An automated method is proposed for anatomic standardization that elastically map one subject's MR image to a standard reference MR image to enable inter-subject and cross-group studies. In this method, linear transformations based on bicommissural stereotaxy are first applied to grossly align the input image to the reference image. Then, an active contour model is employed to refine the contour and surface description of the input image. Based on the contour and surface correspondence established in these previous steps, a non-linear transformation is determined using the proposed weighted local reference coordinate systems to warp the input image. In this method, geometric correspondence established based on contour matching is used to control the warping and the actual image values corresponding to registered coordinates need not be similar. We tested this algorithm on various synthetic and real images for inter-subject registration of MR images.

The estimation of the fractal dimension is essential in fractal-based image segmentation, classification and shape analysis. The most popular estimation approach is based on box-counting. However, the partition and counting methods used in the regular box-counting scheme produces inaccurate results. In this paper, a more accurate fractional box-counting approach is proposed to estimate the fractal dimension in an image. By separating the concepts of base scale and counting scale, the new approach is able to use a deformable box to capture fractal property at some predetermined resolution. Preliminary results using the fractional box-counting approach have demonstrated that it is an accurate and efficient method.

This paper is concerned with the problems of reconstructing a closed surface from scattered, noisy 3-D data. A progressive shell model is a 3-D extension of the 2-D progressive contour model. We employ finite element methods (FEMs) to reduce the number of the required variables and improve the efficiency in storage and computation. The fundamental forms in differential geometry are used to measure rigid-motion invariant properties and formulate the internal energy of the shell. We also develop a wireframe model associated with a subdivision scheme to overcome the difficulty of generating a smooth boundary between two adjacent patches. This is a direct application of the 2-D contour model where curve segments or wires are used instead of patches. In the subdivision scheme, we impose the co-plane constraints to determine a unique normal vector at the interpolated mid-point. To demonstrate the descriptive ability of a wireframe model, we conduct experiments on 3-D data set of a tumor and a face.

This paper presents a progressive contour model based on the idea of deforming a contour from an initial shape as a source of prior knowledge by minimizing a defined contour energy to extract a desired contour from an image. The internal component of the contour energy imposes smoothness constraints on the displacements of deformations and the external component establishes the correspondence between the contour and image edges. A sequence of deformations is determined by repeatedly deforming and updating the initial contour. We show that the contour deformed by this sequence will smoothly and progressively approach a uniquely defined contour. We implement this model using a finite-element method, a multigrid algorithm, and an unconstrained optimization method. This approach offers several attractive advantages including a satisfactory convergence rate and the adaptation of the smoothness constraints.

An interpolation method, morphological field morphing, using contours of organs as the control parameters is proposed to recover the intensity information in the physical gaps of serial cross-sectional images. Contour information derived from a contour-model-based segmentation process is processed and used as the control parameters to warp the corresponding regions in both input images into comparable shapes. In this way, the reliability of establishing the correspondence among different segments of the same organs is improved and the intensity information for the interpolated intermediate slices can be derived more faithfully. In comparison with the existing intensity interpolation algorithms that only search for corresponding points based on intensity information, this method provides more meaningful correspondence relationships by warping corresponding regions in images into similar shapes before resampling to account for significant shape differences.

Proposes an approach applying artificial neural net techniques to 3D rigid motion analysis based on sequential multiple time frames. The approach consists of two phases: (1) matching between every two consecutive frames and (2) estimating motion parameters based on the correspondences established. Phase 1 specifies the matching constraints to ensure a stable and coherent feature correspondence establishment between two sequential time frames and configures a 2D Hopfield neural net to enforce these constraints. Phase 2 constructs a 3-layer net to estimate parameters through supervised learning. The method performs motion analysis based on sequential multiple time frames. It represents an effective way to achieve optimal matching between two frames using neural net techniques. The energy function of the Hopfield net is designed to reflect the matching constraints and the minimization of this function leads to the optimal feature correspondence establishment. The approach introduces the learning concept to motion estimation. The structure of the net provides the flexibility in estimating motion parameters based on information from multiple frames.

