A novel method allows the determination of three-dimensional object structure from two projection images that are obtained at arbitrary, unknown orientations. Only minimal prior information concerning the imaging system is required. First, the image coordinates of eight or more object points that can be identified unambiguously in both views are used to determine the relative geometry of the two projections. Subsequently, the three-dimensional coordinates of the identified object points are determined, to within a scale factor, from the image coordinates of the points and the calculated imaging system geometry. A theoretical description of the overall method is provided, along with techniques for the reduction of effects of experimental errors and numerical errors that may arise in the course of the calculations. Methods to retrieve the absolute scale of the object are discussed also.
We are developing a technique for determination of the three-dimensional (3-D) structure of vascular objects from two radiographic projection images acquired at arbitrary and unknown relative orientations. No separate calibration steps are required with this method, which exploits an inherent redundancy of biplane imaging to extract the imaging geometry as well as the 3-D locations of eight or more object points. The theoretical basis of this technique has been described previously. In this paper, we review the method from the perspective of linear algebra and describe an improvement, not heretofore reported, that reduces the method's sensitivity to experimental error. We then examine the feasibility and inherent accuracy of this approach by computer simulation of biplane imaging experiments. The precision with which 3-D object structure may be retrieved, together with the dependence of precision on the actual imaging geometry and errors in various measured quantities, is studied in detail. Our simulation studies show that the method is not only feasible but potentially accurate, typically determining object-point configurations with root-mean-square (RMS) error on the order of 1 to 2 mm. The method is also quite fast, requiring approximately one second of CPU time on a VAX 11/750 computer (0.6 MIPS).
We developed an iterative deconvolution technique to determine the size of a "blurred" vessel in a digital subtraction angiographic (DSA) image by taking into account the unsharpness of the DSA system. Initially, a region of interest over a small segment of the contrast-filled vessel was selected in a DSA image, and the center line of the opacified vessel was determined by polynomial curve fitting of the locations of the peak pixel values along the vessel image. The blurred image profile was then obtained from pixel values across the vessel in a direction perpendicular to the center line. This measured profile was compared iteratively with a calculated profile for various size vessels, which was obtained from a cylindrical vessel model and from the line spread function, until the root-mean-square difference between the two profiles was minimized. The size of a cylindrical vessel yielding the matched profile was considered the best estimate of the unknown vessel size. Studies with a blood vessel phantom indicated that vessels larger than 0.5 mm could be measured with an accuracy and precision of approximately 0.1 mm, which is about 1/3 of the pixel size used in our DSA system. Details of our approach and some clinical vessel images with and without simulated stenotic lesions are presented.
The effect of a graded exercise protocol on phosphorus-31 magnetic resonance (MR) spectroscopy of calf skeletal muscle in nine healthy (control) subjects and 16 patients with symptomatic peripheral arterial occlusive disease (PAOD) was assessed. Ankle-brachial pressure indexes were obtained in all 16 patients, and 10 patients underwent peripheral arteriography. Temporal profiles of pH and the inorganic phosphorus (Pi) index were calculated from the spectra. A Pi-index recovery rate constant was calculated for each subject. Arteriograms were graded by calculating the runoff resistance in the limb of interest. The pH profiles during exercise did not differ significantly between the PAOD patients and control subjects. The Pi-index recovery rate constant in the PAOD patients was significantly (P less than .01) smaller than in the control subjects. There was no significant correlation between recovery rate and the ankle-brachial pressure indexes, but there was a strong negative correlation between recovery rates and angiographic resistance grades, with smaller recovery rate constants in patients with increased arterial resistance. It is concluded that P-31 MR spectroscopy shows promise as a direct measure of tissue perfusion.
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