Graphical Models and Image Processing最新文献

In this paper, we present a new approximate algorithm for medial axis transform of a plane domain. The underlying philosophy of our approach is the localization idea based on the Domain Decomposition Lemma, which enables us to break up the complicated domain into smaller and simpler pieces. We then develop tree data structure and various operations on it to keep track of the information produced by the domain decomposition procedure. This strategy enables us to isolate various important points such as branch points and terminal points. Because our data structure guarantees the existence of such important points—in fact, our data structure is devised with this in mind—we can zoom in on those points. This makes our algorithm efficient. Our algorithm is a “from within” approach, whereas traditional methods use a “from-the-boundary” approach. This “from within” nature of our algorithm and the localization scheme help mitigate various instability phenomena, thereby making our algorithm reasonably robust.

A framework for contrast enhancement via image evolution flows and variational formulations is introduced in this paper. First, an algorithm for histogram modification via image evolution equations is presented. We show that the image histogram can be modified to achieve any given distribution as the steady state solution of this differential equation. We then prove that the proposed evolution equation solves an energy minimization problem. This gives a new interpretation to histogram modification and contrast enhancement in general. This interpretation is completely formulated in the image domain, in contrast with classical techniques for histogram modification which are formulated in a probabilistic domain. From this, new algorithms for contrast enhancement, including, for example, image and perception models, can be derived. Based on the energy formulation and its corresponding differential form, we show that the proposed histogram modification algorithm can be combined with image regularization schemes. This allows us to perform simulations contrast enhancement and denoising, avoiding common noise sharpening effects in classical schemes. Theoretical results regarding the existence of solutions to the proposed equations are presented.

The work to be described is motivated by the need to simulate a variety of real–world image textures, all of which can be well approximated by stationary Gaussian random fields (SGRFs). Specifically, given an observed SGRFT, we wish to simulate SGRFs which look like and possess similar statistical properties toT. The main contribution of this paper is the development of an automatic and nonparametric spectrum estimation procedure which is able to produce an estimated spectrum ofTin such a way that SGRFs simulated from this estimated spectrum have these desirable characteristics. Two special features of the procedure are: (i) it relies on a different risk function to that commonly used in nonparametric spectrum estimation, and (ii) it chooses its smoothing parameters by the technique of unbiased risk estimation. Results from a simulation study and a practical example demonstrate the good performance of the procedure. The practical example also illustrates how the proposed procedure can be combined with Monte Carlo testing to tackle target testing problems. Finally, the procedure is applied to the synthesis of some Brodatz textures, with some success.

In this paper a multiresolution wavelet analysis (MWA) and nonstationary Gaussian Markov random field (GMRF) technique is introduced for the detection of microcalcifications with high accuracy. The hierarchical multiresolution wavelet information in conjunction with the contextual information of the images extracted from GMRF provides an efficient technique for microcalcification detection. A Bayesian learning paradigm realized via the expectation maximization (EM) algorithm was also introduced for edge detection or segmentation of mass regions recorded on the mammograms. The strength of the technique is in the effective utilization of the rich contextural information in the images considered. The effectiveness of the approach has been tested with a number of mammographic images for which the microcalcification detection algorithm achieved a sensitivity (true positive rate) of 94% and specificity (true negative rate) of 88%. Considerably good results were also obtained for the segmentation algorithm. In addition, the results for both the detected microcalcifications and the segmented mass regions were superimposed for an interesting case under the methods introduced.

During the past few years several interesting applications of eigenspace representation of images have been proposed. These include face recognition, video coding, and pose estimation. However, the vision research community has largely overlooked parallel developments in signal processing and numerical linear algebra concerning efficient eigenspace updating algorithms. These new developments are significant for two reasons: Adopting them will make some of the current vision algorithms more robust and efficient. More important is the fact that incremental updating of eigenspace representations will open up new and interesting research applications in vision such as active recognition and learning. The main objective of this paper is to put these in perspective and discuss a new updating scheme for low numerical rank matrices that can be shown to be numerically stable and fast. A comparison with a nonadaptive SVD scheme shows that our algorithm achieves similar accuracy levels for image reconstruction and recognition at a significantly lower computational cost. We also illustrate applications to adaptive view selection for 3D object representation from projections.

This paper presents the properties of the discrete analytical hyperplanes. They are defined analytically in the discrete domain by Diophantine equations. We show that the discrete hyperplane is a generalization of the classical digital hyperplanes. We present original properties such as exact point localization and space tiling. The main result is the links made between the arithmetical thickness of a hyperplane and its topology.

Subpixel methods that locate curves and their singularities, and that accurately measure geometric quantities, such as orientation and curvature, are of significant importance in computer vision and graphics. Such methods often use local surface fits or structural models for a local neighborhood of the curve to obtain the interpolated curve. Whereas their performance is good in smooth regions of the curve, it is typically poor in the vicinity of singularities. Similarly, the computation of geometric quantities is often regularized to deal with noise present in discrete data. However, in the process, discontinuities are blurred over, leading to poor estimates at them and in their vicinity. In this paper we propose a geometric interpolation technique to overcome these limitations by locating curves and obtaining geometric estimates while (1) not blurring across discontinuities and (2) explicitly and accurately placing them. The essential idea is to avoid the propagation of information across singularities. This is accomplished by a one-sided smoothing technique, where information is propagated from the direction of the side with the “smoother” neighborhood. When both sides are nonsmooth, the two existing discontinuities are relieved by placing a single discontinuity, or shock. The placement of shocks is guided by geometric continuity constraints, resulting in subpixel interpolation with accurate geometric estimates. Since the technique was originally motivated by curve evolution applications, we demonstrate its usefulness in capturing not only smooth evolving curves, but also ones with orientation discontinuities. In particular, the technique is shown to be far better than traditional methods when multiple or entire curves are present in a very small neighborhood.