Nikolaos P. Galatsanos

A Class-Adaptive Spatially Variant Mixture Model for Image Segmentation

We propose a new approach for image segmentation based on a hierarchical and spatially variant mixture model. According to this model, the pixel labels are random variables and a smoothness prior is imposed on them. The main novelty of this work is a new family of smoothness priors for the label probabilities in spatially variant mixture models. These Gauss-Markov random field-based priors allow all their parameters to be estimated in closed form via the maximum a posteriori (MAP) estimation using the expectation-maximization methodology. Thus, it is possible to introduce priors with multiple parameters that adapt to different aspects of the data. Numerical experiments are presented where the proposed MAP algorithms were tested in various image segmentation scenarios. These experiments demonstrate that the proposed segmentation scheme compares favorably to both standard and previous spatially constrained mixture model-based segmentation

Scene Detection in Videos Using Shot Clustering and Sequence Alignment

Video indexing requires the efficient segmentation of video into scenes. The video is first segmented into shots and a set of key-frames is extracted for each shot. Typical scene detection algorithms incorporate time distance in a shot similarity metric. In the method we propose, to overcome the difficulty of having prior knowledge of the scene duration, the shots are clustered into groups based only on their visual similarity and a label is assigned to each shot according to the group that it belongs to. Then, a sequence alignment algorithm is applied to detect when the pattern of shot labels changes, providing the final scene segmentation result. In this way shot similarity is computed based only on visual features, while ordering of shots is taken into account during sequence alignment. To cluster the shots into groups we propose an improved spectral clustering method that both estimates the number of clusters and employs the fast global k-means algorithm in the clustering stage after the eigenvector computation of the similarity matrix. The same spectral clustering method is applied to extract the key-frames of each shot and numerical experiments indicate that the content of each shot is efficiently summarized using the method we propose herein. Experiments on TV-series and movies also indicate that the proposed scene detection method accurately detects most of the scene boundaries while preserving a good tradeoff between recall and precision.

Maximum a Posteriori Video Super-Resolution Using a New Multichannel Image Prior

Super-resolution (SR) is the term used to define the process of estimating a high-resolution (HR) image or a set of HR images from a set of low-resolution (LR) observations. In this paper we propose a class of SR algorithms based on the maximum a posteriori (MAP) framework. These algorithms utilize a new multichannel image prior model, along with the state-of-the-art single channel image prior and observation models. A hierarchical (two-level) Gaussian nonstationary version of the multichannel prior is also defined and utilized within the same framework. Numerical experiments comparing the proposed algorithms among themselves and with other algorithms in the literature, demonstrate the advantages of the adopted multichannel approach.

Bayesian Restoration Using a New Nonstationary Edge-Preserving Image Prior

In this paper, we propose a class of image restoration algorithms based on the Bayesian approach and a new hierarchical spatially adaptive image prior. The proposed prior has the following two desirable features. First, it models the local image discontinuities in different directions with a model which is continuous valued. Thus, it preserves edges and generalizes the on/off (binary) line process idea used in previous image priors within the context of Markov random fields (MRFs). Second, it is Gaussian in nature and provides estimates that are easy to compute. Using this new hierarchical prior, two restoration algorithms are derived. The first is based on the maximum a posteriori principle and the second on the Bayesian methodology. Numerical experiments are presented that compare the proposed algorithms among themselves and with previous stationary and non stationary MRF-based with line process algorithms. These experiments demonstrate the advantages of the proposed prior

Super-Resolution Based on Fast Registration and Maximum a Posteriori Reconstruction

In this paper, we propose a maximum a posteriori framework for the super-resolution problem, i.e., reconstructing high-resolution images from shifted, rotated, low-resolution degraded observations. The main contributions of this work are two; first, the use of a new locally adaptive edge preserving prior for the super-resolution problem. Second an efficient two-step reconstruction methodology that includes first an initial registration using only the low-resolution degraded observations. This is followed by a fast iterative algorithm implemented in the discrete Fourier transform domain in which the restoration, interpolation and the registration subtasks of this problem are preformed simultaneously. We present examples with both synthetic and real data that demonstrate the advantages of the proposed framework.

