PubMed · 5486121
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F Hund. 1970. [Time asa physical concpt].. https://pubmed.ncbi.nlm.nih.gov/5486121/
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We show that neural networks, with a suitable error function for backpropagation, can be successfully used for metric multidimensional scaling (MDS) (i.e., dimensional reduction while trying to preserve the original distances between patterns) and are in fact able to outdo the standard algebraic approach to MDS, known as classical scaling.
This paper deals with pattern recognition of the shape of the boundary of closed figures on the basis of a circular sequence of measurements taken on the boundary at equal intervals of a suitably chosen argument with an arbitrary starting point. A distance measure between two boundaries is defined in such a way that it has zero value when the associated sequences of measurements coincide by shifting the starting point of one of the sequences. Such a distance measure, which is invariant to the starting point of the sequence of measurements, is used in identification or discrimination by the shape of the boundary of a closed figure. The mean shape of a given set of closed figures is defined, and tests of significance of differences in mean shape between populations are proposed.
PURPOSE: A simple method that verifies the coincidence of the isocenter with the center of the target volume in radiosurgery treatment conditions is described. The accuracy is compared to that of accepted computerized procedures employing fiducial markers. METHODS AND MATERIALS: The center of the beam is identified by a cylindrical localizer, fixed to the plate of the supplemental collimator, with a 2 x 50 mm tungsten rod coincident with the beam axis and is projected onto the x-ray portal verification films. Prior to irradiation, the coordinates of the intersection of the beams axes, which is in a known spatial relationship with the isocenter, are read directly on portal x-ray films and their coincidence with the coordinates set during patient positioning, is checked. RESULTS: The mean displacement in AP, Lat, and Vert coordinates respectively, over 84 patients, between the coordinates calculated by the computerized procedure employing fiducial markers and the coordinates calculated by using the rulers was 0.3 +/- 0.4 mm. CONCLUSIONS: From the results obtained with the two methods we can conclude that rulers method can be used as a fast indirect control of the position of the radiation isocenter. Moreover, the dimensions of the radiation field and the correct alignment of the tertiary circular collimator can be also documented.