object. The morphing transformation modifies pairs of consecutive sets such that they approach in shape and size. The interpolated set is achieved when the two consecutive sets are made idempotent by the morphing transformation. We prove the convergence of the morphological morphing. The entire object is modeled by successively interpolating a certain number of intermediary sets between each two consecutive given sets. We apply the interpolation algorithm for three-dimensional tooth reconstruction.

Prediction and tracking of moving objects in image sequences

We employ a prediction model for moving object velocity and location estimation derived from Bayesian theory. The optical flow of a certain moving object depends on the history of its previous values. A joint optical flow estimation and moving object segmentation algorithm is used for the initialization of the tracking algorithm. The segmentation of the moving objects is determined by appropriately classifying the unlabeled and the occluding regions. Segmentation and optical flow tracking is used for predicting future frames.