Variational Bayesian Sparse Kernel-Based Blind Image Deconvolution With Student's-t Priors

In this paper, we present a new Bayesian model for the blind image deconvolution (BID) problem. The main novelty of this model is the use of a sparse kernel-based model for the point spread function (PSF) that allows estimation of both PSF shape and support. In the herein proposed approach, a robust model of the BID errors and an image prior that preserves edges of the reconstructed image are also used. Sparseness, robustness, and preservation of edges are achieved by using priors that are based on the Students-t probability density function (PDF). This pdf, in addition to having heavy tails, is closely related to the Gaussian and, thus, yields tractable inference algorithms. The approximate variational inference methodology is used to solve the corresponding Bayesian model. Numerical experiments are presented that compare this BID methodology to previous ones using both simulated and real data.

A Bayesian Framework for Image Segmentation With Spatially Varying Mixtures

A new Bayesian model is proposed for image segmentation based upon Gaussian mixture models (GMM) with spatial smoothness constraints. This model exploits the Dirichlet compound multinomial (DCM) probability density to model the mixing proportions (i.e., the probabilities of class labels) and a Gauss-Markov random field (MRF) on the Dirichlet parameters to impose smoothness. The main advantages of this model are two. First, it explicitly models the mixing proportions as probability vectors and simultaneously imposes spatial smoothness. Second, it results in closed form parameter updates using a maximum a posteriori (MAP) expectation-maximization (EM) algorithm. Previous efforts on this problem used models that did not model the mixing proportions explicitly as probability vectors or could not be solved exactly requiring either time consuming Markov Chain Monte Carlo (MCMC) or inexact variational approximation methods. Numerical experiments are presented that demonstrate the superiority of the proposed model for image segmentation compared to other GMM-based approaches. The model is also successfully compared to state of the art image segmentation methods in clustering both natural images and images degraded by noise.

New Additive Watermark Detectors Based On A Hierarchical Spatially Adaptive Image Model

In this paper, we propose a new family of watermark detectors for additive watermarks in digital images. These detectors are based on a recently proposed hierarchical, two-level image model, which was found to be beneficial for image recovery problems. The top level of this model is defined to exploit the spatially varying local statistics of the image, while the bottom level is used to characterize the image variations along two principal directions. Based on this model, we derive a class of detectors for the additive watermark detection problem, which include a generalized likelihood ratio, Bayesian, and Rao test detectors. We also propose methods to estimate the necessary parameters for these detectors. Our numerical experiments demonstrate that these new detectors can lead to superior performance to several state-of-the-art detectors.

Sparse Bayesian Modeling With Adaptive Kernel Learning

Sparse kernel methods are very efficient in solving regression and classification problems. The sparsity and performance of these methods depend on selecting an appropriate kernel function, which is typically achieved using a cross-validation procedure. In this paper, we propose an incremental method for supervised learning, which is similar to the relevance vector machine (RVM) but also learns the parameters of the kernels during model training. Specifically, we learn different parameter values for each kernel, resulting in a very flexible model. In order to avoid overfitting, we use a sparsity enforcing prior that controls the effective number of parameters of the model. We present experimental results on artificial data to demonstrate the advantages of the proposed method and we provide a comparison with the typical RVM on several commonly used regression and classification data sets.

New Detectors for Watermarks with Unknown Power Based on Student-t Image Priors

In this paper we present new detectors for additive watermarks when the power of the watermark is unknown. These detectors are based on modeling the image using student-t statistics. As a result, due to the generative properties of the student-t density function, such models are spatially adaptive and the Expectation-Maximization algorithm can be used to obtain maximum likelihood estimates of their parameters. Using these image models detectors based on the generalized likelihood ratio and Rao tests are derived for this problem. Numerical experiments are presented that demonstrate the properties of these detectors and compared them with previously proposed detectors.