Matching sets of 3D line segments with application to polygonal arcmatching

In this paper, we consider two sets of corresponding 3D line segments of equal length. We derive a closed-form solution for the coordinate transform (rotation and translation) that gives the best match between the two sets; best in the sense of a least-squares distance measure between the sets. We use these results as the basis to construct efficient algorithms for solving other problems in computer vision. Specifically, we address the problem of matching polygonal arcs, that is, the problem of finding a match between a short arc and a piece of long arc     

Underwater imaging with a moving acoustic lens

The acoustic lens is a high-resolution, forward-looking sonar for three dimensional (3-D) underwater imaging. We discuss processing the lens data for recreating and visualizing the scene. Acoustical imaging, compared to optical imaging, is sparse and low resolution. To achieve higher resolution, we obtain a denser sample by mounting the lens on a moving platform and passing over the scene. This introduces the problem of data fusion from multiple overlapping views for scene formation, which we discuss. We also discuss the improvements in object reconstruction by combining data from several passes over an object. We present algorithms for pass registration and show that this process can be done with enough accuracy to improve the image and provide greater detail about the object. The results of in-water experiments show the degree to which size and shape can be obtained under (nearly) ideal conditions.     

A nonparametric method for fitting a straight line to a noisy image

In fitting a straight line to a noisy image, the least-squares method becomes highly unreliable either when the noise distribution is nonnormal or when it is contaminated by outliers. The authors propose a nonparametric method, the median of the intercepts, to overcome these difficulties. This method is free of assumptions about the noise distribution and insensitive to outliers, and it does not require quantization of the parameter space. Thus, unlike the Hough transform, its outcome does not depend on the bin size. The method is efficient and its implementation does not involve practical difficulties such as local minima or poor convergence of iterative procedures     

Optimally isotropic Laplacian operator

Laplacian operators used in the literature for digital image processing are not rotationally invariant. We examine the anisotropy of 3x3 Laplacian operators for images quantized in square pixels, and find the operator which has the minimum overall anisotropy.     

Algorithms for matching 3D line sets

Matching two sets of lines is a basic tool that has applications in many computer vision problems such as scene registration, object recognition, motion estimation, and others. Line sets may be composed of infinitely long lines or finite length line segments. Depending on line lengths, three basic cases arise in matching sets of lines: 1) finite-finite, 2) finite-infinite, and 3) infinite-infinite. Case 2 has not been treated in the literature. For Cases 1 and 3, existing algorithms for matching 3D line sets are not completely satisfactory in that they either solve special situations, or give approximate solutions, or may not converge, or are not invariant with respect to coordinate system transforms. In this paper, we present new algorithms that solve exactly all three cases for the general situation. The algorithms are provably convergent and invariant to coordinate transforms. Experiments with synthetic and real 3D image data are reported.     

Evaluation of quantization error in computer vision

Due to the important role that digitization error plays in the field of computer vision, a careful analysis of its impact on the computational approaches used in the field is necessary. The authors develop the mathematical tools for the computation of the average (or expected) error due to quantization. They can be used in estimating the actual error occurring in the implementation of a method. Also derived is the analytic expression for the probability density of error distribution of a function of an arbitrarily large number of independently quantized variables. The probability that the error of the function will be within a given range can thus be obtained accurately. The tools developed can be used in the analysis of the applicability of a given algorithm     

Closed-form solutions to image flow equations for 3D structure and motion

A major source of three-dimensional (3D) information about objects in the world is available to the observer in the form of time-varying imagery. Relative motion between textured objects and the observer generates a time-varying optic array at the image, from which image motion of contours, edge fragments, and feature points can be extracted. These dynamic features serve to sample the underlying image flow field. New, closed-form solutions are given for the structure and motion of planar and curved surface patches from monocular image flow and its derivatives through second order. Both planar and curved surface solutions require at most, the solution of a cubic equation. The analytic solution for curved surface patches combines the transformation of Longuet-Higgins and Prazdny [25] with the planar surface solution of Subbarao and Waxman [43]. New insights regarding uniqueness of solutions also emerge. Thus, the structure-motion coincidence of Waxman and Ullman [54] is interpreted as the duality of tangent plane solutions. The multiplicity of transformation angles (up to three) is related to the sign of the Gaussian curvature of the surface patch. Ovoid patches (i.e., bowls) are shown to possess a unique transform angle, though they are subject to the local structure-motion coincidence. Thus, ovoid patches almost always yield a unique 3D interpretation. In general, ambiguous solutions can be resolved by requiring continuity of the solution over time.The support of the Defense Advanced Research Projects Agency and the U.S. Army Night Vision Laboratory under Contract DAAK70-83-K-0018 (DARPA Order 3206) is gratefully acknowledged.     

Structural Biology of Calcitonin: From Aqueous Therapeutic Properties to Amyloid Aggregation

Under appropriate conditions, peptides and proteins can assemble from their native state into prefibrillar oligomers and then mature into fibrillar aggregates. This transition forms the molecular basis of several pathologies, often related to the deposition of these amyloid fibrils. Several hormone peptides involved in fundamental biological processes have the tendency to self-assemble into amyloid fibrils, resulting in a loss of their native functions, and more importantly, entailing devastating consequences, such as the formation of amyloid depositions. Calcitonin is a 32 amino-acid hormone peptide that can be considered a molecular paradigm for the central events associated with hormone misfolding. Calcitonin in its native form is involved in various physiological functions, including mediating calcium homeostasis and maintaining bone structure. It is the latter function that has motivated the use of calcitonin as an aqueous therapeutic agent for the treatment of bone-related pathologies such as osteoporosis and Paget's disease. Despite some success as a therapeutic, calcitonin's ability to control these diseases is limited by its aggregation along the canonical amyloid aggregation pathway, compromising its long-term stability as a therapeutic agent. A better understanding of the misfolding process would not only provide the structural basis to improve calcitonin's long-term stability and activity as a therapeutic, but also provide valuable insights into pathological aggregation of other amyloids. In this work, we review the physiological roles of calcitonin, its structure, and aggregation process, and consider the effects of calcitonin's structure on its role as a therapeutic.     

Quantization error in hexagonal sensory configurations

The authors develop mathematical tools for estimating quantization error in hexagonal sensory configurations. These include analytic expressions for the average error and the error distribution of a function of an arbitrary number of independently quantized variables. These two quantities are essential for assessing the reliability of a given algorithm. They can also be used to compare the relative sensitivity of a particular algorithm to quantization error for hexagonal and other spatial samplings, e.g., square, and can have an impact on sensor design. Furthermore, it is shown that the ratio of hexagonal error to square error is bounded between 0.90 and 1.05