Tianhu Lei

MR imaging statistics and its application in image modeling

This paper presents a new framework on a complete statistical description of MR imaging and its application in image modeling. Particular studies include object variability and thermal noise, statistical properties of pixel images, and stochastic regularities of context images. Six stochastic properties (Gaussianity, stationarity, dependence, ergodicity, Markovian property, inhomogeneity) are justified to form the basis for establishing the stochastic image models. The application of these properties to both pixel image modeling (standard finite normal mixture) and context image modeling (Markov random field) is discussed mathematically. The correct use of the statistical models in image analysis is verified in terms of new observations, theorems, and interpretations.

Theoretical information criteria in detection of the number of image regions

The performances of theoretical information criteria (AIC, MDL, and EDC) are compared. The strong consistency of EDC has been verified by the numerical studies. A functional form of the penalty term in EDC is given and a method for determining the coefficient of this penalty is proposed.

Detection of the number of image regions by minimum bias/variance criterion

An unsupervised stochastic model-based image analysis technique requires the model parameters to be estimated directly from the observed image. A new approach is presented to the problem of detecting the number of statistically distinct regions in an image, based on the application of a new information theoretic criterion called minimum bias/variance criterion (MBVC). Different from the conventional approximation and coding based approaches introduced by Akaike and by Rissanen, the new criterion is to reformulate the problem explicitly as a problem of model bias and variance balancing in which the number of image regions is obtained merely by minimizing the MBVC value. Simulation results that illustrate the performance of the new method for the detection of the number of regions in an image are presented with both synthetic and medical images.

Tissue type detection by block processing

A new region detection and segmentation method is presented for performing tissue type classification and quantification. The original image data are transformed to the samples of a sample vector. The covariance matrix of this sample vector and its eigenvalues are computed. These eigenvalues are inputed into the information criterion of minimum description length to determine the region numbers. Then a modified K-mean algorithm and Bayesian classifier are utilized to segment image into the regions. This method does not need image model, considers the spatial correlations among the pixels, and is much faster than the model- based approaches.

An Investigation Into The Effect Of Independence Of Pixel Images On Image Segmentation

This paper proposes a procedure to investigate whether the statistical independence among the pixel images of a picture affects the statistical image segmentation. The results of investi-gation shows that ignoring this independence will degrade the quality of the segmented images: the more pixels which belong to the major image regions will be misclassified into the minor image regions, an artifact of statistical image segmentation. The procedure utilized in this in-vestigation can be used as an accurate statistical image segmentation technique .

Spatial correlation of some computed images

Several theorems regarding to Gaussianity, independency, correlation, stationary, ergodicity, autocorrelation function and spectral density function, etc. of the computed image are presented in this paper. These theorems are focused on one issue-the spatial correlation among the pixels. The applications of these theorems to image analysis are also discussed.

Geometric distortion of digital angiography image

Digital angiography remains valuable in a diagnostic environment where anatomical definition is important. However it is not sufficiently reliable in circumstances where precise geometry is important. The geometric distortion of digital angiography is mainly caused by the inherent, non-uniform electromagnetic field of the image intensifier board. In this paper we quantify this distortion so as to evaluate its clinical relevance. We utilize image fusion with fiducial markers and image exploration with cursor projection in this investigation. Fiducial markers on the images were normalized first and then used as baselines to scale and orient the corresponding images so they could be accurately registered, superimposed, and subtracted. Image exploration with cursor projection allowed for easy identification of the same point on corresponding images, which provided quantitative evaluation of geometric differences between digital and analogue angiography images. Based on our study, we concluded: (1) compared with MRI geometric distortion of as much as 2 mm, digital angiography is clinically appropriate for stereotactic application; (2) with an improved test object, the results would be more accurate.

Performance evaluation of unsupervised stochastic model-based image segmentation technique

This paper provides a new approach for performance evaluation of unsupervised stochastic model-based image segmentation techniques. Performance evaluation is conducted at three (3) aspects: (1) ability in detection of the number of image regions, (2) accuracy in estimation of the model parameters, and (3) error in classification of pixels into image regions. For detection performance, probabilities of over- detection and under-detection of the number of image regions are defined, and the corresponding formulae in terms of model parameters and image quality are derived. For estimation performance, this paper shows that both Classification-Maximization (CM) and Expectation-Maximization (EM) algorithms produce the asymptotically unbiased ML estimates of model parameters in the case of no-overlap. Cramer-Rao bounds of variances of these estimates are derived. For classification performance, misclassification probability, based on parameter estimate and classified data, is derived to evaluate segmentation errors. The results by applying this performance evaluation method to the simulated images demonstrate that for the images with the moderate quality, the detection procedure is robust, the parameter estimates are accurate, and the segmentation errors are small.

Parameter estimation of stochastic model-based image segmentation technique

Since both detection and classification in an unsupervised stochastic model-based segmentation technique require the results from estimation, model parameter estimation becomes a core part of these types of techniques. Based on FNM model, ML likelihood equations and their solutions have been derived. After investigating the Bayesian probability in these solutions and comparing it with probability membership of EM algorithm, this paper proves that both CM and EM algorithms which are used in this segmentation technique do produce asymptotically unbiased ML estimates of FNM parameters, through the iterative process, when the stopping criteria are satisfied. The evolution of probability membership in the iterative process finally leads to the pixel labeling. The corresponding Cramer-Rao bounds of the variances of these estimates are also derived. The results by applying this performance analysis method to the simulated images with signal-to-noise (SNR) as a parameter, are obtained and reported in this paper. These results show that for the images with the moderate quality, the parameter estimates are quite accurate. When SNR >= 14.5 db, all estimates are within the one- standard deviation interval.

Unsupervised nonmodel-based image analysis approach--block processing

An eigenstructure approach for the region detection is presented in this paper. It first defines Block and Snapshot, followed by the data formulation. A covariance matrix is formed as an overall description of the entire image environment. Then information criteria are finally applied to directly determine the number of regions. This approach does not make the heuristic assumptions for the model and considers the spatial correlation among the pixels. it also provides faster and more accurate operation than model-based approaches. The principle of block processing is described and the encouraging results are included.