A comprehensive, but simple-to-use software package for executing a range of standard numerical analysis and operations used in quantitative paleontology has been developed. The program, called PAST (PAleontological STatistics), runs on standard Windows computers and is available free of charge. PAST integrates spreadsheet-type data entry with univariate and multivariate statistics, curve fitting, timeseries analysis, data plotting, and simple phylogenetic analysis. Many of the functions are specific to paleontology and ecology, and these functions are not found in standard, more extensive, statistical packages. PAST also includes fourteen case studies (data files and exercises) illustrating use of the program for paleontological problems, making it a complete educational package for courses in quantitative methods.

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Past: paleontological statistical software package for education and data analysis

Registration is a fundamental task in image processing used to match two or more pictures taken, for example, at different times, from different sensors, or from different viewpoints. Virtually all large systems which evaluate images require the registration of images, or a closely related operation, as an intermediate step. Specific examples of systems where image registration is a significant component include matching a target with a real-time image of a scene for target recognition, monitoring global land usage using satellite images, matching stereo images to recover shape for autonomous navigation, and aligning images from different medical modalities for diagnosis.Over the years, a broad range of techniques has been developed for various types of data and problems. These techniques have been independently studied for several different applications, resulting in a large body of research. This paper organizes this material by establishing the relationship between the variations in the images and the type of registration techniques which can most appropriately be applied. Three major types of variations are distinguished. The first type are the variations due to the differences in acquisition which cause the images to be misaligned. To register images, a spatial transformation is found which will remove these variations. The class of transformations which must be searched to find the optimal transformation is determined by knowledge about the variations of this type. The transformation class in turn influences the general technique that should be taken. The second type of variations are those which are also due to differences in acquisition, but cannot be modeled easily such as lighting and atmospheric conditions. This type usually effects intensity values, but they may also be spatial, such as perspective distortions. The third type of variations are differences in the images that are of interest such as object movements, growths, or other scene changes. Variations of the second and third type are not directly removed by registration, but they make registration more difficult since an exact match is no longer possible. In particular, it is critical that variations of the third type are not removed. Knowledge about the characteristics of each type of variation effect the choice of feature space, similarity measure, search space, and search strategy which will make up the final technique. All registration techniques can be viewed as different combinations of these choices. This framework is useful for understanding the merits and relationships between the wide variety of existing techniques and for assisting in the selection of the most suitable technique for a specific problem.

A survey of image registration techniques

The problem of rotation-, scale-, and translation-invariant recognition of images is discussed. A set of rotation-invariant features are introduced. They are the magnitudes of a set of orthogonal complex moments of the image known as Zernike moments. Scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments. A systematic reconstruction-based method for deciding the highest-order Zernike moments required in a classification problem is developed. The quality of the reconstructed image is examined through its comparison to the original one. The orthogonality property of the Zernike moments, which simplifies the process of image reconstruction, make the suggest feature selection approach practical. Features of each order can also be weighted according to their contribution to the reconstruction process. The superiority of Zernike moment features over regular moments and moment invariants was experimentally verified. >

Invariant image recognition by Zernike moments

This is the first part of a comprehensive and up-to-date survey of the techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. It surveys various mathematical models of target motion/dynamics proposed for maneuvering target tracking, including 2D and 3D maneuver models as well as coordinate-uncoupled generic models for target motion. This survey emphasizes the underlying ideas and assumptions of the models. Interrelationships among models and insight to the pros and cons of models are provided. Some material presented here has not appeared elsewhere.

Survey of maneuvering target tracking. Part I. Dynamic models

We are now in the midst of a revolution in morphometric methodology. The new approaches are more effective in capturing information about the shape of an organism and result in more powerful statistical procedures for testing for differences in s shape. They are also more effective in enabling a researcher to visualize differences in shape and in suggesting simple traditional measurements that could be used in future studies. In this review we emphasize applications to exploratory studies in taxonomy and evolution.

A revolution morphometrics.

Elliptic Fourier features of a closed contour

A procedure for using moment-based feature vectors to identify a three-dimensional object from a two-dimensional image recorded at an arbitrary viewing angle and range is presented. A moment form called standard moments, rather than the usual moment invariants, is considered. A standard six-airplane experiment was used to compare different techniques. Fourier descriptors and moment invariants were both compared to the present scheme for normalized moments. Various experiments were conducted using mixtures of silhouette and boundary moments and different normalization techniques. Standard moments gave slightly better results than Fourier descriptors for this experiment; both of these techniques were much better than moment invariants. >

Three-dimensional shape analysis using moments and Fourier descriptors

A partial-shape-recognition technique utilizing local features described by Fourier descriptors is introduced. A dynamic programming formulation for shape matching is developed, and a method for comparison of match quality is discussed. This technique is shown to recognize unknown contours that may be occluded or that may overlap other objects. Precise scale information is not required, and the unknown objects may appear at any orientation with respect to the camera. The segment-matching dynamic programming method is contrasted with other sequence-comparison techniques that utilize dynamic programming. Experimental results are discussed that indicate that partial contours can be recognized with reasonable accuracy. >

Partial shape recognition using dynamic programming

Accuracy of curve approximation by harmonically related vectors with elliptical loci

The subject of this paper involves tracking the present position of a maneuvering aircraft as well as predicting its future position. A tracking filter is developed that uses aircraft attitude angles (yaw, pitch, roll) in addition to the usual radar measurements. Computer simulation of tracker performance when tracking violently maneuvering aircraft indicates that a dramatic improvement is obtained by using attitude information. The approach taken is to develop a 12-or 15-state extended Kalman filter that models both translational and rotational degrees of freedom. By measuring and estimating attitude it is possible to approximately determine the magnitude and direction of the force system acting on the vehicle and therefore determine vehicle linear acceleration. Knowledge of acceleration is then used to improve the estimate of present and future position of the vehicle being tracked. Simulation of a T-38 aircraft performing a 5 g turn indicates that the new tracker produces maximum trajectory prediction errors that are 36 percent of the errors experienced by more conventional trackers.

Frank P. Kuhl

Papers

Elliptic Fourier features of a closed contour

Three-dimensional shape analysis using moments and Fourier descriptors

Partial shape recognition using dynamic programming

Accuracy of curve approximation by harmonically related vectors with elliptical loci

A Nonlinear Tracker Using Attitude Measurements