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.

Some Extensions of the K-Means Algorithm for Image Segmentation and Pattern Classification

In this paper we present some extensions to the k-means algorithm for vector quantization that permit its efficient use in image segmentation and pattern classification tasks. It is shown that by introducing state variables that correspond to certain statistics of the dynamic behavior of the algorithm, it is possible to find the representative centers fo the lower dimensional maniforlds that define the boundaries between classes, for clouds of multi-dimensional, mult-class data; this permits one, for example, to find class boundaries directly from sparse data (e.g., in image segmentation tasks) or to efficiently place centers for pattern classification (e.g., with local Gaussian classifiers). The same state variables can be used to define algorithms for determining adaptively the optimal number of centers for clouds of data with space-varying density. Some examples of the applicatin of these extensions are also given.

Towards an Example-Based Image Compression Architecture for Video-Conferencing

This paper consists of two major parts. First, we present the outline of a simple approach to very-low bandwidth video-conferencing system relying on an example-based hierarchical image compression scheme. In particular, we discuss the use of example images as a model, the number of required examples, faces as a class of semi-rigid objects, a hierarchical model based on decomposition into different time-scales, and the decomposition of face images into patches of interest. In the second part, we present several algorithms for image processing and animation as well as experimental evaluations. Among the original contributions of this paper is an automatic algorithm for pose estimation and normalization. We also review and compare different algorithms for finding the nearest neighbors in a database for a new input as well as a generalized algorithm for blending patches of interest in order to synthesize new images. Finally, we outline the possible integration of several algorithms to illustrate a simple model-based video-conference system.

Linear Object Classes and Image Synthesis from a Single Example Image

The need to generate new views of a 3D object from a single real image arises in several fields, including graphics and object recognition. While the traditional approach relies on the use of 3D models, we have recently introduced techniques that are applicable under restricted conditions but simpler. The approach exploits image transformations that are specific to the relevant object class and learnable from example views of other "prototypical" objects of the same class. In this paper, we introduce such a new technique by extending the notion of linear class first proposed by Poggio and Vetter. For linear object classes it is shown that linear transformations can be learned exactly from a basis set of 2D prototypical views. We demonstrate the approach on artificial objects and then show preliminary evidence that the technique can effectively "rotate" high- resolution face images from a single 2D view.

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.

Recognition of Surface Reflectance Properties from a Single Image under Unknown Real-World Illumination

This paper describes a machine vision system that classifies reflectance properties of surfaces such as metal, plastic, or paper, under unknown real-world illumination. We demonstrate performance of our algorithm for surfaces of arbitrary geometry. Reflectance estimation under arbitrary omnidirectional illumination proves highly underconstrained. Our reflectance estimation algorithm succeeds by learning relationships between surface reflectance and certain statistics computed from an observed image, which depend on statistical regularities in the spatial structure of real-world illumination. Although the algorithm assumes known geometry, its statistical nature makes it robust to inaccurate geometry estimates.

The Image Dissector "Eyes"

This is a collection of data on the construction operation and performance of the two image dissector cameras. Some of this data is useful in deciding whether certain shortcomings are significant for a given application and if so how to compensate for them.

Recovering Intrinsic Images from a Single Image

We present an algorithm that uses multiple cues to recover shading and reflectance intrinsic images from a single image. Using both color information and a classifier trained to recognize gray-scale patterns, each image derivative is classified as being caused by shading or a change in the surface's reflectance. Generalized Belief Propagation is then used to propagate information from areas where the correct classification is clear to areas where it is ambiguous. We also show results on real images.

Shape Recipes: Scene Representations that Refer to the Image

The goal of low-level vision is to estimate an underlying scene, given an observed image. Real-world scenes (e.g., albedos or shapes) can be very complex, conventionally requiring high dimensional representations which are hard to estimate and store. We propose a low-dimensional representation, called a scene recipe, that relies on the image itself to describe the complex scene configurations. Shape recipes are an example: these are the regression coefficients that predict the bandpassed shape from bandpassed image data. We describe the benefits of this representation, and show two uses illustrating their properties: (1) we improve stereo shape estimates by learning shape recipes at low resolution and applying them at full resolution; (2) Shape recipes implicitly contain information about lighting and materials and we use them for material segmentation.

Multiple Resolution Image Classification

Binary image classifiction is a problem that has received much attention in recent years. In this paper we evaluate a selection of popular techniques in an effort to find a feature set/ classifier combination which generalizes well to full resolution image data. We then apply that system to images at one-half through one-sixteenth resolution, and consider the corresponding error rates. In addition, we further observe generalization performance as it depends on the number of training images, and lastly, compare the system's best error rates to that of a human performing an identical classification task given teh same set of test images.

Inferring 3D Structure with a Statistical Image-Based Shape Model

We present an image-based approach to infer 3D structure parameters using a probabilistic "shape+structure'' model. The 3D shape of a class of objects may be represented by sets of contours from silhouette views simultaneously observed from multiple calibrated cameras. Bayesian reconstructions of new shapes can then be estimated using a prior density constructed with a mixture model and probabilistic principal components analysis. We augment the shape model to incorporate structural features of interest; novel examples with missing structure parameters may then be reconstructed to obtain estimates of these parameters. Model matching and parameter inference are done entirely in the image domain and require no explicit 3D construction. Our shape model enables accurate estimation of structure despite segmentation errors or missing views in the input silhouettes, and works even with only a single input view. Using a dataset of thousands of pedestrian images generated from a synthetic model, we can perform accurate inference of the 3D locations of 19 joints on the body based on observed silhouette contours from real images.

Three-Dimensional Recognition of Solid Objects from a Two-Dimensional Image

This thesis addresses the problem of recognizing solid objects in the three-dimensional world, using two-dimensional shape information extracted from a single image. Objects can be partly occluded and can occur in cluttered scenes. A model based approach is taken, where stored models are matched to an image. The matching problem is separated into two stages, which employ different representations of objects. The first stage uses the smallest possible number of local features to find transformations from a model to an image. This minimizes the amount of search required in recognition. The second stage uses the entire edge contour of an object to verify each transformation. This reduces the chance of finding false matches.

Image Chunking: Defining Spatial Building Blocks for Scene Analysis

Rapid judgments about the properties and spatial relations of objects are the crux of visually guided interaction with the world. Vision begins, however, with essentially pointwise representations of the scene, such as arrays of pixels or small edge fragments. For adequate time-performance in recognition, manipulation, navigation, and reasoning, the processes that extract meaningful entities from the pointwise representations must exploit parallelism. This report develops a framework for the fast extraction of scene entities, based on a simple, local model of parallel computation.sAn image chunk is a subset of an image that can act as a unit in the course of spatial analysis. A parallel preprocessing stage constructs a variety of simple chunks uniformly over the visual array. On the basis of these chunks, subsequent serial processes locate relevant scene components and assemble detailed descriptions of them rapidly. This thesis defines image chunks that facilitate the most potentially time-consuming operations of spatial analysis---boundary tracing, area coloring, and the selection of locations at which to apply detailed analysis. Fast parallel processes for computing these chunks from images, and chunk-based formulations of indexing, tracing, and coloring, are presented. These processes have been simulated and evaluated on the lisp machine and the connection machine.