Aggelos K. Katsaggelos

Hybrid image segmentation using watersheds and fast region merging

A hybrid multidimensional image segmentation algorithm is proposed, which combines edge and region-based techniques through the morphological algorithm of watersheds. An edge-preserving statistical noise reduction approach is used as a preprocessing stage in order to compute an accurate estimate of the image gradient. Then, an initial partitioning of the image into primitive regions is produced by applying the watershed transform on the image gradient magnitude. This initial segmentation is the input to a computationally efficient hierarchical (bottom-up) region merging process that produces the final segmentation. The latter process uses the region adjacency graph (RAG) representation of the image regions. At each step, the most similar pair of regions is determined (minimum cost RAG edge), the regions are merged and the RAG is updated. Traditionally, the above is implemented by storing all RAG edges in a priority queue. We propose a significantly faster algorithm, which additionally maintains the so-called nearest neighbor graph, due to which the priority queue size and processing time are drastically reduced. The final segmentation provides, due to the RAG, one-pixel wide, closed, and accurately localized contours/surfaces. Experimental results obtained with two-dimensional/three-dimensional (2-D/3-D) magnetic resonance images are presented.

Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation

The application of regularization to ill-conditioned problems necessitates the choice of a regularization parameter which trades fidelity to the data with smoothness of the solution. The value of the regularization parameter depends on the variance of the noise in the data. The problem of choosing the regularization parameter and estimating the noise variance in image restoration is examined. An error analysis based on an objective mean-square-error (MSE) criterion is used to motivate regularization. Two approaches for choosing the regularization parameter and estimating the noise variance are proposed. The proposed and existing methods are compared and their relationship to linear minimum-mean-square-error filtering is examined. Experiments are presented that verify the theoretical results.

Regularized reconstruction to reduce blocking artifacts of block discrete cosine transform compressed images

The reconstruction of images from incomplete block discrete cosine transform (BDCT) data is examined. The problem is formulated as one of regularized image recovery. According to this formulation, the image in the decoder is reconstructed by using not only the transmitted data but also prior knowledge about the smoothness of the original image, which complements the transmitted data. Two methods are proposed for solving this regularized recovery problem. The first is based on the theory of projections onto convex sets (POCS) while the second is based on the constrained least squares (CLS) approach. For the POCS-based method, a new constraint set is defined that conveys smoothness information not captured by the transmitted BDCT coefficients, and the projection onto it is computed. For the CLS method an objective function is proposed that captures the smoothness properties of the original image. Iterative algorithms are introduced for its minimization. Experimental results are presented. >

Bayesian Compressive Sensing Using Laplace Priors

In this paper, we model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework. We utilize a hierarchical form of the Laplace prior to model the sparsity of the unknown signal. We describe the relationship among a number of sparsity priors proposed in the literature, and show the advantages of the proposed model including its high degree of sparsity. Moreover, we show that some of the existing models are special cases of the proposed model. Using our model, we develop a constructive (greedy) algorithm designed for fast reconstruction useful in practical settings. Unlike most existing CS reconstruction methods, the proposed algorithm is fully automated, i.e., the unknown signal coefficients and all necessary parameters are estimated solely from the observation, and, therefore, no user-intervention is needed. Additionally, the proposed algorithm provides estimates of the uncertainty of the reconstructions. We provide experimental results with synthetic 1-D signals and images, and compare with the state-of-the-art CS reconstruction algorithms demonstrating the superior performance of the proposed approach.

Projection-based spatially adaptive reconstruction of block-transform compressed images

At the present time, block-transform coding is probably the most popular approach for image compression. For this approach, the compressed images are decoded using only the transmitted transform data. We formulate image decoding as an image recovery problem. According to this approach, the decoded image is reconstructed using not only the transmitted data but, in addition, the prior knowledge that images before compression do not display between-block discontinuities. A spatially adaptive image recovery algorithm is proposed based on the theory of projections onto convex sets. Apart from the data constraint set, this algorithm uses another new constraint set that enforces between-block smoothness. The novelty of this set is that it captures both the local statistical properties of the image and the human perceptual characteristics. A simplified spatially adaptive recovery algorithm is also proposed, and the analysis of its computational complexity is presented. Numerical experiments are shown that demonstrate that the proposed algorithms work better than both the JPEG deblocking recommendation and our previous projection-based image decoding approach.

