A Unified Statistical and Information Theoretic Framework for Multi-modal Image Registration

We formulate and interpret several multi-modal registration methods in the context of a unified statistical and information theoretic framework. A unified interpretation clarifies the implicit assumptions of each method yielding a better understanding of their relative strengths and weaknesses. Additionally, we discuss a generative statistical model from which we derive a novel analysis tool, the "auto-information function", as a means of assessing and exploiting the common spatial dependencies inherent in multi-modal imagery. We analytically derive useful properties of the "auto-information" as well as verify them empirically on multi-modal imagery. Among the useful aspects of the "auto-information function" is that it can be computed from imaging modalities independently and it allows one to decompose the search space of registration problems.

2D-3D Rigid-Body Registration of X-Ray Fluoroscopy and CT Images

The registration of pre-operative volumetric datasets to intra- operative two-dimensional images provides an improved way of verifying patient position and medical instrument loca- tion. In applications from orthopedics to neurosurgery, it has a great value in maintaining up-to-date information about changes due to intervention. We propose a mutual information- based registration algorithm to establish the proper align- ment. For optimization purposes, we compare the perfor- mance of the non-gradient Powell method and two slightly di erent versions of a stochastic gradient ascent strategy: one using a sparsely sampled histogramming approach and the other Parzen windowing to carry out probability density approximation. Our main contribution lies in adopting the stochastic ap- proximation scheme successfully applied in 3D-3D registra- tion problems to the 2D-3D scenario, which obviates the need for the generation of full DRRs at each iteration of pose op- timization. This facilitates a considerable savings in compu- tation expense. We also introduce a new probability density estimator for image intensities via sparse histogramming, de- rive gradient estimates for the density measures required by the maximization procedure and introduce the framework for a multiresolution strategy to the problem. Registration results are presented on uoroscopy and CT datasets of a plastic pelvis and a real skull, and on a high-resolution CT- derived simulated dataset of a real skull, a plastic skull, a plastic pelvis and a plastic lumbar spine segment.

Compact Representations for Fast Nonrigid Registration of Medical Images

We develop efficient techniques for the non-rigid registration of medical images by using representations that adapt to the anatomy found in such images. Images of anatomical structures typically have uniform intensity interiors and smooth boundaries. We create methods to represent such regions compactly using tetrahedra. Unlike voxel-based representations, tetrahedra can accurately describe the expected smooth surfaces of medical objects. Furthermore, the interior of such objects can be represented using a small number of tetrahedra. Rather than describing a medical object using tens of thousands of voxels, our representations generally contain only a few thousand elements. Tetrahedra facilitate the creation of efficient non-rigid registration algorithms based on finite element methods (FEM). We create a fast, FEM-based method to non-rigidly register segmented anatomical structures from two subjects. Using our compact tetrahedral representations, this method generally requires less than one minute of processing time on a desktop PC. We also create a novel method for the non-rigid registration of gray scale images. To facilitate a fast method, we create a tetrahedral representation of a displacement field that automatically adapts to both the anatomy in an image and to the displacement field. The resulting algorithm has a computational cost that is dominated by the number of nodes in the mesh (about 10,000), rather than the number of voxels in an image (nearly 10,000,000). For many non-rigid registration problems, we can find a transformation from one image to another in five minutes. This speed is important as it allows use of the algorithm during surgery. We apply our algorithms to find correlations between the shape of anatomical structures and the presence of schizophrenia. We show that a study based on our representations outperforms studies based on other representations. We also use the results of our non-rigid registration algorithm as the basis of a segmentation algorithm. That algorithm also outperforms other methods in our tests, producing smoother segmentations and more accurately reproducing manual segmentations.

Vectorizing Face Images by Interpreting Shape and Texture Computations

The correspondence problem in computer vision is basically a matching task between two or more sets of features. In this paper, we introduce a vectorized image representation, which is a feature-based representation where correspondence has been established with respect to a reference image. This representation has two components: (1) shape, or (x, y) feature locations, and (2) texture, defined as the image grey levels mapped onto the standard reference image. This paper explores an automatic technique for "vectorizing" face images. Our face vectorizer alternates back and forth between computation steps for shape and texture, and a key idea is to structure the two computations so that each one uses the output of the other. A hierarchical coarse-to-fine implementation is discussed, and applications are presented to the problems of facial feature detection and registration of two arbitrary faces.

Shape from Contour

The problem of using image contours to infer the shapes and orientations of surfaces is treated as a problem of statistical estimation. The basis for solving this problem lies in an understanding of the geometry of contour formation, coupled with simple statistical models of the contour generating process. This approach is first applied to the special case of surfaces known to be planar. The distortion of contour shape imposed by projection is treated as a signal to be estimated, and variations of non-projective origin are treated as noise. The resulting method is then extended to the estimation of curved surfaces, and applied successfully to natural images. Next, the geometric treatment is further extended by relating countour curvature to surface curvature, using cast shadows as a model for contour generation. This geometric relation, combined with a statistical model, provides a measure of goodness-of-fit between a surface and an image contour. The goodness-of-fit measure is applied to the problem of establishing registration between an image and a surface model. Finally, the statistical estimation strategy is experimentally compared to human perception of orientation: human observers' judgements of tilt correspond closely to the estimates produced by the planar strategy.