For pt. I see ibid., p. 1386-93 (1995). An approach applying artificial neural net techniques to 3D nonrigid motion analysis is proposed. The 3D nonrigid motion of the left ventricle of a human heart is examined using biplanar cineangiography data, consisting of 3D coordinates of 30 coronary artery bifurcation points of the left ventricle and the correspondences of these points taken over 10 time instants during the heart cardiac cycle. The motion is decomposed into global rigid motion and a set of local nonrigid deformations which are coupled with the global motion. The global rigid motion can be estimated precisely as a translation vecto and a rotation matrix. Local nonrigid deformation estimation is discussed. A set of neural nets similar in structure and dynamics but different in physical size is proposed to tackle the problem of nonrigidity. These neural networks are interconnected through feedbacks. The activation function of the output layer is selected so that a feedback is involved in the output updating. The constraints are specified to ensure stable and globally consistent estimation. The objective is to find the optimal deformation matrices that satisfy the constraints for all coronary artery bifurcation points of the left ventricle. The proposed neural networks differ from other existing neural network models in their unique structure and dynamics.

A fuzzy neural network based approach to 3-D heart motion understanding is proposed. Knowledge from cardiologists is used to specify different classes of motion and classification rules. The objective of this approach is to find the decisions for all possible classes of motion in the form of possibilities. Experiments on real data have been conducted to corroborate the proposed techniques.

The discrete Gabor (1946) transform algorithm is introduced that provides an efficient method of calculating the complete set of discrete Gabor coefficients of a finite-duration discrete signal from finite summations and to reconstruct the original signal exactly from the computed expansion coefficients. The similarity of the formulas between the discrete Gabor transform and the discrete Fourier transform enables one to employ the FFT algorithms in the computation. The discrete 1-D Gabor transform algorithm can be extended to 2-D as well.

Reports on a new method in which spatially correlated magnetic resonance (MR) or X-ray computed tomography (CT) images are employed as a source of prior information in the Bayesian reconstruction of positron emission tomography (PET) images. This new method incorporates the correlated structural images as anatomic templates which can be used for extracting information about boundaries that separate regions exhibiting different tissue characteristics. In order to avoid the possible introduction of artifacts caused by discrepancies between functional and anatomic boundaries, the authors propose a new method called the "weighted line site" method, in which a prior structural image is employed in a modified updating scheme for the boundary variable used in the iterative Bayesian reconstruction. This modified scheme is based on the joint probability of structural and functional boundaries. As to the structural information provided by CT or MR images, only those which have high joint probability with the corresponding PET data are used; whereas other boundary information that is not supported by the PET image is suppressed. The new method has been validated by computer simulation and phantom studies. The results of these validation studies indicate that this new method offers significant improvements in image quality when compared to other reconstruction algorithms, including the filtered backprojection method and the maximum likelihood approach, as well as the Bayesian method without the use of the prior boundary information.

The authors propose knowledge representation and evidence propagation schemes based on multivariate belief functions and present a medical image recognition system to demonstrate the effectiveness of their application to spatial reasoning. The proposed system, which is based on the blackboard architecture, can mimic the reasoning process of a human expert in identifying the anatomical structures in a set of correlated images acquired from X-ray CT and PD- and T/sub 2/-weighted MRI. In the blackboard-oriented system, different kinds of evidence provided by various knowledge sources form a hierarchy of evidential space to which the Dempster-Shafer theory is applied. The multivariate belief functions are used to represent domain specific knowledge such as rules or facts.>

A new image quality metric consistent with the properties of the human visual system is derived. Using the EM algorithm, the authors restore a blurred image and quantify the improvement in image quality with both the new metric and the mean square error (MSE). From these results, the advantages of the new metric are obvious. The EM algorithm is modified according to the underlying mathematical structure of the new metric, which results in improved performance.>

A medical image recognition system is described whose reasoning module uses the features of the Dempster-Shafer (D-S) theory such as compatible frames and multivariate belief functions. The proposed expert system, which is based on the blackboard architecture, is capable of mimicking the reasoning process of a human expert in dividing a set of correlated X-ray CT and T-1 and T2-weighted MR images into semantically meaningful entities. In the blackboard-oriented system, different kinds of evidence provided by various knowledge sources form a hierarchy of evidential space to which D-S theory is applied. Several experimental results are given to illustrate the performance of the proposed system.>

The authors propose a Bayesian model for the restoration of images based on counts of emitted photons. The model treats blurring within the context of an incomplete data problem and utilizes a Gibbs prior to model the spatial correlation of neighboring regions. The Gibbs prior includes line sites to account for boundaries between regions, and the line sites are assigned continuous values to permit efficient estimation using a method called iterative conditional averages. In addition, the effect of blurring in masking differences between images and the effects of misspecifying the amount of blurring are discussed.>