A regularized iterative image restoration algorithm

The development of the algorithm is based on a set theoretic approach to regularization. Deterministic and/or statistical information about the undistorted image and statistical information about the noise are directly incorporated into the iterative procedure. The restored image is the center of an ellipsoid bounding the intersection of two ellipsoids. The proposed algorithm, which has the constrained least squares algorithm as a special case, is extended into an adaptive iterative restoration algorithm. The spatial adaptivity is introduced to incorporate properties of the human visual system. Convergence of the proposed iterative algorithms is established. For the experimental results which are shown, the adaptively restored images have better quality than the nonadaptively restored ones based on visual observations and on an objective criterion of merit which accounts for the noise masking property of the visual system. >

Iterative Image Restoration Algorithms

This tutorial paper discusses the use of successive-approximation-based iterative restoration algorithms for the removal of linear blurs and noise from images. Iterative algorithms are particularly attractive for this application because they allow for the incorporation of prior knowledge about the class of feasible solutions, because they can be used to remove nonstationary blurs, and because they are fairly robust with respect to errors in the approximation of the blurring operator. Regularization is introduced as a means for preventing the excessive noise magnification that is typically associated with ill-posed inverse problems such as the deblurring problem. Iterative algorithms with higher convergence rates and a multistep iterative algorithm are also discussed. A number of examples are presented.

Noise reduction filters for dynamic image sequences: a review

In this paper, a thorough review is presented of noise reduction filters for digital image sequences. Detailed descriptions of several spatiotemporal and temporal noise reduction algorithms are provided. To aid in comparing between these different algorithms, we classify them based on their support (i.e., 3-D or 1-D filter) and whether or not motion compensation is employed. Several algorithms from each of the four categories are implemented and tested on real sequences degraded to various signal-to-noise ratios. These experimental results are discussed and analyzed to determine the overall advantages and disadvantages of the four general classifications, as well as, the individual filters. >

General choice of the regularization functional in regularized image restoration

The determination of the regularization parameter is an important issue in regularized image restoration, since it controls the trade-off between fidelity to the data and smoothness of the solution. A number of approaches have been developed in determining this parameter. In this paper, a new paradigm is adopted, according to which the required prior information is extracted from the available data at the previous iteration step, i.e., the partially restored image at each step. We propose the use of a regularization functional instead of a constant regularization parameter. The properties such a regularization functional should satisfy are investigated, and two specific forms of it are proposed. An iterative algorithm is proposed for obtaining a restored image. The regularization functional is defined in terms of the restored image at each iteration step, therefore allowing for the simultaneous determination of its value and the restoration of the degraded image. Both proposed iteration adaptive regularization functionals are shown to result in a smoothing functional with a global minimum, so that its iterative optimization does not depend on the initial conditions. The convergence of the algorithm is established and experimental results are shown.

Image restoration using a modified Hopfield network

A modified Hopfield neural network model for regularized image restoration is presented. The proposed network allows negative autoconnections for each neuron. A set of algorithms using the proposed neural network model is presented, with various updating modes: sequential updates; n-simultaneous updates; and partially asynchronous updates. The sequential algorithm is shown to converge to a local minimum of the energy function after a finite number of iterations. Since an algorithm which updates all n neurons simultaneously is not guaranteed to converge, a modified algorithm is presented, which is called a greedy algorithm. Although the greedy algorithm is not guaranteed to converge to a local minimum, the l (1) norm of the residual at a fixed point is bounded. A partially asynchronous algorithm is presented, which allows a neuron to have a bounded time delay to communicate with other neurons. Such an algorithm can eliminate the synchronization overhead of synchronous algorithms.