Youn-Sik Han

Image relaxation: restoration and feature extraction

The techniques of a posteriori image restoration and iterative image feature extraction are described and compared. Image feature extraction methods known as graduated nonconvexity (GNC); variable conductance diffusion (VCD), anisotropic diffusion, and biased anisotropic diffusion (BAD), which extract edges from noisy images, are compared with a restoration/feature extraction method known as mean field annealing (MFA). All are shown to be performing the same basic operation: image relaxation. This equivalence shows the relationship between energy minimization methods and spatial analysis methods and between their respective parameters of temperature and scale. As a result of the equivalence, VCD is demonstrated to minimize a cost function, and that cost is specified explicitly. Furthermore, operations over scale space are shown to be a method of avoiding local minima. >

Pose determination using tree annealing

The problem of pose determination of a surface in a range image is described as a six-degree-of-freedom optimization problem, where the surface is expressed by a quadratic equation. The tree annealing algorithm, a general-purpose technique for finding minima of functions of continuously valued variables, is presented. The technique is applied to the pose determination of analytic surfaces and is shown to be quite effective even in the presence of considerable amounts of noise in the images.<<ETX>>

Adaptive edge-preserving smoothing via adaptive-mean-field annealing

After the stochastic simulated annealing technique was applied in the field of image processing, there have been many research reports on the Markov random field based image processing. These MRF-based edge-preserving smoothing techniques showed good results in the field of restoration, reconstruction, edge detection, and segmentation of the images, however, they have common drawbacks. First, those methods do not work well for smoothing of the nonstationary or signal-dependent noise. In real world images, the noises are often nonstationary and signal-dependent. Second, those edge-preserving smoothing techniques employ implicit or explicit thresholds to determine the existence of the edges, and they use fixed single thresholds throughout the entire image. As a result of these drawbacks, small features in the area of low noise variance are lost or blurred in order to restore the features in the high variance area. In order to cure these problems, we need an adaptive edge-preserving smoothing method which can be applied to nonstationary or signal-dependent noise with adaptive thresholding. The adaptive mean field annealing is an adaptive version of MFA, which fulfills this purpose by taking advantage of the local nature of the MRF and the fact that nonstationary or signal-dependent noise can be approximated by locally stationary additive Gaussian noise. In AMFA, the a priori information about the noise is not necessary and, hence, the difficulty of estimating the parameters is greatly reduced.

Quantitative angiography using mean field annealing

The vessels in the cineangiogram are degraded by the nonuniform point spread function (PSF) and nonstationary noise from the imaging system. The authors present a new method for vessel size measurement which does deblurring, edge-preserving smoothing, and edge enhancement in one process. The method is a version of an adaptive edge-preserving smoothing technique, adaptive mean field annealing (AMFA), extended to the blur problem. AMFA with a deblurring technique is an iterative image restoration technique for the restoration of noisy blurred images. With the progress of annealing, the restored image evolves from the maximum likelihood solution to the annealed maximum a posteriori solution and the restored edges are enhanced. The efficacy of the method is demonstrated with the results of the synthetic images, phantom images, and real cineangiographic images.<<ETX>>

Discontinuity-Preserving Vector Smoothing of Multivariate MR Images Using Vector Mean Field Annealing

We consider PD-, T1-, and T2-weighted magnetic resonance images jointly as a vector-valued image and use the angle of this vector field to formulate maximum a posteriori restoration as a global optimization problem. We use Mean Field Annealing (MFA) to find restorations that are superior to those obtained by previous multivariate approaches when shading artifacts near the MRI antenna are significant. Local homogeneity of the vector field as well as the angle between the components or the ratio of the components of the field are shown to have potential use for improving segmentation.

Reconstruction of positron emission tomography images using maximum a posteriori and mean field annealing techniques

In the reconstruction of positron emission tomography images, each slice of the image volume is individually reconstructed from a sinogram, in which the statistics of the data elements are Poisson and the image data is hidden by the mechanism of projection. We propose a method of image reconstruction which incorporates the given data set and also reflects the a prior knowledge that the image consists of smooth noiseless regions that are separated by sharp edges. This method uses both maximum likelihood and maximum a posteriori techniques in a manner that is similar to techniques used by others, but our method incorporates a bounded prior term and adaptive annealing techniques. These advancements prevent excessive smoothing and address the difficulties presented by parameter selection and image convergence.

A unified theory of edge-preserving smoothing

Abstract Two edge-preserving smoothing techniques are discussed, Mean Field Annealing, Graduated Non-convexity, and compared to a feature extraction technique known as Variable Conductance Diffusion. In previous literature, the first two techniques have been show to be equivalent. In this paper, the third technique is shown to also be equivalent. Furthermore, operations across scale space are shown to be equivalent to annealing. The demonstration of the mathematical equivalence of three independently derived and successful methods leads to conclusions concerning the fundamental nature of image analysis algorithms.

Discontinuity-preserving vector smoothing on multivariate MR images via vector mean-field annealing

One impcrtant potential ci Magnetic Resonance Imaging as comjxrcd to other medical imaging modalities is that MRI can produce well-registered multivariate images. By channg operational parameters, MRI can generate different images which emphasizes one or more tissue parameters, while maintaining reasonable registration among these images. Curremly, these multivariate unages are ocessed or viewed individually. This jiocessing seheme is inconvenient and sometimes gives incurate results. By treating multivariate images as vector-valued images, we can process them as a whole. For quantitative analysis of medical hnages, thscontinnity-preserving or -enhancing smoothing technique becomes important In this mper, a discontinuity-preserving vector smoothing technique is intrOdUced, which is based on current scalar Mean Field Annealing.

Magnetic resonance image analysis

Our intent is to obtain images which most clearly differentiate soft tissue types in Magnetic Resonance Image data. We model the three unknown intrinsic parameter images and the data images as Markov random fields and compare maximum likelihood restorations with two maximum a posteriori (MAP) restorations. The mathematical model of the imaging process is strongly nonlinear in the region of interest, but does not appear to introduce local minima in the resulting constrained multidimensional optimization procedure. The application of non- quadratic prior probabilities however does require global optimization. We have developed a unique approach towards image restoration that produces images with significant improvements when compared to the original data. We have extended previous results that attempt to determine the intrinsic parameters from the MRI data, and have used these intrinsic parameter images to synthesize MR images. MR images with different TE and TR parameters do not require additional use of an MR scanner, since excellent synthetic MR images are obtained using the restored proton density and nuclear relaxation time images.

Restoration of cardiac magnetic resonance images

Motion artifacts due to heart motion and blood flow within the heart chambers are a significant barrier to accurate interpretation of cardiac magnetic resonance images (MRI). The post-processing techniques of Wiener filtering, alternating projections onto convex sets (POCS), and mean field annealing (MFA) to remove these artifacts are studied. Removal of noise from the images is accomplished with MFA by setting up a restoration problem whose objective function encapsulates both data-dependent and a priori knowledge about the image. Two important aspects of MFA are the use of a penalty rather than a constraint, and the fact that it converges twenty times as rapidly as normal simulated annealing. Images of the results of Wiener filtering and MFA are shown, and the methods of POCS and MFA are briefly explained.<<ETX>>